Final: Coordination and Cooperation between Network Nodes

FP7-ICT-2009-4 WHERE2 D3.4 Final: Coordination and Cooperation between Network Nodes Contractual Date of Delivery to the CEC: 30.09.2013 (M39) Actual Date of Delivery to the CEC: 21.11.2013 Editor: Joaquim Bastos Authors: Ronald Raulefs (DLR), Armin Dammann (DLR), Dirk Slock (EUR), Joaquim Bastos (IT), Du Yang (IT), Shahid Mumtaz (IT), Jonathan Rodriguez (IT), Lo¨ıc Brunel (MER), Julien Guillet (MER), Nicolas Gresset (MER), George Agapiou (OTE), Andreas Rigas (OTE), Stamatis ´ Perdikouris (OTE), Alvaro Gomes (PTIN), Diogo Conde¸co (PTIN), Na Yi (UNIS), Yi Ma (UNIS) Participants: DLR, EUR, IT, MER, OTE, PTIN, UNIS Work package: WP3 - Geolocation aided cooperation for future wireless networks Est. person months: Security: (PU) Nature: (R) Version: 1.0 Total number of pages: 190 Abstract: This deliverable presents the final achieved results regarding three different aspects addressed in the WHERE2 project, concerning the coordination and cooperation between network nodes (task T3.1), included in the domain of geolocation aided cooperation for future wireless networks (WP3), with the main objective of improving cellular communications. This objective was targeted in the research work carried out in the project, and presented in this document, by proposing enhanced techniques for the coordination of cell sites, and also the cooperation between them, with reduced signalling overhead, including the cooperation between macro and small cells, by exploiting available location and environment information.

Keyword list: Geolocation-aided cooperation, Fixed relay nodes, Multi-hop communications, Fractional frequency reuse (FFR), Multi-cell processing and communications, Coordinated multipoint (CoMP) transmission, Multilink synchronization, Femtocells, Small cells, Inter-cell interference coordination (ICIC), Self-Organized Networks (SON), LTE, LTE-Advanced.

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Executive Summary The availability of location information offers opportunities to enhance wireless communications through specific advanced techniques, which is the overall objective targeted in WHERE2 WP3. More specifically, the main focus of task T3.1 is to propose such techniques and solutions for improving particularly wireless cellular communications, through means of coordination of, and cooperation between cells, with reduced signalling overhead, including cooperation between femto/small and macro cells, by exploiting location and environment information. This deliverable presents the most significant and final results achieved in the scope of coordination and cooperation between network nodes (task T3.1) regarding three main aspects addressed in the WHERE2 project, included in the domain of geolocation aided cooperation for future wireless networks, targeted in WP3, with the main objective of improving cellular communications. This objective was achieved in the research work carried out in the project, and presented in this deliverable, by proposing enhanced techniques for the coordination of cell sites, and also the cooperation between them, including the cooperation between femto/small and macro cells, all taking advantage of the available geolocation and location-related data. The accomplished investigations took into consideration the work developed in WP1 defining scenarios and use cases, identifying key parameters for the considered communication systems, as well as mobility models. Also, WP2 developments were closely followed, where algorithms and techniques where investigated and proposed to provide more accurate position information, movement prediction, and partial channel state information. Overall, the several approaches investigated in WHERE2 on this specific scope can be considered mostly complementary, divided into the proposed three main aspects of task T3.1, and are summarized as follows: • Fixed Relays for Cellular Systems (LTE-Advanced) – Adaptive Location-Aided Cooperative Relaying – Location-Aided Relay Node Planning – Location-Aided MAC Layer Flexible Round-Robin Scheduling – Location-Aided Physical Layer Channel State Information Feedback – Geolocation-Aided Relay Nodes Selection in Cellular Network • Location-Aided Multi-Cell Processing – Location-Aided Multi-Cell Communications – Location Aware Coordinated Multipoint Transmission Synchronization • Femtocell Based Communications – Downlink Femto-Macro Inter-Cell Interference Coordination with Location-Based Long-Term Power Setting – Location-Aided Home eNodeB Self-Organized Network The approaches studied and developed in the scope of this task can all be applicable to LTE/LTE-A cellular systems communications. All these techniques depend on available location information related to the cellular system elements, namely eNodeBs (eNBs), relay nodes (RNs), Home eNodeBs (HeNBs), mobile terminals (MTs) or user equipment (UE), etc. This information is considered to be available on demand or through internal up-to-date database (DB), allowing significant communications enhancement, as it is shown in the following chapters and sections.

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The appendices in this document include our investigation results, which subsequently were associated to specific dissemination activities within WP5, in relevant conferences and journals. The effective performance of the proposed techniques and algorithms is dependent on the availability and quality of information, and on its appropriate exchange, regarding not only the location information but also other info, such as UEs’ received power measurements, which could be stored and accessed on a DB in the system core network. Other factors, in the scope of the proposed approaches, which have an impact in their respective performance are, for instance, the effective communication between the eNBs and HeNBs, and also with the DB server hosting UEs’ measurements, or the adequately synchronized transmission at eNBs (or at least availability of appropriate information about their asynchrony) when multi-cell communications are concerned, or even full or merely statistical channel knowledge. Proposals for location-aided techniques should to be weighted against classical approaches in order to assess their definitive value. Indeed, in most cases, a location-aided communications approach has a more classical counterpart, often requiring additional overhead. Nowadays, the availability of some location information can be considered as given, not requiring further communication overhead. However, some (but not all) of the location-aided techniques require to frequently access substantial DBs, which have become common in the context of flexible spectrum access, and this also represents communication overhead. Location-aided techniques may furthermore exploit location prediction through mobility trajectory information, which would allow slow fading (and even connectivity) predictability, something that is difficult to achieve without location information. Two joint papers presenting the most significant achievements reflecting the techniques included in this deliverable were made in the closing phase of WHERE2, [1] and [2], having the first been presented at a conference, and the later awaiting notification of acceptance for publication.

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Table of Contents List of Acronyms and Abbreviations

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1 Introduction

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2 General scenario and System architecture 2.1 Common scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 System architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Fixed Relays for LTE Cellular Systems 3.1 Adaptive location-aided cooperative relaying . . . . . . . . . . . 3.2 Location-aided relay node planning . . . . . . . . . . . . . . . . . 3.2.1 Main scenario . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Proposed algorithm . . . . . . . . . . . . . . . . . . . . . 3.2.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . 3.3 Location-aided MAC layer flexible Round-Robin scheduling . . . 3.3.1 Setup and scenario . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Proposed algorithm . . . . . . . . . . . . . . . . . . . . . 3.3.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . 3.4 Location-aided Physical layer channel state information feedback 3.4.1 Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Proposed algorithm . . . . . . . . . . . . . . . . . . . . . 3.4.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . 3.5 Geolocation-aided relay nodes selection in cellular networks . . . 3.5.1 Node selection in a relay network . . . . . . . . . . . . . .

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4 Location-Aided Multi-Cell Processing 4.1 Single-User Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Location and Database aided Channel Estimation/Prediction . . . . . . . . . . . . 4.1.2 Position based Adaptive Modulation and Coding (AMC) and OFDMA Resource Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Single-Cell Multi-User Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Location aided Multi-User Resource Allocation . . . . . . . . . . . . . . . . . . . . 4.2.2 SDMA considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Narrow AoD Aperture (NADA) case . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Location Based SDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5 Location Based MU-MIMO Downlink . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Multi-Cell Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 MISO Interference Channel (IFC) . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 MIMO IFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 MIMO IFC with Decoupled Tx/Rx and Location Aided Design . . . . . . . . . . . 4.4 Location aware CoMP transmission synchronization . . . . . . . . . . . . . . . . . . . . . 4.4.1 Relation to further publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.3 Performance evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.4 System Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 Femtocell Based Communications 5.1 Downlink femto-macro ICIC with location-based long-term power 5.1.1 Location-based long-term power setting . . . . . . . . . . 5.1.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . 5.2 Location-aided HeNB self-organized network system . . . . . . . 5.2.1 Proposed solution . . . . . . . . . . . . . . . . . . . . . .

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5.2.2 5.2.3

System description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Conclusion

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References

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Appendices A.1 Joint WP3 publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2 Adaptive location-aided cooperative relaying . . . . . . . . . . . . . . . . . A.3 Location-aided relay node planning . . . . . . . . . . . . . . . . . . . . . . A.4 Location-aided MAC layer flexible Round-Robin scheduling . . . . . . . . . A.5 Novel Contributions to MISO and MIMO multi-User Single- and Multi-Cell A.6 Location aware CoMP transmission synchronization . . . . . . . . . . . . . A.7 Downlink femto-macro ICIC with location-based long-term power setting . A.8 Location-aided HeNB SON System . . . . . . . . . . . . . . . . . . . . . .

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Authors Partner DLR

Name Ronald Raulefs

Armin Dammann

EUR

Dirk Slock

IT

Joaquim Bastos

Du Yang

Shahid Mumtaz

Jonathan Rodriguez

MER

Lo¨ıc Brunel

Nicolas Gresset

Julien Guillet

OTE

George Agapiou

Andreas Rigas

Stamatis Perdikouris

PTIN

´ Alvaro Gomes

Diogo Conde¸co

Phone/Fax/e-mail Phone: +49 8153 282803 Fax: +49 8153 28 1871 e-mail: [email protected] Phone: +49 8153 282871 Fax: +49 8153 28 1871 e-mail: [email protected] Phone: +33 4 9300 8106 Fax: +33 4 9300 8200 e-mail: [email protected] Phone: +351 234 377 900 Fax: +351 234 377 901 e-mail: [email protected] Phone: +351 234 377 900 Fax: +351 234 377 901 e-mail: [email protected] Phone: +351 234 377 900 Fax: +351 234 377 901 e-mail: [email protected] Phone: +351 234 377 900 Fax: +351 234 377 901 e-mail: [email protected] Phone: +33 2 23455821 Fax: +33 2 23455859 e-mail: [email protected] Phone: +33 2 23455819 Fax: +33 2 23455859 e-mail: [email protected] Phone: +33 2 23455858 Fax: +33 2 23455859 e-mail: [email protected] Phone +30210 6114663 Fax: +30 210 611 4650 e-mail: [email protected] Phone +30210 6389056 Fax: +30 210 611 4650 e-mail: [email protected] Phone +30210 6389053 fax: +30210 611 4650 e-mail:[email protected] Phone: +351 234 377 900 Fax: +351 234 377 901 e-mail: [email protected] Phone: +351 234 377 900 Fax: +351 234 377 901 e-mail: [email protected]

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UNIS

Na Yi

Yi Ma

Phone +44 1483 68 4703 Fax: +44 1483 68 6011 e-mail: [email protected] Phone +44 1483 68 3609 Fax: +44 1483 68 6011 e-mail: [email protected]

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List of Acronyms and Abbreviations 3G 3GPP AMC AoA AoD AP AWGN BC BER BF BS CDF CFB CoMP CP CQI CRLB CSI CSIT DA DB dB DoA DF DL DLR DoF DPC eNB EUR FB FBS FDD FER FFR FMT GDoF GPS GNSS HARQ HeNB HIRZ IA IBC ICI ICIC

3rd Generation (A mobile communications system of the 3rd generation.) 3rd Generation Partnership Project Adaptive Modulation and Coding Angle of Arrival Angle of Departure Access Point Additive White Gaussian Noise Broadcast Channel Bit Error Rate Beamforming Base Station Cumulative Density Function Channel Feedback Coordinated Multi-Point (transmission) Cyclic Prefix Channel Quality Indicator Cram´er-Rao Lower Bound Channel State Information CSI at the Transmitter Deterministic Annealing Database Decibel Direction of Arrival Decode and Forward Downlink Deutsches Zentrum F¨ ur Luft- Und Raumfahrt E.V. Degrees of Freedom Dirty Paper Coding Evolved NodeB EURECOM Feedback Femto Base Station Frequency Division Duplex Frame Error Rate Fractional Frequency Reuse Femto Mobile Terminal (MT served by a FBS) Generalised Degrees of Freedom Global Positioning System Global Navigation Satellite System Hybrid Automatic Repeat Request Home Evolved NodeB High Interference Reference Zone Interference Alignment Interfering Broadcast Channel Inter-Cell Interference Inter-Cell Interference Coordination

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ICT IEEE IFC IR IT LMMSE LoS LTE LTE-A MAP MBS MCS MER MHz MIMO MISO MMT MMSE MRC MSE MT MU NADA NAK NLoS OFB OFDM OFDMA OR O-TDoA OTE PC PDDP PL PMI PSS PTIN QoS RAN RB RI RMSE RN RNP RSS RSSI Rx

Information and Communication Technology Institute of Electrical and Electronics Engineers Interference Channel Incremental Relaying Instituto de Telecomunica¸c˜ oes Linear Minimum Mean Squared Error Line of Sight Long Term Evolution LTE Advanced Maximum a Posteriori Macro Base Station Modulation and Coding Schemes Mitsubishi Electric Merce Megahertz Multiple Input Multiple Output Multiple Input Single Output Macro Mobile Terminal (MT served by a MBS) Minimum Mean Squared Error Maximal-Ratio Combining Mean Square Error Mobile Terminal Multi-User Narrow Angle of Departure Aperture Negative Acknowledge Non Line of Sight Output Feedback Orthogonal Frequency-Division Multiplexing OFD Multiple Access Opportunistic Relaying Observed Time Difference of Arrival Hellenic Telecommunications organisation Power Control Power Delay Doppler Profile Path Loss Precoding Matrix Index Primary Synchronisation Signal Portugal Telecom Inova¸c˜ ao Quality of Service Radio Access Network Resource Block Rank Indicator Root Mean Square Error Relay Node Radio Network Planning Received Signal Strength Received Signal Strength Indication Receive/Receiver/Reception

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SDMA SINR SISO SNR SON SR SSS SU TDD TOA TTI Tx UE UL ULA UMTS UNIS WHERE2 Wi-Fi WP WSINR WSR ZF

Spatial Division Multiple Access Signal to Interference plus Noise Ratio Single Input Single Output Signal to Noise Ratio Self Organising Network Sum Rate Secondary Synchronisation Signal Single User Time Division Duplex Time of Arrival Transmission Time Interval Transmit/Transmitter/Transmission User Equipment Uplink Uniform Linear Array Universal Mobile Telecommunications System University Of Surrey Wireless Hybrid Enhanced Mobile Radio Estimators (Project Acronym Of Phase 2) “Wireless Fidelity”, referring to Wireless Local Area Network IEEE 802.11 Work Package Weighted SINR Weighted Sum Rate Zero Forcing

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1

Introduction

Wireless network based localization offers an alternative and/or complement to Global Navigation Satellite System (GNSS) based localization. Satellite connectivity may be difficult in urban canyons and indoors, and not all mobile terminals (MTs) are GNSS equipped. Wireless network based localization is now part of LTE-A, based on the following techniques: Enhanced Cell Id (Cell Id associated with Received Signal Strength), O-TDoA (Observed Time Difference of Arrival) and AoA (Angle of Arrival) at the Evolved NodeB (eNB). The availability of location information of MTs, relay nodes (RNs), femto/small cells and macro cells’ eNBs in turn provides opportunities to greatly enhance the operation of wireless communication systems. Three different aspects concerning the coordination and cooperation between network nodes were tackled in the WHERE2 project, in the ambit of geolocation aided cooperation for future wireless networks. This deliverable, presents the latest and final achieved results on this topic, and is split accordingly into five main chapters, briefly described as follows. The overall scenario, which is essentially common to all the investigated and proposed approaches presented in this deliverable, is introduced and illustrated in Chapter 2. This chapter also includes some brief introductory considerations regarding system architecture and the adaptations eventually required to implement the proposed techniques and algorithms. Chapter 3 — Fixed Relays for LTE Cellular Systems — presents the work developed in WHERE2, in several fronts, targeting significant performance improvement of fixed-relay LTE-A cellular networks by exploiting location information, as relaying is one of the key technologies standardized by 3GPP in LongTerm-Evolution-Advanced (LTE-A) Release-10. Five different schemes are proposed and detailed in this chapter’s sections, respectively including brief introductions, the proposed algorithms and its simulation results. Chapter 4 — Location-Aided Multi-Cell Processing — initially briefly recalls some location-aided communications opportunities already identified in the WHERE project, and introduced in WHERE2 deliverable D3.1 [3], after which are presented the two other main investigations carried out in this project. The first of these two introduces the concepts behind multi-cell communications, and the second one presents the work on location aware coordinated multipoint (CoMP) transmission synchronization, which was partially already introduced in deliverable D3.1. Chapter 5 — Femtocell Based Communications — addresses inter-cell interference coordination, which is key after the operators trend of heterogeneous cellular network deployments mixing macro eNBs and femto/home base stations (HeNBs) covering small cells. In the first proposed approach, downlink femtomacro interference is controlled through long-term femto power setting using the available location information, while in the second one HeNB-eNB and HeNB-HeNB interferences are mitigated in a more centralised manner, as a self-organised network, by appropriately configuring each new small cell’s HeNB using HeNBs and eNBs location information but also their sensing capabilities. Finally, the most important conclusions attained concerning the different presented topics and aspects tackling the coordination and cooperation between network nodes, addressed in WHERE2 research work, are summarized in Chapter 6. The Appendices in this deliverable include further details concerning the presented proposed approaches, namely in the form of publications.

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2

General scenario and System architecture

The approaches studied and developed in the scope of task T3.1 can all be applicable to LTE/LTE-A cellular systems communications. The main scenario in which the proposed techniques and algorithms can bring benefits in terms of communications performance, based on the scenarios and use cases investigations carried out in the first year of the project and presented in WHERE2 deliverable D1.1 [4], and further detailed in this chapter, is based on a LTE/LTE-A cellular network, where significant performance gains can be envisaged.

2.1

Common scenario

A general common scenario can be described as an LTE/LTE-A cellular network composed of several Evolved NodeB (eNBs) or Macro Base Stations (MBSs), together with Donor eNBs serving relay nodes (RNs), and Home eNBs (HeNBs) deployed indoors, covering a broad geographical area through respective macro and small cells, and serving several mobile or static user equipment (UE). A representation of this overall scenario is shown in Figure 1. The RNs associated to a donor eNB providing coverage in a cell are used for cell-edge enhancement assuring communication to UEs close to the cell-edge through multihop. Femto or small cells’ coverage areas are accomplished through Femto Base Stations (FBSs)/HeNBs in MBS/eNB coverage area, eventually implementing appropriately Inter-Cell Interference Coordination (ICIC) as proposed in the respective WHERE2 specific study in Section 5.1.

Figure 1: General scenario for task T3.1 proposed techniques.

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In general, a static or mobile UE is served directly by an eNB if it is not far from the cell-center, or it can be assisted by a RN if the UE is near the cell-edge. Ultimately, the UE can also be served by multiple eNBs from adjacent cells if it is at cell-edge through Coordinated Multipoint (CoMP) transmission, providing it is implemented appropriately in the system, or through other advanced multi-cell based communication techniques. All these situations are represented in Figure 1. All the proposed T3.1 approaches, exploit the location information related to the cellular system elements, namely eNBs, RNs, HeNBs, UEs, etc., which is considered to be available on demand or through internal up-to-date database (DB), allowing significant communication performance gains, as presented in the following chapters. The effective performance of the proposed techniques and algorithms is dependent on the availability and quality of information, and on its appropriate exchange, regarding not only the location info but also other information, such as UEs’ received power measurements, which are stored and accessed on a DB in the system core network. Other factors, in the scope of the proposed approaches, which have an impact in their respective performance are, for instance, the effective communication between the eNBs and HeNBs, and also with the DB server hosting UEs’ measurements. Also, adequately synchronized transmission at eNBs (or at least availability of appropriate information about their asynchrony) when multi-cell communications are concerned, or even full or merely statistical channel knowledge, e.g. for optimal rate selection.

2.2

System architecture

LTE/LTE-A cellular systems already have most of the technology required by the WHERE2 techniques and algorithms developed in the present scope. The entities, already existing in these systems, which should be used and eventually adapted with the proposed WHERE2 technology can be identified as follows. eNB, RN, HeNB, namely their PHY and MAC layer protocol stacks (e.g. frame and symbol synchronization PHY block), and respective Uu/Un and X2 interfaces, should be subject to appropriate modifications to host the specific changes in order to implement and comply with the proposed coordination and cooperation techniques. A representation of these LTE/LTE-A entities, their interfaces, interconnections and the relevant layers involved in the proposed approaches is shown in Figure 2.

Figure 2: LTE/LTE-A entities, interfaces and relevant layers involved in T3.1 proposed approaches. 13

In the proposed technology it is also assumed that the user equipment (UE) include technology to provide information on its own position, e.g. through GPS as in most modern smartphones, and/or that it is possible to estimate and provide the UEs’ position by means of specific signalling in the system core network, e.g. through UE-based LTE positioning, to the proposed WHERE2 system add-ons in question. Such UEs’ location estimation provided by the network is achieved with the intervention of the Evolved Serving Mobile Location Centre (E-SMLC) defined in 3GPP specifications, also represented in Figure 2, which can eventually implement some WHERE2 WP2 advanced UEs’ positioning algorithms. The proposed techniques and algorithms will rely on the currently defined LTE/LTE-A architecture and depend on the possibility to add further functionalities through the modification of some of the existing system components, which can be more or less significant in terms of system impact depending on the required specific changes involved. For instance, several of the proposed WHERE2 enhancements here in question imply the need to have a database server in the system core network, possibly hosted at the Mobility Management Entity (MME), holding UEs’ received power measurements, e.g. needed for power setting at the HeNBs, and also statistical channel knowledge associated with location, concerning a whole cell or specific coverage area. Also, it would be necessary to implement equivalent Radio Resource Control (RRC) signalling to report the required received power measurements from UEs to eNB(s) via Uu interface(s), and also the necessary signalling exchange between eNBs and the DB server, possibly through the S1-MME interface. It is important to take into account that the possibilities for such implementations in the existing systems would have to be carefully further investigated and assessed. On a lower level, in the implementation of the proposed technology, specific modules inside of particular system components would have to accommodate additional blocks in the signal processing chain. For example, in the proposed Location Aware Coordinated Multipoint Transmission Synchronization approach, at PHY layer the frame and symbol synchronization block should be modified in order to process a-priori information about frame and symbol timing, together with the implementation of a new block which calculates a-priori timing info based on eNBs and UEs’ position information, as detailed in Section 4.4.

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3

Fixed Relays for LTE Cellular Systems

Relay is one of the key technologies standardized by 3GPP in Long-Term-Evolution-Advanced (LTE-A) Release-10. This chapter presents the work developed in the whole project duration, in several fronts, targeting significant performance improvement of fixed-relay LTE-A cellular networks by exploiting location information. Essentially, it is assumed that two types of location-related information are available to be used in the proposed techniques and algorithms: • The instantaneous error-free coordinates of eNodeBs (eNBs), Relay Nodes (RNs), and Mobile Terminals (MTs), in a two-dimensional space; • Location dependent long-term channel properties. Five schemes are proposed and detailed in the following sections, respectively, including brief introductions, the proposed algorithms and its simulation results. Section 3.1 summarizes the work initiated in the first half of the project, and already introduced in WHERE2 deliverable D3.1 [3], on location-aided cooperative relaying, which has been extensively published, as indicated in the section in question. The work presented in Section 3.2 is mostly included also in D3.1, and published in [5]. The algorithm presented in Section 3.3 was proposed after D3.1, and is published in [6]. Section 3.4 presents one of the most recently carried-out investigation, including results, in task T3.1, and although it is not yet published, it has been already submitted for appropriate publication (see Appendix A.1.2). Finally, Section 3.5 presents the performed study concerning relay node selection in cellular networks, supported by geolocation info, also already introduced in D3.1.

3.1

Adaptive location-aided cooperative relaying

Cooperative relaying has attracted many researchers’ interest from capacity theorems to practical relaying protocols [7]. Moreover, it has been deployed into wireless standards, i.e., in European 3GPP long-term evolution (LTE-Advanced) wireless relays are deployed to enhance coverage of cellular services. Such mobile systems can be modelled as a single-source, multi-relay, and single destination network when sources transmit information over orthogonal medium. However, the orthogonality between source and relays require extra cost either in time or frequency, which reduces the spectral efficiency. To solve this problem, adaptive protocols based relaying are considered in our work, i.e., incremental relaying (IR) and opportunistic relaying (OR). However, adaptive techniques require excessive signalling overhead. Meanwhile, it is considered in our work, that every involved node has the location information of all communication nodes through advanced positioning systems. This motivated us to employ location information to reduce signalling overhead and/or further improve the spectrum efficiency in such multiple relay networks. The first part of our work contributes to the IR. Deliverable D3.1 introduces intermediate contributions, namely a location-aided relay selection that has been investigated for IR over asymmetric fading channel in [8]. Based on our derived theoretical results, a relay can be selected according to the minimum outage probability, provided total transmit-power constraint and average SNR with location information assisted. Here, the role of location information is to help mobile nodes having the statistical channel knowledge of communication links, which is important for the calculation of outage probability. Following this, a novel adaptive hybrid automatic repeat request (HARQ) scheme has been proposed by exploiting the knowledge of channel quality information (CQI), with which we can determine the suitable transmission mode to guarantee a specific Frame Error Rate (FER) during the first transmission. The proposed HARQ scheme is suitable for machine-type communications with low mobility, whereby location information can be easily translated into channel quality information [9]. Our work in another fold contributes to the OR, which the basic idea is to choose the best relay node amongst all available relays through a certain policy. To improve the spectrum efficiency for the OR with decode-forward (DF) relaying protocol, a novel adaptive modulation scheme for opportunistic DF relaying (see [10]) has been introduced in deliverable D3.1, which allows both the source and relay to transmit information in different modulation formats. Then, we have investigated the adaptive protocol for OR with location information [11]. The proposed scheme is based on two steps: at the first step, a set of

15

candidates are selected based on their geolocations; the second step is in charge of selecting the best relay from the set of candidates. It has been shown that the proposed scheme can reduce signalling overhead by 97% with the spectral efficiency comparable to the conventional best-relay selection scheme. These studies have been further investigated in our continued work [12]. It is shown at the typical SNR of 10 dB, the schemes proposed for non-reciprocal channels can reduce the signalling overhead by around 90.7% with the cost of 2.46% in spectrum efficiency by employing location information. For the same set-up concerning SNR, the schemes proposed for reciprocal channels can reduce around 97.2% in signalling overhead when assisted with location information, and a cost of 1.5% gain in spectral efficiency. Finally, we investigated spectral efficiency when using relay with opportunistic channel assignment with three resource scheduling algorithms [13]. Location information is employed to help relay to do best-user selection algorithm. It was shown that the best-user selection relaying has the best performance since the source selection offers the chance to achieve higher spectral efficiency with better channel quality.

3.2

Location-aided relay node planning

In urban areas, relay nodes successfully enhance cellular system capacity. Normally, the locations for installing a RN must satisfy numbers of practical requirements, for example, sufficient power supply, Light-of-Sight (LoS) connection with a donor eNB/BS, etc.. As a result, the number of candidate locations for installing a RN is limited in a cell area. Finding the optimal RNs’ locations from the candidate set is an important task in the phase of network planning. Deploying RNs at the optimal locations allows minimizing the number of required RNs, maximizing the coverage area and performance, etc. These access points are usually installed in areas having heavy traffic demand. Hence, optimizing their location according to spatial data demand is crucial to the achievable performance. Taking the advantage of today’s high performance smartphones and their localization capability, we propose a new scheme to obtain time-dependent traffic-demand of a certain area, and to optimize location of relay nodes according to the spatial traffic demand distribution. 3.2.1

Main scenario

The network considered is illustrated in Figure 3. The 0-th base station (BS) is located in the centre of a d × d (m2 ) square-shape cell area, and is surrounded by six other BSs. The distances between the 0-th BS and the other six BSs are all equal to d meters, and the angle separation between any two adjacent surrounded BSs is 60 degree. Moreover, M MTs arbitrarily distribute in the central cell with index {1, . . . , m, . . . , M }.

Figure 3: Layout of the target scenario 16

Furthermore, the yellow dots represent N number of RN candidate locations. The MTs in the cell may move from one place to another. We assume the smallest recognizable spatial resolution is a small square-shape area denoted as Ai as shown in Figure 3, and the entire cell area consists in |A| number Ai of such areas. The MTs in the same area Ai are denoted as M Tm , and are assumed to have the same channel quality. Our target is to optimize the RNs location according to the traffic spatial distribution so as to minimize the required resources such as bandwidth. 3.2.2

Proposed algorithm

To address the presented issue, our proposed scheme consists in three main steps: • Construct a database recording MTs’ mobility patterns; • Periodically aggregate the demanded traffic from every MT, so as to obtain the long-term averaged spatial traffic distribution; • Use linear programming to optimize the locations of relay nodes. A simplified example of users’ mobility and communication pattern is demonstrated in Table 1. In this example, M T1 is switched off during the night at home area A3 . It’s in idle state from 9 am to 6 pm in the office area A5 , and it’s used for phone calls from 6 pm to midnight at home A3 . Although the situation in real life is much more complicated, this methodology is applicable supported by research results in [14] showing that 93% predictability in user mobility. Hence, because of this regularity, it is promising to record a MT’s mobility pattern without requiring huge amount of storage resources. Index M T1

mobility pattern Time period location 0 am - 9 am home A3 9 am - 6 pm office A5 6 pm - 12 pm home A3

prob. 1 1 1

communications service (Kbps) off(0) idle(0) calls(64)

pattern prob. 1 1 1

Table 1: An example of user mobility and communication pattern. Downlink transmission employing LTE-A defined physical layer technology is assumed in this scenario. All BSs and RNs employ their maximal allowable transmit power PBS and PRN (PBS > PRN ), respectively. We assumed that two different frequency bands are employed for BS-RN and for RN-MT transmission. The Signal to Noise plus Interference Ratio (SINR) between BS and a RN/MT is formulated as SIN RBS−RN/M T =

6 P

b=1

PBS P L(dBS0 −RN/M T ) PBS P L(dBSb −RN/M T )

,

(1)

+ N0

where P L(d) represents the path-loss between two nodes, which is a function of the distance d between 6 P PBS them. P L(dBS −RN/M T ) denotes the inter-cell interference from other six BSs, and N0 denotes the b=1

b

PRN P L(d

)

RN −M T noise variance. The SINR between RNs and MTs are formulated as SIN RRN −M T = . The N0 inter-cell interference from other BSs is zero because RNs and eNBs employ different frequency bands. According to the SINR, one out of the 16 Modulation and Coding Schemes (MCS) defined in LTE-A is chosen and applied. Each MCS is corresponding to one transmission efficiency value denoted as η (bits/s/MHz). Non-cooperative relaying with at most two hops from BS to MT is assumed. Each MT in the same area Ai compares the achievable transmission efficiency ηBS0 −M T Ai connecting directly with the BS, to m

17

the one ηBS0 −RNn −M T Ai via the n-th RN. The transmit efficiency of ηBS0 −RNn −M T Ai is formulated as m

m

ηBS0 −RNn −M T Ai = m

1 ηBS0 −RNn

1 +η

1

.

(2)

A RNn −M Tm i

If the directly connected transmission has a higher efficiency (ηBS0 −M T Ai ≤ ηBS0 −RNn −M T Ai ), the m m m-th MT communicates directly to the 0-th BS; otherwise, it communicates via the n-th RN. We define a decision vector x = [x1 , . . . , xn , . . . , xN ], where xn equals one if and only if a RN is deployed at the n-th candidate site, otherwise xn equals zero. Hence, if the location of RNs are determined and represented by the vector x, the transmit efficiency of all MTs in the same area Ai is formulated as    η(M T Ai |x) = max ηBS0 −M T Ai , max ηBS0 −RNn −M T Ai . (3) m

n

m

m

Naturally, MTs located away from the BS at the cell-edge are more likely to communicate via a RN. We further define a (|A| × N )-size matrix Yx ,     n = arg maxn ηBS0 −RNn −M T Ai  1 m x yin = (4) Ai < η A and η BS −M T BS −RN −M Tm i  0 0 n m  0 otherwise P x where yin = 1 represents the MTs in area Ai communicating via n-th RN, n yin = 0 indicates the MTs in area Ai communicating directly with the BS0 . The traffic demanded by the MTs at time t is denoted as rt Ai (bits/s), which varies over time and M Tm locations. The peak value of demanded traffic RAi for a certain area Ai is formulated as ! X t RAi = max rM T Ai . (5) t

m

m

The area Ai is covered if the RN-BS is able to allocate WAi MHz frequency-band so that RAi ≤ η(M T Ai |x) WAi . Naturally, if the RNs are deployed in an optimized manner, and provide high transmission m efficiency to the high traffic demand area, the precious bandwidth can be minimized. Our target is to optimize the RNs location so as to minimize the required bandwidth and provide full coverage to the target cell area at the same time. This could be formulated as follows min Wtotal (RAi , η(M T Ai |x) , Yx , ηBS0 −RNn ), x

m

(6)

subject to: xn ∈ 0, 1, ∀n ∈ {1, N },

(7)

dRNk −RNj ≥ dRN −min , ∀xk , xj = 1.

(9)

x yin

∈ 0, 1, ∀n ∈ {1, N }, i ∈ {1, |A|},

(8)

The constraint (9) guarantees that the minimum distance between any two selected locations is larger than dRN −min so as to avoid intra-cell interference. Moreover, the total required bandwidth Wtotal is calculated as   |A| P x R y |A| N Ai in  X X RAi   i=1 + (10) Wtotal =  ,  i=1 η(M T Ai |x) n=1 ηBS0 −RNn  m

which consists of two parts representing the bandwidth required for the BS-RN-MT communication and the bandwidth allocated for BS-RN link. The optimization problem of Equation (6) is a NP-hard problem, which can not be solved within polynomial time. We adopt an heuristic solution similar to the algorithm proposed in [15]. The detail of the algorithm is illustrated in Algorithm 1. 18

Algorithm 1: RN deployment algorithm 1 2 3 4 5 6 7 8 9 10 11

counter ← 0, x ← 0, f ← 0; while counter < N and ∃n, fn = 0 do Calculate G(RNn , x, f ), ∀n, fn = 0; Find k = arg max{G(RNn , x, f ) > 0}; if k is nil then return x; else xk = 1, counter ← counter + 1;; Mark fj = 1 if dRNk −RNj < dRN −min ; end end

3.2.3

Simulation results

To demonstrate the proposed algorithm, we considered a network layout as illustrated in Figure 3. Figure 4(a) shows the distribution of demanded traffic as well as the selected RN locations. The square blocks having colour from black to white represent the demanded traffic in bits/s. The BS is located in the centre. 7 RN locations out of 19 candidate places are identified, reflecting the users/requiredtraffic geo-distribution. The slash white lines represent the coverage area edges of RNs and the central BS. Figure 4(b) shows the total bandwidth reduction when employing more and more RNs. Compared to eNB-direct transmission, the required bandwidth reduces from 320 to 140 MHz using the selected 7 relays, which achieves 180 MHz (approximately 56%) bandwidth reduction.

(a)

(b)

Figure 4: a) Geographic distribution of the demanded traffic, the locations of the central BS, the selected relay nodes and the corresponding coverage area; b) The achievable bandwidth reduction versus the number of RNs employed, from 0 to 7.

19

3.3

Location-aided MAC layer flexible Round-Robin scheduling

Mobile terminals in relay-based networks suffer inter-cell interference not only from the surrounding BSs, but also from the RNs in other cells, which may locate closer to a MT than the interfering BSs do. The cell-edge area throughput will not be improved if the interference issue is not properly controlled. One solution is to employ Fractional Frequency Reuse (FFR), where the three different bands assigned to a certain RN, to its donor BS/eNB, and to its adjacent interfered RNs, separately [16]. As a result, the RNs using the same frequency band are no longer in any adjacent cells, so that the resultant co-channel interference is reduced. One consequence of employing FFR is that the allocated bandwidth at the BSs and the RNs are only a fraction of the entire available bandwidth, which may not satisfy the heavy traffic demand which can occasionally occur in busy hours. In this scenario, one solution is to allow the BSs and RNs to temporarily use the same frequency band. We propose a location-aided round robin [17] scheduling algorithm to achieve this goal. By exploiting the location information of the MTs, the proposed algorithm is capable of minimizing the resultant co-channel interference, and enhancing the cell-centre achievable throughput. 3.3.1

Setup and scenario

The considered network layout is illustrated in Figure 5. Without RNs, directional antennas are employed at each eNodeB, which separates the entire site into three cells. For example, the centre site with eNodeB id 5 consists of three cells having id 13, 14, and 15 separately. On top of such a single-hop network, one low-power RN is employed in each cell covering the cell-edge area using omnidirectional antenna. We consider a FDD LTE-A downlink transmission scenario. The RNs operate in half-duplex mode. More explicitly, in the even numbers of Transmission Time Interval (TTI), the eNodeBs communicate to the MTs and the RNs. In the odd numbers of TTIs, the eNodeBs communicates to the MTs only, and the RNs transmit information to their associated MTs. The scheduling of all MTs is centrally controlled by the eNodeBs.

Figure 5: The layout of a relay-aided LTE-A cellular network. 20

To reduce the co-channel interference, especially the strong interference from RNs in adjacent cells, the entire available bandwidth B is divided into four portions. More explicitly, donor eNodeBs use frequency band B0 to communicate with its associated MTs located in the centre of the entire site. The frequency band B1 , B2 and B3 are used by RN20 , RN21 and RN22 separately to communicate with the donor eNodeB at even TTIs, and with MTs located at the cell-edge at odd TTIs. The FFR relay network can reduce the co-channel interference. However, the resultant frequency reuse factor is reduced below 1 per cell, which may cause some issues such as in the scenario shown in Figure 6. Supposing that a round robin scheduler is employed at the donor eNodeB in cell15 , there are P MTs connected directly to the eNodeB in frequency band B0 having their QoS requirements just satisfied. Moreover, there are K edge MTs connected to the network via RN22 using frequency band B3 . The service quality for these K users/MTs is higher than their required QoS. A request comes in to the eNodeB asking to communicate with M T(P +1) which is located near the eNodeB. If FFR is not applied, the scheduler could reduce the allocated bandwidth to the K edge MTs, and allocate the redundant resource in frequency band B3 to M T(P +1) . However, with fixed FFR, this request will be denied or delayed since the frequency band B0 is fully used. To overcome the drawbacks of FFR, one possible solution is to allow the direct communication to temporarily use some frequency resources in B3 . In fact, the reused frequency resource could be chosen from B2 and B1 as well, which may introduce less interference because of the directional antenna. Nevertheless, the principle is the same regardless the specific frequency band. So we continue to use B3 throughout this section.

Figure 6: Target scenario. Although satisfying the QoS requirements is our ultimate objective, we use overall achievable throughput as performance metric instead in this paper for simplicity. From now on, we use RBs to represent different frequency band, since RB is one of the basic units for scheduling in LTE-A system. One RB occupies 180 kHz bandwidth in one TTI (1 ms) time duration, which consist of 12 × 14 = 168 modulated symbol assuming normal cycle prefix. If a user M T1 can achieve spectral efficiency of η1 (bits/symbol), the achievable throughput of M T1 using one RB is 168η1 Kbit/s. We further simplify the problem by assuming that each user is located with only one RB. More explicitly, our target problem is rephrased as follows: • Assumption 1 – The frequency band B0 consists of P RBs, which are equally shared by P MTs denoted as M Tpc (1 RB/MT). The frequency band B3 consists of K RBs, which are also equally shared by K cell-edge MTs denoted as M Tke (1 RB/MT). The superscription (·)c and (·)e represent “centre” and “edge” separately; 21

• Assumption 2 – The location information of all MTs are available. A database recording the longterm averaged pathloss and shadowing for every location in cell15 is also available; • Target 1 – Choose one MT p out of {1, 2, . . . , P + 1} cell-centre MTs, choose another cell-edge MT k out of {1, 2, . . . , K} cell-edge MTs. The chosen M Tp and M Tk will employ the same RB k originally scheduled to M Tk . As a result, cell-centre M T(P +1) can be served; • Target 2 – Minimize the throughput loss at cell-edge, and at the same time maximize the achievable throughput increase for centre MTs. 3.3.2

Proposed algorithm

The first target can be easily satisfied even by randomly choosing one RBs m currently used by M Tk from frequency band B3 , and allocating this RB to the new user M T(P +1) . However, this cannot satisfy the second target, since the location of M Tk and M T(P +1) is random. If M Tk is close to the eNodeB, it will receive high interference. An intuitive solution is that the chosen MT M Tk and M T(P +1) should be separated as far as possible, so that the resultant co-channel interference is minimized. We compare the long-term channel degradation between all K edge users and the donor eNodeBs, and choose the one having the highest degradation, so that to minimize the potential co-channel interference from eNodeBs. Similarly, we compare the long-term channel degradation between all P centre MTs and the RN, then also choose the one having the highest channel degradation, so as to minimize the potential co-channel interference from RNs. These two chosen users will share the same RB. Other users are scheduled normally using the round robin algorithm. More precisely, the proposed algorithm is summarized in the following steps: 1. For each M Tke with coordinates (xek , yke ), searching out the database so as to determine the channel degradation value between this MT and the donor eNodeB PeN odeB−M Tke ; 2. Choose the cell-edge user le = arg maxk {PeN odeB−M T1e , . . . , PeN odeB−M TKe }; 3. For each M Tpc with coordinates (xcp , ypc ), searching out the database so as to determine the channel degradation value between this MT and the RN PRN −M Tpc ; 4. Choose the cell-centre user mc = arg maxp {PRN −M T1c , . . . , PRN −M TPc }; 5. Assign RB l in frequency band B3 to center user m; 6. Schedule other users using the normal round robin algorithm. 3.3.3

Simulation results

We consider a transmission scenario in a central cell cell15 . We set up our simulation with the following parameters P = 9, K = 4. The MTs locations are randomly generated, and the simulation results are averaged over 5000 different locations. Figure 7 demonstrates the experimental cumulative density function of the total throughput of cell-centre users. Three scenarios are compared: 1) There are 9 cell-central user, and 4 cell-edge user. One Orthogonal RB is assigned to each of them. 2) One RB in the cell-edge frequency band is randomly chosen and allocated to the 10-th cell-central MT. 3) One cell-edge MT is chosen to share its RB with a cell-central MT using the proposed location-aided round robin scheduling algorithm. Basically, if the cumulative density function (CDF) curve shifts towards the right, it indicates higher throughput is achieved. As a result, the two experimental CDFs demonstrate that the achievable total throughput for the central MTs is increased by RB reusing. The proposed algorithm achieves higher total throughput than the random selection method.

22

Figure 7: Experimental CDF of the total throughput of central MTs, when 1) no RB reuse, 2) 1 RB reuse with random selection, and 3) 1 RB reuse using the proposed scheduling algorithm.

3.4

Location-aided Physical layer channel state information feedback

Having accurate channel state information (CSI) feedback from MTs at eNB is crucial for achieving higher downlink throughput. CSI is used for adapting modulation and coding schemes (MCS), and adjusting multiple antenna transmission modes such as ”single-antenna transmission”, ”open-loop transmit diversity”, ”beamforming”, etc. However, the acquisition of accurate downlink CSI is very difficult in a wide-band relay-aided LTE-A network for several reasons. First of all, channel state is time-variant, which requires periodic updates. Secondly, channel state is also frequency-dependent, which results in multiple CSI values for a wide-band system. Thirdly, the deployment of relays further increases the amount of CSIs since the channels between MT and multiple relays are required to be feedback as well. In current LTE-A solution, CSI is quantized, and includes CQI (Channel Quality Indicator, related to SINR), Rank Indicator (RI, related to channel rank), and Precoding Matrix Index (PMI, related to instantaneous channel matrix). In time-domain, CSI is fed back in periodic and aperiodic mode. In the first mode, the feedback contents are DL-tx-mode dependent. For example, if SISO (Single-Input Single-Output) is used, only CQI is required to feed back. CQI, RI, and PMI have different signalling time-intervals. For instance, RI changes slower than CQI and PMI, and it is fed back less frequently. Aperiodic mode has higher priority than periodic mode, and the feedback contents could be DL-tx-mode dependent or configured by higher-layer. In frequency-domain, CQI is also organized in two ways: 1) Wideband CQI, where only 1 averaged CQI value for the entire bandwidth; and 2) Sub-band CQI, where multiple CQI values to represent the frequency diversity. The sub-band width is captured by ”sub-band granularity”. In summary, the current solution reduces the amount of CSI feedback, and its efficiency depends on a sensible choice of signalling interval in periodic mode, the active time of aperiodic mode, as well as sub-band granularity. The above-mentioned three values depend on the long-term channel properties. More explicitly, signalling interval is related to correlation-time, and sub-band granularity depends on coherent bandwidth. Since the above-mentioned long-term channel properties are location-dependent, it motives us to exploit 23

location information to reduce the feedback overhead. In this work, we focus on reducing the CQI value feedback overhead, by exploiting location-dependent long-term channel properties including averaged-SNR and NLoS/LoS conditions. 3.4.1

Scenario

We consider a single-user single-cell scenario as shown in Figure 8, which consists of one eNB (xeN B , yeN B ) and 2 relay nodes RN1 (x1 , y1 ), RN2 (x2 , y2 ). A MT moves within this cell following a certain trajectory. The MT’s location is presented as (xM T , yM T ). The total available bandwidth containing a set of Resource Blocks (RBs) R is divided into 3 subsets, R0 , R1 , R2 satisfying |R0 | + |R1 | + |R2 | = |R|. These three subsets of RBs are allocated to eNB (B0 ) and two relay nodes separately. Fractional Frequency Reuse (FFR) is employed so that intra-cell interference is avoided. We assume that the nearby RNs in adjacent cells are associated with different frequency bands. Hence, inter-cell interference can be ignored for simplicity. Supposed that a set of RBs S, (S ⊆ R0 /R1 /R2 ) with fixed cardinality |S| are assigned to the target user, our objective is to maximize the achievable downlink throughput, and minimize the required CSI feedback at every known location.

Figure 8: Target scenario. The following assumptions are made in this study: • The transmit power at the eNB is 10 dB higher than the emission power at the RNs; • Transmit power is equally distributed within all resource elements; • Multiple antennas are employed at eNB/RNs/MT with omnidirectional emission pattern; • Block fading model is used, assuming the channel remains unchanged within every TTI; • Zero-forcing (ZF) detector is used at the MT. 3.4.2

Proposed algorithm

Our target can be realized by jointly: 1) associating the MT to the RN/eNB providing the highest received signal strength; 2) employing adaptive transmission mode (e.g. transmit diversity, open-loop MIMO, etc.); 3) deploying different modulation and coding scheme (MCS) for every RB; and 4) scheduling the best set of RBs to the target user according to instantaneous channel quality. The process is illustrated in Figure 9 starting with estimation of the instantaneous MIMO channel H j at every j-th sub-carrier. 24

Figure 9: The process of CSI feedback and scheduling. k Assuming ZF receiver at MT, effective channel matrix H txm ef f for the k-th transmission mode, as well as the corresponding instantaneous SNR γj at j-th sub-carrier can be calculated. Based on the pre-set parameters Ri and RB granularity RBgran , MISEM [18] function and CQI-SNR-mapping [19] are used to generate feedback information including CQI, PMI and Rank-index. As shown in Figure 9, RBgran = 1 is used for RB set R1 , while single CSI averaged over 15 RBs is calculated for RB set R2 . Hence, the number of total feedback CQI is formulated as:

NCQI =

|{Ri }| K X X i

k

|Ri | × ranktxmk RBgran

(11)

The feedback information is transmitted over uplink control channel, received by the eNB and overheard by the RNs. The scheduler at the eNB takes this feedback information as its input, and assigns appropriate RBs, transmission mode, etc., according to a certain criterion such as maximizing total throughput, satisfying QoS constraints, etc. In this study, the objective of scheduling is to maximize the achievable throughput of the single target user using a fixed number of RBs without considering other issues such as fairness with other users. Hence, the scheduling rule can be formulated as X ˆ = arg max max max ˆ ˆi, k} {S, fthr−put (RBj , txmk ), (12) i,(S⊆Ri )

S

k

RBj ⊂S

ˆ ˆi, kˆ represents the optimal set of RBs, the best eNB/RN, and the transmission mode. In Figure 9 where S, for example, the output of the scheduler has chosen to transmit data through RN1 using two RBs S = {RB1 , RB2 }, OLSM mode and corresponding CQI, PMI and rank level. The throughput calculation

25

function fthr−put (· · · ) is formulated as  Rank P   fCQI−ef f (CQIr )  C× r=1 fthr−put = Rank P    0.5 × C × fCQI−ef f (CQIr )

if RBj belongs to eNB (13) if RBj belongs to RNs

r=1

while fCQI−ef f is the one-to-one mapping between CQI (corresponding to one combination of modulation and coding scheme) and information efficiency with a unit of (bit/sym), and C is a constant value equal to 7 × 12/0.5 = 168(Ksym/sec) under the assumption of using normal cyclic prefix. Hence, the obtained throughput using Eq. (13) has a unit of (Kbps). The additional fraction of 0.5 for RNs is due to the half-duplex nature, and implicitly assumed that the access link (RN-to-MT) is poorer than the back-haul link (eNB-to-RN). Based on Eq. (11), the feedback overhead can be reduced if it is allowed to use larger value of RBgran and smaller cardinality of {Ri }, with no/little influence on scheduling results represented by Eq. (12) and (13). The core idea of the proposed scheme is to exploit UE’s location information and location-dependent long-term channel knowledge, so as to optimize the selection of Ri and RBgran . More explicitly: • Without location information, MT compared instantaneous SNR (γj ) averaged over frequency domain (¯ γj ), and selects the access point (AP) Ri providing the highest throughput. RBgran = 1 is used as an upper bound, which results in the highest throughput and feedback overhead. By contrast, wideband CQI feedback mode is used as an lower bound, which results in the lowest throughput and the lowest feedback overhead. This could be formulated as γj ), Ri = arg max fthr−put (¯

(14)

RBgran = 1, |Ri |

(15)

γj ∈Ri

• With location information, eNB choose the access point according to averaged-SNR (path-loss + shadow), and selects the access point Ri providing the highest throughput. Sub-band CQI feedback having |S| number of CQIs is used if the MT satisfying three criteria: 1) MT is in NLoS; 2) The averaged-long-term-SNR is within the range of -6 and 20 dB; and 3) the employed rank equals 1. Otherwise, wide-band feedback mode with RBgran = |Ri |. This could be formulated as

3.4.3

Simulation results

Ri = arg max fthr−put (γavg−long ), γj ∈Ri  |S| NLoS    γavg−long ∈ [−6, 20] RBgran = rank = 1    |Ri | otherwise

(16)

(17)

We consider a scenario having one eNB with coordinate (1,174), two RNs located at (250,87) and (250,260) respectively. The target MT moves from the left-bottom to the right-upper of the cell area along the √ trajectory yM T = 3(xM T − 109), xM T ∈ [110, 300]. Two omnidirectional antennas are deployed at eNB/RN/MT. WINNER channel model type ”C3” representing the typical outdoor urban scenario is used. Figure 10(a) shows the averaged achievable throughput at different locations via RN1/RN2/eNB. The feedback mode uses {Ri } = {R0 , R1 , R2 } and RBgran = 1. The bold blue line shows the optimal achievable throughput by choosing the best access points (APs). The probability of associating this MT at different locations with RN1/RN2/eNB over 100 frames with independent small-scale fading is illustrated in Figure 10(b). It demonstrates that at some locations such as location id from 40 to 50, the MT is always associated with one certain AP regardless of the small-scale fading. Hence, it is possible to reduce the cardinality 26

(a)

(b)

Figure 10: a) Achievable averaged throughput over different locations via RNs/eNB and the optimal one with adaptive AP choice; b) Probability of associated with RN1/RN2/eNB at different locations. of {Ri } at these locations. Compared to the no-location aided performance using RBgran = 1, the degradation of achievable throughput using the proposed location-aided feedback scheme is illustrated in Figure 11(a), while the corresponding feedback overhead reduction is shown in Figure 11(b). These two figures demonstrate that the proposed algorithm reduces about 70% feedback overhead at best case, while degrades the achievable throughput by 40 Kbps maximum. Compared to the no-location information scheme, using RBgran = 1 and RBgran = |Ri |, the proposed scheme achieves a better trade-off between throughput and feedback overhead.

(a)

(b)

Figure 11: a) Comparison of the achievable averaged throughput over locations using different feedback schemes, compared to the benchmark with RBgran = 1; b) Comparison of reduction of feedback overhead over locations using different schemes, also compared to the benchmark using RBgran = 1.

27

3.5

Geolocation-aided relay nodes selection in cellular networks

Optimal node selection algorithms for a network with cooperative relays has received a lot of attention in the latest years. As such, there has been a lot of research work in relay selection mechanisms that can be divided in single relay selection and multiple relay selection. Single relay selection mechanisms have been investigated in [20] where the neighbour node with the maximum signal to interference and noise ratio (SINR) is selected as the most appropriate node, while in [21] the node that is closest to the base station is used as the best relay. The research is extended to multiple relay selection in [22] by exploiting the concepts of relay ordering and recursion. The above algorithms select the node according to one criterion which may not be an optimal solution for maximising the performance of communication links. 3.5.1

Node selection in a relay network

This section utilizes the geolocation of the user, which is implicitly related to two criteria of quality of service (QoS), that are the received signal strength indicator (RSSIi ) of the i-th cell that a relay node has, and the link data rate Ri between the user0 s terminal and the selected relay node. The RSSI term has a higher value when the user0 s terminal is closer to the node and decreases when the user gets away from it. The scenario used in this section is represented in Figure 12. From this figure it can be seen that the distance of the user from the relay node and the base station varies, which reflects changes to the rate and to the RSSI.

Figure 12: User in a network with relays. The power of the averaged signal strength considering only the long-term path-loss effect denoted as RSSI in dBs is related to the geolocation of the user by the following equation: Pic = Pimax − 10γ log (ri )

(18)

where ri represents the distance of the user0 s terminal from the relay node i. In the same way the data rate has a peak value when the user is next to the node and decreases as the user steps away from it. Both of these quantities are implicitly related to the location of a user, and are expected to be the above two metrics to be higher when a user is closer to a node. Rimax is the peak rate in a link. In general, stronger signal strengths indicate better signal quality between the node and the user0 s terminal. However, since nodes may have different transmitted power and received signal strength levels, then it is more accurate to use relative levels. Therefore,Rir is the relative value of the maximum rate or the normalised rate for the link between the i-th relay node and the user terminal, and is equal to: Rir =

Ric Rimax

f or 28

i = 1, 2, . . . , n

(19)

where Ric is the current utilisation of the i-th link and Rimax is the maximum utilisation. In the same way RSSIimax is the peak signal strength of the i-th link, RSSIir is the relative value and RSSIic is the current signal strength, which are related as: RSSIir =

RSSIic RSSIimax

(20)

A cost function that represents a combined performance metric for the network is defined as CiF which is generated by combining the above two factors; the supported rate of the i-th network for transferring traffic and the receive signal strength at both sides-the terminal side and the node one. This cost function is defined as: CiF = wRSSI · RSSIir + wR · Rir (21) where wRSSI and wR take values of 0 ≤ wRSSI ≤ 1 and 0 ≤ wR ≤ 1 are the weights that denote the values that an operator sets in its network in order to provide services to the end users with proper QoS. In addition the constraint is that: wRSSI + wR = 1 (22) The value of the cost function in Eq.(21) denotes the best selected node in the network. The values of the weights and the relative values of the receive signal strength and the capacity of the network produce values for the cost function. The higher values of the cost function denote the best established links between the user and the selected relay node. From Eq.(21) there can be distinguished two distinct cases: 1. When the value of the weight wRSSI is equal to zero then the cost function Ci depends only on the bit rate Rir of the link. 2. When the weight wR is equal to zero then the cost function Ci depends only on the signal strength RSSIir of the link which depends directly on the distance of the user from the relay node. The weights wRSSI and wR can take any value between 0 and 1 depending on the location of the user from the node and from the rate that an operator decides to assign and give priority to different users depending on their profile. The cost function CiF graph, as a function of the distance of the user to the node when wRSSI = 1 and wR = 0 for a cell of 2 km, is shown in Figure 13 A node selection mechanism, to be used in a relay network, is presented here, utilising the geolocation of the user which is implicitly related to two criteria: RSSI and link data rate. A cost function for the node selection, representing a combined performance metric for the network was defined, generated by combining the above mentioned two factors. The weights in the cost function are dependent on the location of the user in relation to the node, and on the rate that the operator decides to assign, given the priority of different users, depending on their profile.

Figure 13: Cost function vs user’s distance 29

4

Location-Aided Multi-Cell Processing

The availability of location information offers opportunities to enhance wireless communications systems. The position based information that can be exploited comprises slow fading channel characteristics of various links: • NLoS/LoS ((Non) Line-of-Sight) • Attenuation • Delay spread, frequency selectivity • Angular spreads, MIMO channel characteristics (rank) • Speed, direction of movement, acceleration (predictability of movement), trajectory Some of these aspects may require the use of databases, containing these characteristics as a function of position, compatible with a cognitive radio setting. Compared to feedback (FB) based approaches: some of these characteristics can not easily be determined from isolated channel estimates, or not predicted at all (e.g. slow fading prediction). What can not be inferred on the basis of position, as generally believed, is the fast fading state, the instantaneous complex channel impulse response. However, Nokia-Siemens in 0 [23] work with a database of channel impulse responses directly, which are claimed to be stable over 40 in some measurements, to overcome the problem of delay in channel FB. They consider a combination of FB together with location aided approaches as realistic. In the next two sections, 4.1 and 4.2, we first recall briefly some location-aided communications opportunities identified in the WHERE project, see e.g. [24], and also introduced in WHERE2 deliverable D3.1 [3]. Section 4.3 introduces the concepts behind multi-cell communications, and finally Section 4.4 presents the work on location aware coordinated multipoint (CoMP) transmission synchronization carried out in WHERE2, which was partially introduced in D3.1. All the work presented in these sections has been published in several conferences and publications, as pertinently indicated in the sections in question.

4.1

Single-User Aspects

On the receiver (Rx) side: position information can lead to information about the channel statistics via a database, which can be used to improve channel estimation. This could be compared to learning of the channel statistics from previous channel estimates (which is hardly possible though in short packet mode!) or with sparse techniques. On the transmitter (Tx) side: adapt AMC and resource allocation (see further). 4.1.1

Location and Database aided Channel Estimation/Prediction

These days, optimized LMMSE channel estimation and tracking is often considered [25], which requires 2D covariance information in the form of the Power Delay Doppler Profile (PDDP). In multi-antenna systems the space dimension could also be added to that profile. For fast fading channel estimation and short-term prediction, the channel PDDP an be: (1) learned from consecutive channel estimates, but knowledge will often come a bit late in this way and may require long data and stationarity for extensive PDDPs, or (2) determined from position information + (extensive) database, leading to instantaneous knowledge & extended (short-term) channel prediction range. A Kalman filter performing integrated position tracking and channel tracking is one solution here. Approach (2) allows furthermore longer-term prediction, but of channel statistics only. If the database content is limited, a combination of both approaches could be considered. See section 4.1.1 of deliverable D3.6 for some initial work in this direction.

30

4.1.2

Position based Adaptive Modulation and Coding (AMC) and OFDMA Resource Allocation

(Position information leads to) Environment information which in turn leads to information on the channel diversity structure, on the channel frequency selectivity and would allow to adapt frequency allocation/interleaving. One could consider adapting the (OFDM) Cyclic Prefix (CP) and pilot structure on the basis of environment parameters. This would lead to minimized overhead and would avoid to design for the worst case. Information on the MIMO channel richness (e.g. rank) allows to adapt the spatial multiplexing and the (linear) space-time coding. Information on the mobility provides temporal diversity information, which can be used to adapt interleaving in time. All these adaptations can take into account channel non-Rayleigh aspects (e.g. LoS/NLoS, LoS leads to reduced or no fading).

4.2

Single-Cell Multi-User Communications

This is single-cell, but the opportunities of multiple Rx antennas in MU-MIMO are still not well understood. Furthermore, we advocate that the use of SDMA techniques, introduced in the 90’s, needs to be reconsidered, and location information can come in handy here. See [26] for further details. 4.2.1

Location aided Multi-User Resource Allocation

Some possibilities are: • Multi-user MIMO: Use environment information to preselect users, to limit channel feedback to a reduced set of preselected users, similar to the relay selection problem discussed earlier. The user preselection can e.g. involve: users with similar attenuation, users with rank 1 MIMO channels (close to LoS), ... • Multicell aspects (interference coordination) or for Cognitive Radio (interference from secondary to primary systems): the interference level can be predicted from position information. A transversal aspect is also that location tracking can lead to location prediction. This leads in turn to slow fading predictibility (and not just fast fading prediction, which can in principle be done also from past channel response estimates). Another aspect is that user selection (multi-user diversity) potentially leads to an explosion of CSIT requirements and associated overhead. Location based covariance CSIT might offer a (partial) solution. In this section, we shall focus on the Spatial Division Multiple Access (SDMA) problem, which in Information Theory is called the Broadcast Channel (BC). The SDMA terminology dates from the early nineties. These days it is referred to as the multi-user MISO (or MIMO) communications problem, and we shall particularly focus on the more difficult downlink. 4.2.2

SDMA considerations

Whereas single user (SU) MIMO communications represented a big breakthrough and are now integrated in a number of wireless communication standards, the next improvement is indeed multi-user MIMO (MU MIMO). This topic is nontrivial as e.g. illustrated by the fact that 3gpp had a lot of difficulty to get it included in the LTE standard. MU MIMO is a further evolution of SDMA, which was THE hot wireless topic in the early nineties. The MU MIMO area has now sufficiently evolved to allow us to understand the following key elements: • SDMA is a suboptimal approach to MU MIMO, with transmitter precoding limited to linear beamforming, whereas optimal MU MIMO requires Dirty Paper Coding (DPC). • Channel feedback has gained much more acceptance, leading to good CSIT, a crucial enabler for MU MIMO, whereas SDMA was either limited to TDD systems (channel CSIT through reciprocity) or Covariance CSIT. In the early nineties, the only feedback that existed was for slow power control.

31

• Since SDMA, the concepts of multiuser diversity and user selection have emerged and their impact on the MU MIMO sum rate is now well understood. Furthermore, it is now known that user scheduling allows much simpler precoding schemes (such as Zero-Forcing (ZF) beamforming (BF)) to be close to optimal. • Whereas SU MIMO allows to multiply transmission rate by the spatial multiplexing factor, when mobile terminals have multiple antennas, MU MIMO allows to reach this same gain with single antenna terminals. • Whereas in SU MIMO, various degrees of CSIT only lead to a variation in coding gain (the constant term in the sum rate), in MU MIMO however CSIT affects the spatial multiplexing factor (multiplying the log(SNR) term in the sum rate). In the process attempting to integrate MU-MIMO into the LTE-A standard, a number of LTE-A contributors had at some point become quite sceptical about the usefulness of the available MU-MIMO proposals. The issue is that they consider MU-MIMO in the same spirit as SU-MIMO, i.e. with FB of CSI limited to just a few bits! However, MU-MIMO requires very good CSIT! Some possible solutions are: • Increase CSI FB enormously (possibly using analog transmission); LTE-A went recently a bit in this direction. • Exploit channel reciprocity in TDD (there may be an electronics calibration issue though [27]). • Limit MU-MIMO (SDMA) to NADA (see below) users and extract essential CSIT from position information (or from DoA estimates - in both cases the knowledge of the antenna araay manifold is (eventually) required). 4.2.3

Narrow AoD Aperture (NADA) case

The idea here is to focus on the category of mobiles for which the angular spread seen from the BS is limited [28]. This is a small generalization of the LOS case. In the NADA case, the MIMO channel H (assumed frequency-flat here or we assume a narrowband case (e.g. an OFDM subcarrier)) is of the form h i X H= hr (θi )hTt (φi ) = B AT , A = ht (φ) h˙ t (φ) (23) i

where hr (.) is the receive side antenna array response, ht (.) is the transmit side antenna array response, θi is the Angle of Arrival (AoA) of path i and φi is the Angle of Departure (AoD) of path i. In the case of narrow AoD spread, we have φi = φ + ∆φi (24) where φ is the nominal (LOS) AoD and ∆φi is small. Hence ht (φi ) ≈ ht (φ) + ∆φi h˙ t (φ) .

(25)

This leads to the second equality in (23). Hence H is of rank 2 (regardless of the AoA spread). The LOS case is a limiting case in which the power of the h˙ t (φ) term becomes negligible and the channel rank becomes 1. The factor A in H depends straightforwardly on position (which translates into LOS AoD), only B remains random. In what follows, we shall focus on the LOS limit for considerations of location based processing. We propose that location based MU MIMO transmission involves position based user selection (attenuation, nominal AoD, AoD spread) and associated beamforming (BF) and power control (PC).

32

4.2.4

Location Based SDMA

Although some extension to the more general NADA case could probably be considered, we shall focus here on the LOS case. So a first restriction in the SDMA user selection process is that for MU-MISO purposes, users to be considered need to be in LOS mode. So in this case we get for the downlink channel to user k: h†k = γk ejψk hTt (φk ) (26) where ht (.) is the (unit norm) BS antenna array response, φk is the AoD for user k, which in the LOS case can be computed from the user’s position, γk > 0 is an attenuation factor, and ψk is a phase that is unimportant for transmitter considerations. There are a variety of ways in which the information of γk can be obtained: • User feedback of just the scalar γk . • Infer γk from the uplink. Not only in TDD but even in FDD, in the case of a LOS channel, the channel gain should be reciprocal (because there is no frequency-dependent superposition of multipath contributions). • Determine the attenuation from the position and simple (e.g. free space (LoS!)) propagation laws. One remark is in order here about antenna spacing. For the purpose of DoA estimation, and considering a uniform linear array (ULA) of antennas, it is generally considered that an antenna spacing of λ/2 (half a wavelength) is good. However, for the purpose of SDMA, in which we would like the antenna array responses between different angles to be easily orthogonal, it is preferable that the antenna spacing is larger. Indeed, the larger the antenna spacing, the larger the number of angles within a sector for which the array response is orthogonal to the array response at a given angle in the same sector. This multiplicity of ”orthogonal” angles on the other hand leads to ambiguities in the DoA estimation problem. In the case where the DoA is not estimated from received signal data but is computed on the basis of the position, these ambiguity problems are irrelevant and then antenna spacing should indeed be as large as possible (although not too large to invalidate the far field and narrowband assumptions). 4.2.5

Location Based MU-MIMO Downlink

In MU MISO, all ZF has to be done by the Tx. In MU MIMO however [29],[30], the ZF can be shared between Tx and Rx. All possible distributions of the ZF task between Tx and Rxs lead to many possible local optima of the sum rate at high SNR, hence providing potential for improved performance while complicating the task of Tx/Rx design. Assume now that in the multipath channel for any user, one of the paths is the LoS path which is known by the BS (location aided). The situation that arises now is similar to chip equalization in the 3G downlink: due to the synchronicity of the downlink, 3G systems use CDMA with orthogonal codes such that a simple correlator at the Rx would suffice to suppress all intracell interference. This ideal scenario is perturbed by the multipath propagation channel whose frequency-selectivity perturbs the orthogonality of the spreading codes. However, since in the downlink from the BS to a particular user all intracell signals pass through the same channel of that user, it suffices for the user to equalize that channel to restore the code orthogonality and to allow a correlator to suppress the interference. In SDMA, the temporal spreading of CDMA is replaced by spatial filtering at the BS. This spatial filtering is based on the hypothesis of a LoS channel. Hence, for the reception at the user through the LoS path, all interference will be supressed. But the interference arrives at the user through the multipath components (NADA components or other). However, regardless of the beamforming employed at the BS, all interference received by user k passes through the same multipath components of the channel of that user. Now, if the user has as many Rx antennas as number of (distinct) multipath components, the user can employ Rx spatial filtering to suppress all paths, except for the LoS path, so that the MIMO channel - Rx MISO cascade only contains the LoS path. Combined with the LoS based BF design, this allows to suppress all interference.

33

For the previous reasoning to work, it would have been sufficient (in terms of Degrees of Freedom (DoF)) that the BS knows any vector in the row space of the MIMO channel, but clearly the LoS path is typically much stronger than the other paths. Hence the knowledge of the LoS path leads to better performance at finite SNR. When there is no LoS path, it suffices to use another path, preferably the strongest path. Whereas the LoS path can be computed on the basis of only the user position (and a calibrated antenna array), in case another (and hence single- or multi-bounce) path needs to be used, this will typically require a database containing the information of the AoD of the strongest path, as a function of the position of the user. So far, we have taken into account that the location information leads to knowledge of the LoS component of each user’s MIMO channel. On the basis of the BS antenna array responses along the LoS of the users, we can design zero forcing (ZF) beamformers. However, such beamformers may exhibit quite suboptimal performance in the presence of multipath and/or at a finite SNR. Hence, the point of view taken in [31] is: how to design beamformers with partial CSIT which includes not only the LoS (location) direction information but also a minimal amount of information about that LoS path strength and the SNR, and the power of multipath components modeled as i.i.d. Rayleigh channel components. As the MIMO case is considered, the LoS antenna array response at the UE is modeled as i.i.d. random (and hence unknown). Optimized beamformer design is then proposed for this MIMO version of Ricean channels at finite SNR. Related work appears in [32],[33] where a not so rich propagation environment leads to subspaces (slow CSIT) for the channel vectors so that the fast CSIT can be reduced to the smaller dimension of the subspace. A further evolution would be to consider mixed CSIT [34], in which NADA users with location based CSIT get mixed with other users which have FB based CSIT. Another interesting recent development appears in [35] where blind ZF is proposed, interweaving PDP (or PDDP) polyphase components.

4.3

Multi-Cell Communications

Whereas single cell designs are applicable even in a multi-cell context, for users in the interior of the cell, intercell interference needs to be considered for the cell edge users. In the single antenna case: the multi-cell aspect requires Tx power coordination, which can fairly easily be done location-aided (locations translate into distances and attenuations; databases could be used for further statistical characteristics (e.g. slow fading)). Multi-antenna techniques: require downlink channel knowledge, in principle of all channels at all transmitters (cells). Several approaches are possible, in increasing complexity: • single-cell Tx, multi-cell Rx: the BS perform single-cell Tx; inter-cell interference gets handled by the MT Rx antennas. The CSIT requirements remain local, per cell. In the LOS case, the MT needs to have a number of antennas at least equal to the number of cells (BS signals) to be handled (ZF). In the NADA case, the required number of antennas gets doubled. • multi-cell coordinated beamforming: also called the MISO or MIMO Interference Channel (IFC) in the case of one MT per cell. In the MISO case, the BSs need to ZF towards the users in other cells. In the MIMO case, this ZF can be shared between Txs and Rxs (interference alignment (IA)). The case of multiple MTs per cell, with interfering cells, is called the Interfering Broadcast Channel (IBC), or sometimes also simply the multi-cell problem. The IFC/IBC models are applicable also when the interfering cells correspond to heterogeneous systems (e.g. macro-femto coexistence), as illustrated in Figure 14. • network MIMO: also called Coordinated Multi-Point Tx (CoMP): requires not only global CSIT at all Txs (BSs) but furthermore distribution of all Tx signals over the BSs. Whenever we mention ZF BF above, this refers to the high SNR case, and could be replaced by optimized BF at finite SNR. Also BF could be replaced by DPC or other more optimal Tx techniques.

34

Figure 14: IFC in macrocellular and HetNets (coexsitence of macro and femto/small cells). 4.3.1

MISO Interference Channel (IFC)

SINR Balancing and Beamforming for the MISO Interference Channel In this contribution we consider a K user multi-input single-output (MISO) interference channel (IFC), Figure 15, where the interference at each receiver is treated as additional Gaussian noise (Noisy IFC).

1 BS1

h11

g1

MU1

M1

hK1 …

… h1K 1

BSK

gK MK

hKK

MUK

Figure 15: MISO Interference Channel. We address in [36] the MISO downlink (DL) beamformer design and power allocation for maximizing the minimum SINR with per base station power constraints and imposing a minimum quality of service (QoS) requirement γi for each receiver (also called SINR priority). This problem, called max min weighted SINR (WSINR), can be mathematically expressed as:

s.t.

Rk max min SIN γk g1 ,...,gK k=1,...,K gkH gk ≤ Pk , ∀k = 1, . . . , K

(27)

We propose an iterative algorithm that solves the problem in a decentralized manner. The solution is based on the relation between the SINR balancing problem and the power minimization problem. We solve the max min W SIN R problem using a sequence of power minimization problems where the 35

QoS constraints in the beamforming problem are increased gradually until an infeasible point is found. Then, using a bisection method, the optimal solution is determined. In the MISO IFC with per user power constraints, a subset of users always transmits with full power according to the antenna and user distribution in the system. We introduce an iterative algorithm that solves the max min SINR problem for systems where only one user transmits with full power. In systems where the MISO IFC is separable, it can be shown that all users transmitting with full power maximizes the minimum SINR. Finally we show that is possible to characterize the entire Pareto boundary of the SINR (Rate) region for a general K-user MISO IFC solving a sequence of Weighted SINR (WSINR) problems, see [37] also. Rate Region 11 10 9

Rate 1 [bps/Hz]

8 7 6 5 4 γ1 = 100, γ2 = 100

3

γ1 = 80, γ2 = 160

2

γ1 = 800, γ2 = 20

1

γ1 = 400, γ2 = 80

0

0

1

2

3

4

5

6

7

8

9

Rate 2 [bps/Hz]

Figure 16: 2-User MISO IFC Rate Region. In Figure 16 we report the rate region of a 2-User MISO IFC, the colored line curves represent the directions given by the QoS constraints. The red dots are the optimal solutions of the corresponding max min WSINR problems and they fell on the Pareto boundary of the rate region. This setting is relevant to describe several problems in cellular communication systems. For example in the case of a network of femtocell base stations (BS) where each femtocell BS is serving a single user in the time-frequency unit of interest. Each user has its proper QoS requirement that should be satisfied, fairness then leads to a max min WSINR problem. 4.3.2

MIMO IFC

Weighted Sum Rate Maximization in the Noisy MIMO Interference Channel We consider the Noisy MIMO Interference Channel (IFC) with linear transmitters and receivers and full CSI reported in Figure 17. From the perspective of a network operator, the maximization of the total throughput represents probably the most important objective. In heterogeneous networks, there are users with different priorities which could be a function of their subscription. In such networks, the throughput maximization translates into a weighted sum rate (WSR) maximization. Hence it is very natural and equally insightful to use this cost function in the optimization procedure for the design of transmit and receive strategies. Here we propose an iterative algorithm to maximize the WSR for a multi-stream MIMO IFC. The main problem with the maximization of the WSR is the severe non convexity of the cost function. This implies that even if it is possible to prove convergence of the proposed algorithms to a local optimal point, convergence to a global optimum can not been shown. In addition, convergence to only a local optimum 36

1

...

G1

H11 H21 M1

d1 1

1

F1

N1

HK1

d1

1

1

...

1

...

...

1

1

H22 M2

N2

d2

...

HK2

...

d2

F2

...

...

G2

...

...

H12

H1K

dK

1

...

GK

H2K

1

HKK NK

MK

FK

...

1

...

...

1

dK

Figure 17: K-User MIMO IFC. is not a rare event if the initialization of the algorithm is not carefully chosen. To avoid convergence to a local optimum Deterministic Annealing (DA) has been proposed in this work. The WSR maximization problem can be mathematically expressed as follows. X {G?k , F?k } = arg min −uk Rk s.t. Tr(GH k Gk ) = Pk ∀k {Gk , Fk }

k

with uk ≥ 0 denoting the weight assigned to the k-th user’s rate Rk and Pk it’s transmit power constraint. Gk and Fk represent, respectively, the transmit and receive filter matrix at BS and UE number k. This problem is non convex and hence finding a solution is a complex task. Our approach [38] to design WSR maximizing transmit filters for the MIMO IFC is based on introducing an augmented cost function in which two additional optimization variables are introduced. The new cost function is based on the well known relationship between rate and minimum mean squared error (MMSE). This new cost function is concave or even quadratic in one set of variables, keeping the other two fixed. Hence we shall optimize it using alternating maximization. To handle the non-convexity of the cost function we propose to introduce Deterministic Annealing (DA) [38]. The principle behind this approach is that the optimum of a problem at the next value of the temperature (in our case inverse SNR) is in the region of attraction of the solution of the problem at the previous temperature. In DA, an increase of the temperature parameter allows to convexify the problem: the temperature parameter transforms (deterministically) the originally non-convex cost function into a convex cost function (convex should be replaced by concave in the case of maximization). Here we further study the concept of DA applied to WSR maximization in a general K-User MIMO interference channel where a general distribution of the number of streams is assumed. We propose an iterative algorithm that maximizes WSR succeeding to avoid to be trapped in local optima using DA. DA is an extension of homotopy methods, augmented with phase transitions, representing the appearance of a new stream. At low SNR (high temperature), all user power gets focused on only one stream, and since noise dominates interference, the optimal Tx and Rx filters are simple matched filters (maximal singular vectors) for the through channels. In addition the Interference Alignment (IA) feasibility problem has been studied in the DA context (IA corresponds to joint Tx/Rx ZF). In particular we propose a new analysis that is based on the principle 37

that IA feasibility is unchanged when the MIMO crosslink channel matrices have a reduced rank equal to the maximum of the number of streams passing through them in forward and dual IFC. Then increasing constantly the rank of the channels the number of IA solutions will not decrease. At high SNR, the optimum WSR design becomes ZF (IA), with typically many possible solutions due to the nonlinearity of the ZF conditions. Nevertheless, we may remark, as in [38],[39], that the ZF problem simplifies enormously in the LOS case. Indeed, let fi,n be the Rx spatial filter for stream n of user i and gk,m the Tx filter for stream m of BS k, and Hi,k the MIMO channel from BS k to MT i, then the ZF (IA) requirement for this particular cross link is fi,n Hi,k gk,m = 0. These ZF condistions need to be considered jointly for all cross links and hence they are coupled through the Tx and Rx filters. Stating the solutions for the filters analytically is impossible in general. However, consider the case in which all H MIMO channels would be in LoS and hence of rank one: Hi,k = ui,k vi,k . Then the ZF condition just considered becomes H H fi,n ui,k vi,k gk,m = 0 iff fi,n ui,k = 0 or vi,k gk,m = 0 . (28) Hence, apart from elucidating the distribution of the ZF roles over Txs and Rxs (the idea is that a stream transmitted from TX k and causes interference to the non intended RX j needs to be suppressed at either the Tx or at the Rx), the design of the Tx and Rx filters becomes decoupled, and their design only requires knowledge of the channels connected to them (in general the design of a Tx or Rx filter in the MIMO IFC problem requires the knowledge of all channels appearing in the IFC). Furthermore, the factors ui,k depend only on the antenna array of BS k and the location of MT i. Hence the design of the Tx filters can be carried out on the basis of the location information of the various MTs. To go beyond LoS, the NADA and mixed CSIT cases could be considered. Another issue is the strength of the interfering links. In a ZF/IA approach, all link strengths are considered of equal order of magnitude, but in reality not all interfering links equally important. In [40], the concept of generalized degrees of freedom (gdof) is introduced. The dof are the prelog of user rates at high SNR. In a MIMO IFC, the dof of a link correspond to the number of streams for which ZF/IA is feasible. Those dof become gdof when one models the Interference to Noise Ratios (INRs) as evolving with the SNR to a certain power, e.g. smaller than one for the case of weak interference. Whereas such analysis may lead to qualitative insights into the relative effect of certain interference terms, the gdof results are quantitatively of limited use since in practice one needs to work at a finite SNR, at which one cannot unambiguously define α and β in a relation of the form INR = β SNRα . The problem is due to only considering exponents in asymptotic analysis. Analysis needs to evolve from ”GDoF” or ”tier 1 interferers only” (a model introduced in [41] in which interferers beyond tier one are ignored for dof analysis) to location (distance & propagation) dependent interference strengths. Recent work on ”Topological Interference Alignment” goes in this direction, and can clearly benefit from location based attenuation information. The Noisy MIMO Interference Channel with Distributed CSI Acquisition and Filter Computation In order to appreciate the potential gain brought about by location aided approaches, it is important to understand how CSIT can get acquired without location information. We study in [42], [43],[44] the frequency-flat noisy MIMO interference channel (IFC), in Figure 17, with initial assumption of no channel state information (CSI) neither at the base stations (BS) nor at the user equipments (UE). In the noisy IFC, interference is treated as noise and hence linear transmit (Tx) and receive (Rx) filtering is considered. In their seminal work, Cadambe and Jafar have shown that the conventional approach of orthogonalizing the signal dimensions can be overcome by the use of a new signaling technique called Interference Alignment (IA). The main idea of IA is based on the assumption that each transmitter has perfect and global channel state information (CSI). This assumption is unrealizable in practical time varying channels. In [42], [43],[44] we propose a transmission strategy through which the BS and the UE get the necessary CSI for CSI based transmit and receive processing by channel training and analog channel feedback, corresponding to transmission overhead. The main message there is that when all this coordination is done over the air, its overhead is proportional to K 2 , where K is the number of interfering links.

38

4.3.3

MIMO IFC with Decoupled Tx/Rx and Location Aided Design

In [45] we study interference alignment (IA) (the number of spatial signal streams for which the interference can be zero forced (ZF’d)) first for the case of rank reduced MIMO channels in which the channel matrices can be written with reduced dimension factors of the form Hik = Bik Aik

(29)

and then for the case in which we require the design of Tx and Rx filters to be decoupled. Indeed, the big problem of MIMO IFC is that the design of the Tx filter at any BS depends on all the UE Rx filters and vice versa. As a result, for the design of its Tx filter, any BS needs to know the channels from all BSs to all UEs (global CSIT). A decoupled design would in a first instance only require local CSIT (knowledge of the channels from that BS only). LoS Case In what follows, we shall focus on the LoS limit for considerations of location based processing. Consider an IFC (multi-cell) with K cells in which all BS have M antennas and all UE have N antennas. The LoS case is an ultimate reduced rank case and leads to the requirement M +N ≥K +1

(30)

for IA feasibility with a single stream per user. In the MISO or SIMO cases this becomes M ≥ K or N ≥ K. The meaning of (30) is: (M − 1) + (N − 1) ≥ K − 1: that each BS performs ZF towards M − 1 UEs. As a result, each UE still receives interference from (K − 1) − (M − 1) cross links but with its N antennas it can ZF N − 1 streams. In the decoupled approach, the design of any Tx only depends on the Tx side channel factors Aik in (29) of the channels connected to it and in general even only on a subset of this local CSIT (e.g. in the LoS case, only M − 1 cross link Aik are required to be known for any given BS). In the LoS case, the factors (vectors) Aik are clearly only a function of the positions of the BS and UEs (and the BS antenna array response). One can go somewhat beyond the LoS case by considering (LoS) NADA and other multipath components. The number of components (and hence the rank) to be considered could vary with the cross links. An issue that arises here is that different cross links may have multipath components with the same AoD from a certain BS, because the paths may bounce on the same scatterer. In this case the multiple paths get ZF’d simultaneously, leading to a reduction in required Tx antennas.

4.4

Location aware CoMP transmission synchronization

Particularly at cell edge areas of a mobile communications system, signals are received from different base stations (BSs) with similar power levels. This causes interference even for synchronization since sync signals transmitted at different BSs are usually not perfectly orthogonal and received with different propagation delays. Knowledge about the mobile terminal (MT) position allows us to relate sync signals received from different BSs to each other regarding their propagation delays. With this relation formerly interfering signal energy from adjacent BSs can be exploited for synchronization as well. The implementation of this synchronization scheme requires a coordinated (synchronized) transmission of downlink frames from the BSs in a cellular communication system. This requirement is mandatory for Coordinated Multipoint (CoMP) transmission concepts [47]. 4.4.1

Relation to further publications

The investigations presented in this section continue the work which has been described in the WHERE2 Deliverable D3.1 [3]. In this deliverable we have investigated location aware synchronization for a onedimensional environment, where the MT was located at the cell edge, i.e., in the middle between the two BSs. The synchronization performance metric has been the standard deviation of the signal propagation 39

estimates. For 3GPP-LTE secondary synchronization signals we have obtained a gain in synchronization performance of up to 35% compared to a single link (single BS) scenario. This gain can be achieved if information about the MT position is sufficiently accurate. Both theoretical evaluations using the Cram´erRao lower bound and numerical results where we have used maximum-likelihood multilink synchronization have shown excellent match. Subsequently, we summarize the continuation of the work mentioned above. This continuation comprises the extension to a 2-dimensional environment and the inclusion of large scale (flat) fading according to [48]. These investigations are described in detail in [46], which is included in the appendix of this document. 4.4.2

Environment

We consider 3 BSs (BSp , p = 1, . . . , 3) with an inter site distance of 1 km as shown in Figure 18. These BSs synchronously transmit LTE secondary synchronization signals (SSSs) [49] with different IDs, denoted as Sp [`] in frequency domain. At the MT, which is located at the cell edge central to the 3 BSs, we receive R[`] =

3 X p=1

|

αp Sp [`] e−2π ` fSC τp +N [`] {z

(31)

}

˜ =S[`]

n o 2 in frequency domain, where N [`] is additive white Gaussian noise with zero mean and variance E |N [`]| = σ 2 . The propagation delays τp depend on the distances between the MT and BSs. In LTE the subcarrier spacing is fSC = 15 kHz [49]. The flat fading coefficients αp contain path loss and shadow fading according to the WINNER C2 typical urban macro cell channel model [48].

BS2 (x2, y2) s2 t BS1 (x1, y1)

st)

s1

st)

st)

s3

t

MT (x, y)

rMT



t

t

BS3 (x3, y3)



Figure 18: The principle of exploiting position information in CoMP transmission: With knowledge about the position of the MT, propagation delays of signal components coming from different BS can be related to each other.

40

4.4.3

Performance evaluation

We calculate the Cram´er-Rao lower bound (CRLB) for the variance of unbiased estimates about the signal propagation delays τ1 , . . . , τ3 . For that we need the Fisher information matrix (FIM) F = Fsig + Fpos ,

(32)

which is composed of Fisher information Fsig obtained from the received signal and an additional Fpos part coming from knowledge about the MT position. The components of the FIM based on the signal model in Eq. (31) are [50]  N   N  +2 +2 2 2 ∗ X X ˜ ˜ 2 ∂ S [`] ∂ S[`]  8π fSC = Re  (33) [Fsig ]p,q = 2 Re  `2 Sp∗ [`] Sq [`] e2π ` fSC (τp −τq )  , 2 σ ∂τ ∂τ σ p q N N `=−

`=−

2

2

p, q = 1, . . . , 3. For the calculation of Fisher information Fpos about signal propagation delays τp from MT position estimation, we assume that there is an estimate [ˆ x, yˆ] = [x, y] + [x , y ] about the MT position. The model for this estimate is the true MT position plus an additive Gaussian error with zero mean and  2 variance E 2x = E 2y = σpos/2. As the positioning accuracy increases, i.e., σpos gets lower, the Fisher information Fpos increases and, and consequently, the signal propagation delay estimation performance increases. Details about the calculation of Fpos can be found in [46]. In particular we are interested in the estimation performance of τ1 , corresponding to the serving BS. The CRLB for this parameter is obtained from the first diagonal element of the CRLM matrix h i   −1 [CRLB]1,1 = F−1 1,1 = (Fsig + Fpos ) (34) 1,1

The flat fading coefficients αp in the signal model (31) and consequently the CRLB are random. For this reason we draw the cumulative distribution function (CDF) for the CRLBqabout τ1 . Figure 19(a) shows the CDF for the square root of the CRLB, i.e., the standard deviation [CRLB]1,1 , in meters. From these CDFs use the 90th percentiles as performance metrics. The CRLB is lower or equal to these value with probability 0.9. Figure 19(b) shows the square root of these 90th percentiles vs. the BS transmission power PTX . We consider the estimation performance without exploiting position information (dashed graph) as reference. Compared to the ideal case where no interference is present from BS2 and BS3 we obtain a degradation in terms of TX power of about 0.4 dB. With knowledge about the MT position we can relate the different propagation delays to each other. As a result the Fisher information about the propagation delays τp increases and the CRLB improves as the positioning error σpos decreases. The results show that up to 8 dB in TX power can be gained with accurate knowledge (σpos → 0) about the position of the MT. 4.4.4

System Integration

The intention of location aided CoMP synchronization is to improve synchronization performance in particular at cell edges, where signals from adjacent base stations are received with similar power levels. Synchronization performance improvement can be expressed in terms of: • minimum mean square error (MSE) of the synchronization error and/or • reduction of the required transmission power for pilot/synchronization symbols. For CoMP synchronization we require: • synchronized transmission at base stations (or at least information about their asynchrony) and • knowledge about the positions of: – the received base stations, which are usually known, and 41

3

10

0.9

Sync. Error (90% StdDev) [ns]

Prob(CRLB < Synchronization Error)

1

0.8

0.6 σpos → ∞ σpos = 100m σpos = 30m σpos = 10m σpos = 3m σpos → 0 Single BS

0.4

0.2

0 0

10

20 30 40 50 Synchronization Error [ns]

60

no pos. info σpos = 100m σpos = 30m σpos = 10m σpos = 3m σpos → 0 no interf.

0.4 dB loss due to interference

2

10

8 dB gain is achievable

1

10 10

70

15

20 25 30 Transmit Power PTX [dBm]

(a)

35

40

(b)

Figure 19: Performance results a) CDFs for the CRLB (standard deviation) for the estimation performance of signal propagation delay τ1 with different MT position accuracies. The BS transmission power is 30 dBm; b) The CRLB (standard deviation) for the estimation performance of signal propagation delay τ1 vs. the BS transmission power for different MT position accuracies. – the mobile terminal, e.g., coming from a GPS device inside the MT. The implementation affects the physical (PHY) layer of a MT as shown in Figure 20. Here, the symbol/frame synchronization block has to be modified in order to process (synchronization) signals received from different BSs. This could be implemented as a bank of correlators using the different synchronization sequences from adjacent BSs. The correlator results must be related in time according to the expected times of arrival (TOAs) of sync signals received from the different BSs. These expected TOAs are a-priori information for the symbol/frame synchronization block and have to be calculated from position information of the considered BSs and the MT in an additional signal processing block. The positions of the BSs are usually known and can be provided by protocols of higher layers of the communication system. The Location Aware CoMP Synchronization MT position can be obtained from a positioning device inside the MT such as GPS.

General Physical Layer Interface to higher Layer and Modules Positions of Base Stations (e.g. from Application Layer)

Modify this block for processing a-priori information about timing!

Symbol and Frame Sync

a-priori Info

Position of this Mobile Device (e.g. from GPS Module)

Frame and Symbol Timing Downconversion

Deframing, CP removal

Time Domain Signal Samples

Insert this block for providing a-priori info about timing!

Calculation of a-priori Information about Timing

Data Symbols FFT

Time Domain OFDM Symbols

Data/Pilot Demux

Soft Codebits

Demodulation

Pilot Symbols

Data Bits

Decoding

Channel Coefficients

Channel Estimation

Standard PHY Layer

Slide 2 > Location Aware CoMP Synchronization > A. Dammann, R. Raulefs

Figure 20: Principle implementation of location aware CoMP synchronization in a MT receiver.

42

We have investigated the benefit of position information for synchronization in a multi cellular signal propagation environment using the secondary synchronization signals of 3GPP-LTE. We have derived and evaluated the Cram´er-Rao lower bounds for synchronization (timing estimation) taking into account information about signal propagation delays coming from an estimation of the mobile terminal’s position. The evaluations have shown that a synchronization gain from position information can be obtained, if the position estimation accuracy is in the same order of magnitude compared to the synchronization performance expressed in meters. For the considered scenario, up to 8 dB in transmit power can be gained by exploiting position information at the cell border compared to the performance of optimum joint estimation without position information.

43

5

Femtocell Based Communications

In current mobile cellular networks, like 3GPP Long Term Evolution (LTE) networks, heterogeneous deployments mixing macro base stations (MBS) or eNodeBs (eNBs) and home base stations, Home eNBs (HeNBs) or femto base stations (FBS) covering femtocells are foreseen as an effective way to ensure both mobility within a large geographical area and high data throughput at home, indoors [51][52]. The use of femtocells, also known as small cells, does not only benefit operators and service providers, but also the customers as end users of this technology. Their deployment has already been adopted by operators from different countries, using various technologies, and is growing exponentially. The number of FBSs is estimated to reach near 50 millions by 2015 [53]. However, despite the FBS or HeNB low power, their transmissions create interference on MBS/eNB and other FBS/HeNB transmissions. In order to apply centralised interference cancellation techniques, the time synchronisation of transmissions from neighbouring FBSs/HeNBs is beneficial, as already introduced previously in deliverable D3.1 [3]. Both Sections 5.1 and 5.2 address inter-cell interference coordination. In section 5.1, downlink femto-macro interference is controlled through long-term femto power setting using the available location information, as also introduced in D3.1 and published in [54]. In section 5.2, HeNBeNB and HeNB-HeNB interferences are mitigated in a more centralised manner, as in a Self-Organised Network (SON), by appropriate HeNB configuration using HeNBs and eNBs location information but also their sensing capabilities, being the system able to configure each new small cell’s HeNB in order to obtain the best results from its deployment.

5.1

Downlink femto-macro ICIC with location-based long-term power setting

In current mobile cellular networks, like 3GPP Long Term Evolution (LTE) networks, heterogeneous deployments mixing macro base stations (MBS) and home base stations or femto base stations (FBS) are foreseen as an effective way to ensure both mobility within a large geographical area and high data throughput at home [51] [52]. As in homogeneous macro deployments, fairness between cell-center and cell-edge users [55] must be sought and inter-cell interference coordination (ICIC) [55] [56] appears as a proper way to mitigate the interference impact. In heterogeneous co-channel deployments, FBSs may strongly interfere with MBSs and even create coverage holes in downlink (DL). In order to secure the operator MBS traffic, priority should be put on minimizing the interference created by FBSs on MBSs. However, the FBS throughput inside home should remain reasonably high. Furthermore, due to the high number of FBSs under the MBS coverage, macro-femto ICIC minimizing the MBS-FBS exchanges is desirable. As depicted in Figure 21, for the No ICIC case, the area where macro mobile terminals (MTs) are strongly interfered by the FBS varies, depending of the FBS position relative to MBSs.

Step1: FBS position transmitted to the server

Server

Step2: Information about power measurements of MMTs in HIRZ transmitted to FBS No ICIC

HIRZ Impact of the FBS on the MMTs is set constant

FBS MBS

Step3: FBS transmit power computed

FBS ICIC

Figure 21: ICIC providing macro-degradation equalization (single cell, no shadowing). 44

5.1.1

Location-based long-term power setting

A non-location-based DL macro-femto ICIC approach consists of the independent long-term transmit power setting of the FBS [57] [58] according to its knowledge of the additive white Gaussian noise (AWGN) level and the received power from neighbouring MBSs. Received powers are obtained through measurements performed by the FBS on MBS DL signals. Nevertheless, mobile cellular networks also propose positioning services [59]. Positioning is also implemented in most MTs through Global Navigation Satellite System (GNSS). The MT and FBS location information, together with an appropriate database (DB), can benefit to the ICIC power setting, by providing precise information on received powers at MMTs surrounding a given FBS. Thus, this location-based approach provides more information on actual powers received at MMTs and avoids wall penetration loss error effects on these variables. For situations where the indoor and outdoor received powers from MBS are very different, a better macro-femto performance trade-off can be achieved by the power setting thanks to the additional information provided by the database. From an operator point-of-view, it is desirable that the impact of a FBS on surrounding MMTs is independent of its location in the MBS coverage. The proposed power setting achieves this property, which we call macro-degradation equalization. For the sake of macro-degradation equalization, we introduce a high interference reference zone (HIRZ), as depicted in Figure 21 and denoted ZMMT , which is a given area in which the level of MMT performance degradation is controlled. When the same HIRZ and the same MMT performance degradation definition and level are considered for all FBSs, all FBSs are expected to have the same impact on the MMTs and macro-degradation equalization is achieved. As the path gain properties are not the same for all positions in ZMMT , the FBS transmit power is set such that, in ZMMT , the probability that the macro performance degradation is lower than or equal to a given threshold, equals a given probability. The FBS transmit power depends on statistics on PM , the MMT useful power received from the serving MBS, and I the interference power from neighbouring MBSs. The statistical model for PM and I powers received from MBSs at MMTs in ZMMT is based on the FBS position information and the use of a geo-referenced database. The geo-referenced DB is constructed thanks to MMTs reporting to their serving MBS, containing received powers from neighboring MBSs and FBSs, and MMTs locations. Note that the received powers are also helpful for determining an MMT location as proposed for instance in Appendix 22 of WHERE2 deliverable D2.4 [60]. Upon installation or reinitialization, a FBS obtains its location information and transmits it to the server maintaining the DB. Thanks to this information, the server can transfer appropriate information about MMTs located in ZMMT to the FBS. This information allows accurate power setting at FBS. Details on the power setting can be found in [54]. In this DB approach, depicted in Figure 21, the transferred information suffers from different types of errors: FBS position error, MMT position errors, MMT power measurement errors and quantization errors. 5.1.2

Simulation results

In order to evaluate the gain brought by the proposed power setting and the impact of above-mentioned errors, we simulate a 2x2 10 MHz LTE system using a multi-cell system-level simulator. We compare three approaches: the constant FBS transmit power, the non-location-based FBS power setting based on FBS power measurement and the proposed location-based FBS power setting (denoted by NoICIC, ICIC Pow. and ICIC Loc., respectively). We assume a zero-mean iid Gaussian error model for positioning and for received power measurements. Without any power measurement and positioning errors and with a high database density, the distribution of PM and I estimated from the database exactly matches the long-term reality. For the non-location-based power setting, FBS received power measurements suffer from a iid Gaussian error, with a RMSE different from MMT measurements in order to take into account the positive impact of time averaging and the negative impact of shadowing decorrelation between indoor and outdoor. We evaluate the global FMT-MMT performance trade-off, i.e., the 5%-ile FMT spectral efficiency over all FBSs as a function of the 5%-ile MMT spectral efficiency over all outdoor MMTs. We consider typical measurement errors, namely 10 m RMSE for the location-based approach and 5 dB (resp. 3 dB) RMSE on FBS (resp. MMT) power measurement. Three FBS densities are considered: 25, 125 and 250 FBSs per km2 , i.e., 22, 109 and 217 FBSs per MBS sector, respectively. Figure 22 shows that the 45

Figure 22: Global FMT-MMT performance trade-off in term of cell-edge spectral efficiency. Blue: 25 FBS/km2 , red: 125 FBS/km2 , green: 250 FBS/km2 . proposed location-based power setting exhibits a better FMT-MMT performance trade-off than the two other approaches, the relative gain increasing with the FBS density. Let us consider the sensitivity to positioning errors. Figure 23 shows, for the three approaches and medium FBS density, the FMT cell-edge spectral efficiency for a 10 % degradation of MMT cell-edge spectral efficiency (i.e., a 0.42 b/s/Hz spectral efficiency) as a function of positioning RMSE. With typical FBS power measurement RMSE of at least 3 dB, the proposed location-based approach outperforms the non-location-based approach for positioning RMSE lower than 30 m. For a 20 m RMSE, the FMT celledge spectral efficiency is increased by more than 50 % (resp. 10 %) over the non-location-based approach with a 5 dB (resp. 3 dB) RMSE on FBS power measurement. Compared to the constant transmit power approach, it is increased whatever the positioning accuracy (RMSE lower than 100 m) by up to 400 %. Considering now the sensitivity to wall penetration loss error and assuming typical 10 m, 3 dB and 5 dB RMSE for positioning, MMT power measurements and FBS power measurements, respectively, and medium FBS density, Figure 24 confirms the lower sensitivity of the proposed location-based approach compared to the non-location-based approach explained in [54].

Figure 23: Localization error effects: Femto performance for 10 % cellular cell-edge decrease with 125 FBS/km2 46

Figure 24: Penetration loss error effects: Femto performance for 10 % cellular cell-edge decrease with 125 FBS/km2

For 3 dB wall penetration loss RMSE, the non-location-based approach does not outperform the constant FBS transmit power approach whereas the proposed location-based approach still exhibits a 300% gain over the constant FBS transmit power approach. With 7 dB wall penetration loss RMSE, the location-based approach still outperforms the two other approaches. Long-term power setting for femto-macro ICIC can take benefit from positioning. The concept of HIRZ for controlling the macro degradation due to FBS transmission is used, resulting in an equalization of the macro-degradation among FBSs. The positioning information is used in conjunction with a database available in the core network, providing relevant information to each FBS on powers measured by MMTs in its vicinity. This information guarantees efficient power setting. In the simulated 3GPP-LTE context, the proposed power setting relying on positioning and database improves the global FMT-MMT performance trade-off compared to constant FBS transmit power and the non-location-based power setting and proves robustness against relatively high positioning error. Compared to non-location-based power setting, higher robustness against wall penetration loss error is also observed.

5.2

Location-aided HeNB self-organized network system

A growing number of users and services challenge everyday the operators’ network, increasing the demands to their infrastructures, which traditional architectures are not able to cope with. Existing mobile networks, composed by normal BSs deployed in fixed sites, are unable to respond to users’ demands, mainly limited by two factors: mobility and indoor coverage. The amount of resources to overcome these two problems, using traditional means (fixed outdoors BSs) would be enormous, leaving to the operators, not only a high operational cost, but also a highly inefficient network. Users’ mobility creates load peaks in the network at some point(s) in time, but outside of those temporal windows, the network use is substantially lower, and plausible of being overcome with traditional solutions. Furthermore, when using BSs to provide indoors coverage, the amount of power, wasted in the air, to reach the buildings’ indoors environment, is a problem that also requires other options otherwise it may origin serious inter-cell interference (ICI) issues, and once again the operator is dissipating energy in the air without taking advantages from it. 5.2.1

Proposed solution

A solution for this problem could be in the use of smaller cells, with reduced transmitting power, and a high level of deployment freedom, which can be easily installed by a user (without requiring specialised technicians), requiring nothing more than an high speed internet connection, and an electrical supply source. Such concept is based on the use of HeNBs, which have the same basic working principles as a common Wi-Fi access point. These devices connect the UEs to the network’s core, i.e. they are the interface between the radio transceiver of the UE and the operator’s core network. Their reduced power and reduced capacity are sufficient to accommodate several users with active communications and keep several others in idle mode. This solution can be scalable to meet the capacity and/or coverage requirements, by integrating as many cells as need to overcome the users’ demands. There are two main application scenarios for the use of HeNBs based on the networks needs, as: • Access primary cells – used to provide coverage where there is no other access to the network, like in remote locations; • Auxiliary access cells – to enhance capacity and overcome overloads in the primary operators’ cell entities, such as in (crowd) events. Although, such devices have restrictions in terms of transmitting power capabilities, it is important to prevent ICI problems. Once a device is freely allowed to be placed and moved it may origin interference problems when closely placed to other entities operating in the same spectrum area (either other HeNBs, or eNBs). These interference problems reduce the QoS of the network, and instead of enhancing the radio coverage area where one can access the network, they will reduce that same area in the close-by surroundings. 47

5.2.2

System description

Different HeNBs operating at different carriers would be the ideal solution to avoid ICI problems. While operating at different frequencies, the interaction between devices is minimised and preventing the generation of interference. Unfortunately, due to a highly crowded spectrum, operators face serious restrictions in terms of available bandwidth, which in fact highly limits the number of available carriers, making it an impractical and unfeasible solution. A solution (see Appendix A.8) to solve these inter-cellular interference problems involves the creation of a system able to endow the network with self-organising capabilities, which allow a careful planning of the HeNBs parameters, even though they are unpredictably deployed. Once attached to a high speed internet connection, the HeNB reports back its location to the network, which is used by the operator to get the information about other cells and its parameters. Such information is stored and available in the network, thus there is a structural knowledge about how the close-by network is arranged. Combining that information using a radio network planning (RNP) tool, allows to evaluate and ascertain the best parameters (carrier and maximum transmitting power) to be configured on the new device. The system, developed by this research work, simulates a real scenario estimating the best configuration parameters to be configured on the new HeNB, and is able to monitor the final result and interaction of the new cell with the rest of the network through the monitoring capabilities of the cells. By using other cells as network probes to assess the results practical effect in the network, the system is able to detect any problems on the process and if necessary re-initiate it. In some scenarios it may occur that a new HeNB, would not present any enhancements to the network both in terms of coverage or capacity, in which cases the system will not configure the new HeNB, and it could/should be disconnected from the mains power. An evaluation of the system was done taking into account that there is no carrier sharing between eNBs and HeNBs, this means that each type of cell has their own group of carriers. However, the system was projected to work with carrier sharing between cells. Another subject addressed was the quantity of carriers assigned to the HeNBs, and how that influences the overall network area coverage, as well as the ICI problems between cells. The recreation of the scenario is based on the availability of accurate location information, since the entire scenario analysis is based on the nearby network infrastructure, it is important to assure that there are accurate positioning systems available, both in indoor and outdoor environments to locate accurately the cells. An error in the location estimation of the HeNB may lead to a incorrect identification of the close-by cells and consequently to an incorrect identification of the optimal configuration parameters to be set on the new cell, destroying all the ICIC process. 5.2.3

Simulation results

A test simulation environment (detailed in Appendix A.8) was recreated to evaluate the SON system performance regarding the effects on the network coverage and interference issues. The simulation scenario is composed by 19 tri-sectorised eNBs placed on an hexagonal configuration and 60 HeNBs randomly placed. Figure 25 shows a detailed view of the centre area of the simulation scenario for a use case where the HeNBs have the minimal amount of carriers (two), for which the frequency control is called. The dark blue tones represent the coverage area of the eNBs in that area, and the other colours represent a HeNB. Figure 26 shows the gain of the SON system for two use case scenarios: two and five carriers. These use cases represent, respectively, the minimal operation number of carriers and the optimal operation number, considering the carriers occupation vs the available bandwidth. The gain on the coverage area is around 15% for a 2 carrier scenario and slightly lower for the same scenario, but using 5 carriers. Such difference is expected as the probability of having two carriers assigned to different HeNBs is lower once the number carriers increases and the number of HeNBs is the same.

48

Figure 25: Network coverage (left). SON system enhancement (right).

Figure 26: Cell Coverage Area Improvement Intra-cellular interference problems within a HeNB cellular network are a direct consequence of the increasing use of this kind of cells to enhance the operator’s traditional network, either in terms of coverage or capacity. As shown a limited number of carriers, which highly limits the configuration parameters of those cells, results on serious interference problems, reducing the cells coverage area and user’s QoS. A possible and promising solution for the problem is the use of Self-Organised Networks, which the system developed falls under. Using the location information, the system is able to configure each new cell to obtain the best results from its deployment. The gain in coverage of the system is clearly visible from the results presented, showing an increase on the cells coverage area, for a conservative scenario as the one presented. For denser networks the benefit on the results are expected to be greater, since the intercellular interference problems increase, consequence of an increase on the probability of close-by cells be assigned to the same carrier. The consequences of the increase on the coverage area of the HeNBs has also an important role on the operator’s network by allowing to balance the load between both networks. As a result an increment on the QoS is expected for both networks. Some users are unloaded from the eNBs to this new network, freeing some bandwidth on the first. Regarding the HeNBs, since the interference problems are lower, the SNIR is higher allowing the use of more efficient modulations and higher codification indexes. 49

6

Conclusion

This deliverable presents the most significant results achieved in the WHERE2 project, concerning our research on coordination and cooperation between network nodes, in the form of several approaches, in the scope of geolocation aided cooperation for future wireless networks, targeting to achieve enhanced communications performance. All the investigation work carried out in the project and the subsequent proposed WHERE2 techniques, in the present scope, take advantage of location information related to cellular system elements, namely eNBs, RNs, HeNBs, UEs, etc., which is considered to be available on demand or through internal up-todate database, allowing significant communications enhancement, as pointed out in the previous chapters. The effective performance of the proposed techniques and algorithms is therefore dependent on the availability and quality of information, and on its appropriate exchange, regarding not only location info but also other information, such as UEs’ received power measurements, which can be stored on a database, and accessed, in the system core network. Other factors in the scope of the proposed approaches, which have an impact in their respective performance are, for instance, the effective communication between the eNBs and HeNBs, and also with the database server hosting UEs’ measurements, or the adequately synchronized transmission at eNBs (or at least the availability of appropriate information about their asynchrony) when multi-cell communications are concerned, or also the full or merely statistical channel knowledge, e.g. for optimal rate selection. The research work performed in WHERE2 in the present scope is condensed in this deliverable in nine distinct approaches to address the main objectives specified in task T3.1. Some final considerations regarding each of these pieces of work can be summarized as follows. In the Adaptive Location-Aided Cooperative Relaying proposed schemes, location information is employed to reduce signalling overhead and/or further improve the spectrum efficiency in networks with multiple relays. The proposed scheme can reduce signalling overhead by 97% with the spectral efficiency comparable to the conventional best-relay selection scheme. Also, at the typical SNR of 10 dB, the schemes proposed for non-reciprocal channels can reduce signalling overhead by around 90.7% with a drawback of 2.46% decrease in spectrum efficiency. For the same setup in terms of SNR, the schemes proposed for reciprocal channels can reduce around 97.2% in signalling overhead with a decrease of 1.5% gain in spectral efficiency. Users’ geolocation info is used in Location-Aided Relay Node Planning for the optimization of relay nodes location, in their deployment or activation, so as to minimize the required bandwidth and provide full coverage in the target cell area at the same time. When employing the proposed location-aided algorithm, considering the specific setup, 7 relay nodes’ locations out of 19 candidate places are identified, reflecting the users/required-traffic geo-distribution. Compared to eNB-direct transmission, using the selected 7 relays it is possible to achieve roughly 56% of bandwidth saving covering that same area. In Location-Aided MAC Layer Flexible Round-Robin Scheduling, inter-cell interference impact on user equipment, or mobile terminals, in a relay network, not only from surrounding eNBs but also from relay nodes in other cells, can be contained, and cell-edge throughput can also be maintained, by using location information. Employing Fractional Frequency Reuse and allowing eNBs and relay nodes to temporarily use the same frequency band through the proposed location-aided round robin scheduling algorithm, it is possible to minimize the resultant co-channel interference, and enhancing the cell-centre achievable throughput. The achievable total throughput for the mobile terminals at the cell center is increased by reusing resource blocks, and it is possible to achieve higher total throughput than when using a random selection method. Since long-term channel property is location-dependent, it motivated us in Location-Aided Physical Layer Channel State Information Feedback to exploit location info to reduce the channel state information

50

signalling overhead by optimizing feedback related parameters such as CSI feedback mode (wideband/subband/multi-band). The proposed algorithm reduces feedback overhead by about 70% at best case, while degrading marginally the achievable throughput. Compared to the no-location info dependent scheme, the proposed approach achieves a better trade-off between throughput and feedback overhead. Geolocation information of user equipment, which is implicitly related to two criteria of relay node selection, has been used in Geolocation-Aided Relay Nodes Selection in Cellular Network study. The two criteria are the received signal strength indicator that a relay node has and the link data rate between the user equipment, or mobile terminal, and the selected relay. The proposed relay node selection mechanism utilizing the location of the mobile terminal is based on a cost function, defined by combining the above mentioned two factors, representing a combined performance metric for the network. The weights in the cost function are dependent on the location of the mobile terminal in relation to the relay node, and on the data rate that the operator decides to assign, given the priority of different users, depending on their profile. Whereas single cell designs are applicable even in a multi-cell context, for users in the interior of the cell, inter-cell interference needs to be considered for the cell edge users. In the single antenna case, the multi-cell aspect requires transmit power coordination, which can fairly easily be done location-aided, as considered in Location-Aided Multi-Cell Communications, since locations translate into distances and attenuations, and databases could be used for further statistical characteristics, such as slow fading. Regarding multi-antenna approaches, they require downlink channel knowledge, in principle of all channels at all transmitters (eNBs/cells). An extensive investigation was carried out and presented here, contemplating various levels of complexity. In Location Aware Coordinated Multipoint Transmission Synchronization, location-aided CoMP synchronization targets to improve synchronization performance in particular at cell edges, where signals from adjacent eNBs are received with similar power levels. With knowledge about the position of a UE, propagation delays of signal components coming from different eNBs can be related to each other by processing the synchronization signals received at the user equipment from the different eNBs. Evaluations have shown that a synchronization gain from position information can be obtained if the position estimation accuracy is in the same order of magnitude compared to the synchronization performance expressed in meters. In our investigation, up to 8 dB in transmit power can be gained by exploiting position information at the cell border compared to the performance of optimum joint estimation without that information. Long-term power setting for femto-macro inter-cell interference coordination (ICIC) can benefit from positioning information, which is used in Downlink Femto-Macro Inter-Cell Interference Coordination with Location-Based Long-Term Power Setting in conjunction with a database available in the core network providing relevant information to each HeNB on received power measurements made by mobile terminals in its vicinity. This information guarantees efficient power setting at the HeNB. The proposed power setting technique relying on positioning and database improves the global user equipment performance trade-off compared to constant HeNB transmit power and the non-location-based power setting. Moreover, it proves robustness against relatively high positioning errors. Compared to non-location-based power setting, higher robustness against wall penetration loss error is also observed. The knowledge of the position of a recently activated HeNB, which may origin interference, is used in Location-Aided Home eNodeB Self-Organized Network by the network to perform radio network planning concerning the new associated small cell. Implementing the proposed self-organizing network (SON) approach based on HeNBs geolocation info improves the overall coverage area by roughly 15% when compared with conventional HeNBs deployment, for a conservative scenario as the one considered in our study. For denser networks the benefits are expected to be greater since the inter-cellular interference problems increase. The consequences of the increase on the coverage area of the HeNBs has also an important role on the operator’s network by allowing to balance the load between both eNB and HeNB subnetworks, which results in an expected enhancement on the quality of service in the overall network. 51

Proposals for location-aided techniques should to be weighted against classical approaches in order to assess their definitive value, in line with what was done in the present work. Indeed, in most cases, a location-aided communications approach has a more classical counterpart, often requiring additional overhead. Nowadays, the availability of some location information can be considered as given, not requiring further communication overhead. However, some (but not all) of the location-aided techniques require to frequently access substantial databases, which have become common in the context of flexible spectrum access, and this also represents communication overhead. Location-aided techniques may furthermore exploit location prediction through mobility trajectory information, which would allow slow fading (and even connectivity) predictability, something that is difficult to achieve without location information. The effective implementation of the proposed WHERE2 technology presented in this deliverable, in actual LTE or LTE-A communications equipment and networks would need further dedicated and exhaustive investigation as pointed out in Section 2.2 and introduced in WHERE2 deliverable D1.9 [61]. Additional pertinent details concerning the proposed technology can be found in the Appendices of this document, mainly in WHERE2 generated publications.

52

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[50] Steven M. Kay. Fundamentals of Statistical Processing — Estimation Theory. Prentice Hall, 1993. ISBN 0-13-345711-7. [51] V. Chandrasekhar, J. G. Andrews, and A. Gatherer. Femtocell Networks: A survey. IEEE Comm. Mag., 46(9):59–67, Sept. 2008. [52] D. L´ opez-P´erez, A. Valcarce, G. de la Roche, and Jie Zhang. OFDMA Femtocells: A Roadmap on Interference Avoidance. IEEE Comm. Mag., 47(9):41–48, Sept. 2009. [53] Femtocell market status - Quarterly Market Status Report. Technical report, Informa Telecoms & Media, June 2011. [54] J. Guillet, L. Brunel, and N. Gresset. Downlink femto-macro icic with location-based long-term power setting. In Proceedings 17th IEEE International Workshop on Computer-Aided Modeling Analysis and Design of Communication Links and Networks (CAMAD 2012), Barcelona, Spain, Sept. 2012. [55] V. D’Amico, A. Dekorsys, A. Gouraud, S. Kaiser, B. Le Floch, P. Marsch, and H. Schneich. ARTIST4G: A way forward to the interference problem in future mobile networks. In Future Network and Mobile Summit 2010 Conference Proceedings, June 2010. [56] G. Fodor, C. Koutsimanis, A. R´ acz, N. Reider, A. Simonsson, and W. Muller. Intercell Interference Coordination in OFDMA Networks and in the 3GPP Long-Term Evolution System. Journal of Communications, 4(7):445–453, Aug. 2009. [57] 3GPP. TDD Home eNode B (HeNB) radio frequency (RF) requirements analysis. Technical Report 36.922 V9.0.0, 3GPP TSG-RAN - E-UTRA, April 2010. [58] V. Chandrasekhar, M. Kountouris, and J. G. Andrews. Coverage in multi-antenna two-tier networks. 8(10):5314–5327, October 2009. [59] S. Plass and R. Raulefs. Combining wireless communications and navigation - the WHERE project. In Proc. IEEE Vehicular Technology Conference, VTC, volume 68, Calgary, Canada, September 2008. [60] Final report on synergetic cooperative location and communications for dynamic heterogeneous networks. FP7-ICT-2009-4 WHERE2 Deliverable D2.4, October 2013. [61] WHERE2 system description. FP7-ICT-2009-4 WHERE2 Deliverable D1.9, October 2013.

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Appendices A.1

Joint WP3 publications

This appendix includes the following papers, already published or submitted for publication: • Armin Dammann, George Agapiou, Joaquim Bastos, Lo¨ıc Brunel, Mariano Garc´ıa, Julien Guillet, Yi Ma, Junjie Ma, Jimmy J. Nielsen, Li Ping, Ronald Raulefs, Jonathan Rodriguez, Dirk Slock, Du Yang, Na Yi, ”WHERE2 Location Aided Communications”, in 19th European Wireless Conference 2013 (EW 2013), Guildford, UK, April 2013. • Armin Dammann, Joaquim Bastos, Lo¨ıc Brunel, Mariano Garc´ıa, Miguel A. Garc´ıa, Julien Guillet, Junjie Ma, Jimmy J. Nielsen, Li Ping, Ronald Raulefs, Jonathan Rodriguez, Dirk Slock, Du Yang, Santiago Zazo, ”Location Aided Wireless Communications”, in IEEE Communications Magazine (submitted).

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WHERE2 Location Aided Communications Armin Dammann⇤ , George Agapiou† , Joaquim Bastos¶ , Lo¨ıc Brunelk , Mariano Garc´ıa†† , Julien Guilletk , Yi Ma§ , Junjie Ma‡‡ , Jimmy J. Nielsen⇤⇤ , Li Ping‡‡ , Ronald Raulefs⇤ , Jonathan Rodriguez¶ , Dirk Slock‡ , Du Yang¶ , Na Yi§ ⇤ German

Aerospace Center (DLR), Germany, Email: {Armin.Dammann, Ronald.Raulefs}@DLR.de † OTE Telecom, Greece, Email: [email protected] ‡ EURECOM, Sophia-Antipolis, France, Email: [email protected] § CCSR, University of Surrey, UK, Email: {y.ma,n.yi}@surrey.ac.uk ¶ Instituto de Telecommunicac¸o ˆ es, Aveiro, Portugal, Email: {duyang, jbastos,jonathan}@av.it.pt k Mitsubishi Electric R&D Centre Europe, Rennes, France, Email: {l.brunel, j.guillet}@fr.merce.mee.com ⇤⇤ Dept. Electronic Systems, Aalborg University, Denmark, Email: [email protected] †† ETSI Telecom., Universidad Polit´ecnica de Madrid, Spain, Email: [email protected] ‡‡ Dept. of EE, City University of Hong Kong, Email: {junjiema2@student., eeliping@}cityu.edu.hk Abstract—This paper presents an overview of preliminary results of investigations within the WHERE2 Project [1] on identifying promising avenues for location aided enhancements to wireless communication systems. The wide ranging contributions are organized according to the following targeted systems: cellular networks, mobile ad hoc networks (MANETs) and cognitive radio. Location based approaches are found to alleviate significant signaling overhead in various forms of modern communication paradigms that are very information hungry in terms of channel state information at the transmitter(s). And this at a reasonable cost given the ubiquitous availability of location information in recent wireless standards or smart phones. Location tracking furthermore opens the new perspective of slow fading prediction.

I. I NTRODUCTION The availability of location information offers opportunities to enhance the wireless communications. The position based information that can be exploited comprises slow fading channel characteristics of various links: • LOS/NLOS ((Non) Line of Sight) • attenuation • delay spread, frequency selectivity • angular spreads, MIMO channel characteristics (rank) • speed, direction of movement, acceleration (predictibility of movement), trajectory Some of these aspects may require the use of databases (containing these characteristics as a function of position), compatible with a cognitive radio setting. Compared to feedback (FB) based approaches: some of these characteristics can not easily be determined from isolated channel estimates, or not predicted at all (e.g. slow fading prediction). Further details on the topics addressed below can be found in the deliverables of Work Package 3 (WP3) of the WHERE2 project [1] and in the references mentioned below. II. L OCATION A IDED C ELLULAR C OMMUNICATIONS A. Location aided Multi-User Resource Allocation Some possibilities are: • Multi-user MIMO/SDMA: Use environment information to preselect users, to limit channel feedback to a reduced

set of preselected users. The user preselection can e.g. involve: users with similar attenuation, users with rank 1 MIMO channels (close to Line-of-Sight (LOS)), ... • Multicell aspects (interference coordination) or for Cognitive Radio (interference from secondary to primary systems): the interference level can be predicted from position information. A transversal aspect is also that location tracking can lead to location prediction. This leads in turn to slow fading predictibility (and not just fast fading prediction, which can in principle be done also from past channel response estimates). Another aspect is that user selection (multi-user diversity) potentially leads to an explosion of Channel State Information at the Transmitter (CSIT) requirements and associated overhead. Location based covariance CSIT might offer a (partial) solution. Below, Tx may stand for transmit/transmitter/transmission and Rx for receive/receiver/reception. B. Single-Cell Multi-User Communications Consider the Spatial Division Multiple Access (SDMA) problem, which in Information Theory is called the Broadcast Channel (BC). The SDMA terminology dates from the early nineties. These days it is referred to as the multi-user (MU) MISO (or MIMO) communications problem, and we shall particularly focus on the more difficult downlink. Whereas single-user (SU) MIMO allows to multiply Tx rate by the spatial multiplexing factor when mobile terminals have multiple antennas, MU MIMO allows to reach this same gain with single antenna terminals. However, to achieve this, MU-MIMO requires very good CSIT! Some possible solutions are: • Increase CSI FB enormously (possibly using analog transmission); LTE-A went recently a bit in this direction. • Exploit channel reciprocity in TDD (there may be an electronics calibration issue though [2]). • Limit MU-MIMO (SDMA) to Narrow AoD (Angle of Departure) Aperture (NADA) users and extract essential CSIT from position information (or from Direction of Arrival (DoA) estimates - in both cases the knowledge

of the antenna array manifold is (eventually) required, and location information (plus reduced rate FB) may be used to perform its calibration). The idea of NADA is to focus on the category of mobiles for which the angular spread seen from the Base Station (BS) is limited [3]. This is a small generalization of the LOS case. In the NADA case, the MIMO channel matrix is of rank 2 (regardless of the DoA spread or of the number of paths in the narrow AoD spread), involving on the Tx side the BS antenna array response and its angular derivative. The LOS case is a limiting case in which the AoD spread becomes negligible and the channel rank becomes 1. The Tx side channel matrix factor depends straightforwardly on position (which translates into LOS AoD), only the Rx side factor remains random [4]. We propose that location based MU MIMO transmission involves position based user selection (attenuation, nominal AoD, AoD spread) and associated beamforming (BF) and power control (PC). C. Multi-Cell Communications Whereas single cell designs are applicable even in a multicell context for users in the interior of the cell, intercell interference needs to be considered for the cell edge users. In the single antenna case: the multi-cell aspect requires Tx power coordination, which can fairly easily be done location-aided (locations translate into distances and attenuations; databases could be used for further location dependent statistical characteristics (e.g. slow fading)). Multi-antenna techniques: require downlink channel knowledge, in principle of all channels at all transmitters (cells). Several approaches are possible, of increasing complexity: • single-cell Tx, multi-cell Rx: the BSs perform single-cell Tx; inter-cell interference gets handled by the terminal Rx antennas. The CSIT requirements remain local, per cell. In the LOS case, the Mobile Terminal (MT) needs to have a number of antennas at least equal to the number of cells (BS signals) to be handled (ZF). In the NADA case, the required number of antennas gets doubled. • multi-cell coordinated beamforming: also called the MISO or MIMO Interference Channel (IC) in the case of one MT per cell. In the MISO case, the BSs need to zero-force (ZF) towards the users in other cells. In the MIMO case, this ZF can be shared between Txs and Rxs (interference alignment (IA)). The case of multiple MTs per cell, with interfering cells, is called the Interfering Broadcast Channel (IBC), or sometimes also simply the multi-cell problem. The IC/IBC models are applicable also when the interfering cells correspond to heterogeneous systems (e.g. macro-femto coexistence). • network MIMO: also called Coordinated Multi-Point Tx (CoMP): requires not only global CSIT at all Txs (BSs) but furthermore distribution of all Tx signals over the BSs. Whenever we mention ZF BF above, this refers to the high SNR case, and could be replaced by optimized BF at finite SNR. Also BF could be replaced by Dirty Paper Coding (DPC) or other more optimal Tx techniques.

Fig. 1.

User in a network with relays and base stations

The MIMO IC approach is perhaps the most interesting. However, its joint Tx/Rx design is plagued by numerous local optima. At high SNR, the optimum weighted sum rate (WSR) design becomes ZF (IA), with typically many possible solutions due to the nonlinearity of the ZF conditions. Nevertheless, the ZF problem simplifies enormously in the LOS case [4]. Indeed, the usually coupled roles of the Tx and Rx in overall ZF get now distributed over Txs and Rxs: the design of the Tx and Rx filters becomes decoupled, and their design only requires knowledge of the channels connected to them (in general the design of a Tx or Rx filter in the MIMO IC problem requires the knowledge of all channels appearing in the IC). Furthermore, the Tx filters can be designed knowing only the antenna array responses of the BSs and the location of the terminals. III. C ELLULAR : G EOLOCATION A IDED R ELAY S ELECTION Optimal node selection algorithms for a network with cooperative relays has received a lot of attention in recent years. As such, there has been a lot of research work in relay selection mechanisms that can be divided in single relay selection and multiple relay selection. Single relay selection mechanisms have been investigated in [5] where the neighbor node with the maximum signal to interference and noise ratio (SINR) is selected as the most appropriate node, while in [6] the node that is closest to the base station is used as the best relay. The research is extended to multiple relay selection in [7] by exploiting the concepts of relay ordering and recursion. The above algorithms select the node according to one criterion which may not be an optimal solution for maximizing the performance of communication links. This report utilizes the geolocation of the user which is implicitly related to two criteria of quality of service (QoS) which are the received signal strength indicator (RSSIi ) of the ith cell that a relay node has and the link data rate Ri between the user’s terminal and the selected relay node. The RSSI has a higher value when the user’s terminal is closer to the node and decreases when the user gets away from it. The senario used in this section is represented in Fig. 1. From this figure it can be seen that as the distance of the user from the relay node and the base station varies, the rate and the RSSI change. The incorporation of relays in a network provides an attractive solution for

Fig. 2. The layout of a Type-II relay-aided LTE-A cellar network using Fractional Frequency Reuse (FFR).

Fig. 3. Experimental Cumulative Density Function of the total throughput of central MTs, in the scenario of 1) conventional Round-Robin Scheduling; and 2) proposed location-aided scheduling algorithm.

improving and enhancing the coverage of a network. This leads to an effort for finding the best route between the relays and base stations for minimizing the latency and maximizing the network throughput. It uses metrics for the path selection which are the (RSSIi ) and the link data rate Ri as mentioned above. A management database in MySQL is configured that stores the values of the user’s geolocation, the RSSI and the data rate. It communicates with the user’s terminal and when it calculates the optimal function based on the measured metrics, it gives instruction to the terminal to switch to the best node. This way the network can be improved in terms of minimizing the latency of the transmitted data and maximizing the data rate.

selection could exploit the location knowledge of each user and the long-term channel knowledge (e.g. pathloss) associated with locations. The latter scheme requires less amount and less frequent (if users are in low speed movement) feedback information compared to the former one. Hence, we propose a location-aided round robin scheduling algorithm [10] to allow central MTs to temporarily share part of the RN frequency band with cell-edge MTs with minimum intra-cell interference, so as to satisfy the traffic demand in the central area in busy hours. As demonstrated in Fig. 3, the proposed algorithm achieves higher total throughput than the conventional method.

IV. C ELLULAR : L OCATION A IDED S CHEDULING FOR LTE-A R ELAYS WITH F RACTIONAL F REQUENCY R EUSE

V. C ELLULAR : L OCATION AIDED COOPERATIVE RELAYING

In order to achieve higher cell-edge throughput in an urban area, 3GPP has defined Type-II Relay Nodes (RN) [8], which share the same cell id and locate within the coverage of its donor eNodeB. Cell-edge Mobile Terminals (MTs) in such a network receive better connection from the RNs, but also suffer more interference not only from the surrounding BSs, but also from the closer RNs in other cells. One solution is to employ Fractional Frequency Reuse (FFR) [9], in which the entire bandwidth is divided into four portions as shown in Fig 2. The frequency band B0 is reused in the central area of every cell, while the other frequency bands are applied at the RN covered cell-edge area with a reuse factor of 3. One problem of employing FFR is that the available bandwidth at the central areas becomes only a fraction of the entire bandwidth, which may not satisfy the heavy traffic demand which may occur during busy hours. One solution is to select some central-MTs and some edge-MTs to temporarily share the same frequency band with minimum intra-cell interference. The selection could be implemented according to instantaneous channel knowledge, which requires all users to feedback channel state information of B0 , ..., B3 . Alternatively, the

Cooperative relaying has attracted much research interest, ranging from capacity theorems to practical relaying protocols [11]. Moreover, it has been deployed in wireless standards, e.g., in 3GPP Long Term Evolution (LTE-Advanced), wireless relays are deployed to enhance coverage of cellular services. Such mobile systems can be modeled as a single source, multi-relay, and single destination network when sources transmit information over an orthogonal medium. However, the orthogonality between source and relays require extra cost either in time or frequency, which reduces the spectral efficiency. To solve this problem, adaptive relaying protocols including incremental relaying (IR) and opportunistic relaying (OR) have been introduced. Meanwhile, it is considered here that every node involved has the location information of all communication nodes through an advanced positioning system. This motivates us to exploit location information to further improving the spectrum efficiency in such multiple relay networks, using IR or OR. First, location-aided relay selection has been investigated for IR over asymmetric fading channels in [12]. Based on the analytical results derived there, a relay can be selected according to minimum outage probability, under constraints of

VI. C ELLULAR H ET N ETS : L OCATION A IDED S YNCHRONIZATION Particularly at cell edge areas of a mobile communications system, signals are received from different base stations (BSs) with similar power levels. This causes interference even for synchronization since sync signals transmitted at different BSs are usually not perfectly orthogonal and received with different propagation delays. Knowledge about the mobile terminal (MT) position allows us to relate sync signals received from different BSs to each other regarding their propagation delays. With this relation, formerly interfering signal energy from adjacent BSs can be exploited for synchronization as well [16]. We consider 3 BSs (BSp , p = 1, . . . , 3) with an inter site distance of 1 km. These BSs synchronously transmit LTE secondary synchronization signals (SSSs) [17] with different IDs, denoted as Sp [`] in frequency domain. At the MT, which is located at the cell edge central to the 3 BSs, we receive R[`] =

3 X

↵p Sp [`] e

⌘2⇡ ` fSC ⌧p

+ N [`]

(1)

p=1

in frequency domain, where N [`] is additive white n o Gaussian 2 noise with zero mean and variance E |N [`]| = 2 . The propagation delays ⌧p depend on the distances between the MT and BSs. In LTE the subcarrier spacing is fSC = 15 kHz [17]. The flat fading coefficients ↵p contain path loss and shadow

3

10 Sync. Error (90% StdDev) [ns]

total transmit power and average SNR, assisted by location information. Here, the role of location information is to provide the mobile nodes (via a database) with the statistical channel knowledge of the communication links, which is important for the evaluation of the outage probability. Furthermore, a novel adaptive HARQ scheme has been proposed by exploiting the knowledge of channel quality information (CQI), which allows to determine the suitable transmission mode to guarantee a specific Frame Error Rate (FER) during the first transmission. The proposed HARQ scheme is suitable for machine-to-machine (M2M) type communications with low mobility, where location information can easily be translated into channel quality information [13]. In Opportunistic Relaying (OR) on the other hand, the goal is to choose the best relay node amongst all available relays through a certain policy. To improve the spectrum efficiency for OR with the Decode and Forward (DF) relaying protocol, a novel adaptive modulation scheme for opportunistic DF relaying is proposed in [14], which allows the source and relay to transmit information in different modulation formats. Then we investigated the adaptive protocol for OR with location information [15]. The proposed scheme is a two-step procedure. In a first step, a set of candidate relays are selected based on their geolocation; the second step then selects the best relay from the set of candidates. It has been shown that the proposed scheme can reduce signalling overhead by 97% with the spectral efficiency comparable to that of the conventional best-relay selection scheme.

0.4 dB loss due to interference

no pos. info pos = 100m pos = 30m pos = 10m pos = 3m pos ! 0 no interf.

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Fig. 4. CRLB for the synchronization error (standard deviation) vs. the base station transmit power PTX . The MT is at the cell edge central to 3 BSs. Distance between BSs is 1 km. LTE SSS-IDs are 142, 411, 472.

fading according to the WINNER C2 typical urban macro cell channel model [18]. Based on the signal model in (1) we calculate the Cram´erRao lower bound (CRLB) [16] for the variance of unbiased estimates of the signal propagation delays ⌧1 , . . . , ⌧3 . In particular we are interested in the estimation performance of ⌧1 , corresponding to the serving BS. The flat fading coefficients ↵p and consequently the CRLB are random. For this reason we use the 90 %-variance as performance measure. The CRLB is lower or equal to that value with probability 0.9. Fig. 4 shows the square root of these variances vs. the transmit power PTX at each BS. The estimation performance without exploiting position information (dashed graph) is our reference. Compared to the ideal case where no interference is present from BS2 and BS3 we obtain a degradation in terms of Tx power of about 0.4 dB. Now let’s assume that there is an estimate [ˆ x, yˆ] = [x, y] + [✏x , ✏y ], which is the true MT position plus an additive Gaussian error with zero mean and variance E ✏2x = E ✏2y = 2 pos/2. With that knowledge about the MT position we can relate the different propagation delays to each other. As a result the Fisher information about the propagation delays ⌧p increases and the CRLB improves as the positioning error pos decreases [16]. The results show that up to 8 dB in Tx power can be gained with accurate knowledge ( pos ! 0) about the position of the MT. VII. C ELLULAR H ETNETS : L OCATION -BASED L ONG -T ERM P OWER S ETTING In heterogeneous co-channel deployments of macro base stations (MBSs) and femto base stations (FBSs), inter-cell interference coordination (ICIC) appears as a proper way to secure the MBS traffic. Priority should be put on minimizing the interference created by FBSs on MBSs while maintaining a reasonably high FBS throughput inside the home. Besides, due to the high number of FBSs, ICIC minimizing the MBSFBS exchanges is desirable. In the downlink, the impact of interference generated by a FBS on mobile terminals served by a MBS (MMTs) depends in particular on the power received by each MMT around the FBS from its serving MBS and surrounding base stations. Based on this received power in-

Step1: FBS position transmitted to the server

Server

Step2: Information about power measurements of MMTs in HIRZ transmitted to FBS No ICIC

High Interference Reference Zone (HIRZ) Impact of the FBS on the MMTs is set constant

FBS MBS

Step3: FBS transmit power computed

FBS ICIC

Fig. 5. ICIC providing macro-degradation equalization (single cell, no shadowing). 1 NoICIC ICIC Pow. ICIC Loc.

5%−ile Femto spectral efficiency (b/s/Hz)

0.9 Pow. RMSE = 0 dB 0.8

Pow. RMSE = 3 dB

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intermediate node is used as a relay [20], [21]. In mobile networks, the mobility of nodes leads to outdated information about links’ qualities and can therefore lead to suboptimal relay decisions where the chosen relay no longer delivers a sufficient QoS. If the locations of nodes and propagation characteristics are known, the QoS degradation in terms of large and medium scale path loss due to mobility and delayed information can be estimated and used to enhance the relay decision. For studying this idea, this work has considered the following simple scenario. We consider downstream communication between a static access point (AP) and a destination node, where a set of K nodes in the vicinity can act as relay nodes. For simplicity, we consider the case with a static destination and a single mobile relay node, shown in Fig. 7. A location estimate for node R is periodically obtained using a localization system and transmitted to the AP, which is responsible for the relay decision. For a specific scenario, the AP uses a corresponding relay policy to map the location of the relay to a transmission mode (direct or relayed).

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VIII. MANET S : R ELAY S ELECTION P OLICY O PTIMIZATION FOR T WO -H OP R ELAYING In WLANs, it is well known that two-hop relaying can be used to improve throughput for poor links if a proper

80 m

formation, location-based long-term power setting [19] ensures that the FBS impact on surrounding MMTs is independent of its location within the MBS coverage, as depicted in Fig.5. Using the MMT and FBS location information, together with an appropriate database, benefits the ICIC power adjustment, by providing precise information on received powers at MMTs surrounding a given FBS. The geo-referenced database is built thanks to MMT reports to their serving MBS, containing received power from neighboring MBSs and FBSs and the MMT location. Upon installation or reinitialization, a FBS transmits its location information to the server maintaining the database. This server can reply appropriate information about MMTs located around the FBS. This information allows more accurate power setting at FBS, compared to the non-locationbased approach where the FBS sets its transmit power without any external knowledge, measuring received powers by itself and assuming that they properly approximate received powers at surrounding MMTs. Focusing on a reasonable 10% macro spectral efficiency loss compared to the case without FBSs, Fig.6 shows that even with location errors the location-based approach (ICIC Loc.) provides a gain against the non-locationbased approach (ICIC Pow.), especially if the FBS power measurement is erroneous due to the decorrelation between indoor and outdoor shadowing.

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Fig. 7. System with static AP, mobile relay (R), and static destination (D). Position uncertainty is shown by the dashed circle around R.

Fig. 8. Example Markov mobility model that is used in numerical results. N ⇥ N discrete grid-points represent the geographic space.

In order to investigate optimal relay policies when the location information is subject to the delays of the location update procedures, we have developed a Markov model consisting of two parts: 1) a continuous time Markov chain model for the spatial mobility of the mobile relay shown in Fig. 8; and 2) a model of location update procedures accounting for delays and losses (not shown here, but we refer to [22] for details). This model together with a novel optimization algorithm, enables policy optimization for a specific scenario, resulting in optimal relay policies that account for the risk of a suboptimal relay decision (due to outdated location information). An example of the possible improvement is shown in Fig. 9, where the avg. achieved throughput increases slightly when using the optimized relay policy. IX. MANET S : L OCATION A IDED ATTACK D ETECTION Wireless ad hoc networks are particularly vulnerable to different threats. The so-called wormhole or relay attack is one of the most destructive. This attack is carried out by two malicious nodes that use a high-speed link (tunnel) to transparently forward data packets from one point to another (Fig. 10). Wormholes distort the network topology and disrupt

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neighbor discover (ND) protocols, because they make distant nodes to appear as local for any node looking for its neighbors [23].

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Fig. 11. Performance of parametric and nonparametric wormhole detection schemes.

accurately estimated.

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If a set of trustworthy beacon nodes (BNs) located at reference positions are available, they can be used to effectively detect wormholes by using a two-step approach: a compromised node (CN) suspected to be the target of a wormhole attack could use the positions of the BNs along with distance related measurements, such as received signal strength (RSS), of the links between the BNs and the CN to localize itself and then report its estimated position back to the BNs; these reference nodes can, in turn, check whether the supposed position of the node is compatible with the RSS measurements of the reverse links from the CN to the BNs. Both parametric and nonparametric localization techniques can be used for wormhole detection. Nonparametric approaches have a distinct advantage over parametric methods, because they do not require any previous calibration of the environment and are, therefore, insensitive to inaccuracies in the path-loss model parameters. To illustrate this fact, let us assume the attack model illustrated in Fig. 10, where two nodes set a wormhole to force a remote compromised node to appear as a neighbor of a set of local network nodes. As a parametric approach to secure ND, we have used a linearized weighted least-squares (WLS) approach to localize the node, followed by a likelihood ratio test (LRT) to verify the quality of the estimation, assuming a conventional log-distance path loss model for the RSS measurements. A nonparametric attack detection procedure is also implemented by using the scheme described in [24]. Some simulation results are presented in Fig. 11, where 20 BNs are deployed in a square room of 400 m2 . We can see that the parametric approach performs better than the nonparametric scheme for moderate shadowing losses, but quickly deteriorates if the channel model parameters are not

X. L OCATION A IDED C OGNITIVE R ADIO A. Single Receive Antenna Case Underlay Cognitive Radio (CR) is a popular CR design problem, in which a secondary network is allowed to operate in the presence of a primary system with interference limits at the primary Rxs, and this without any collaboration or even awareness of the primary system. To make underlay feasible, the exploitation of position information to determine attenuations constitutes probably the only realistic approach. In the MISO case, the location information could also be translated to Direction of Departure (DoD) based ZF BF. The cases of LOS and NADA need to be explored. B. Multi-Antenna Cognitive Radio Paradigms The extension of a number of standard cognitive radio paradigms to the multi-antenna case is not as straightforward and unambiguous as it may seem at first. In [25] we proposed some possible multi-antenna extensions for these paradigms. Spatial Overlay: MISO/MIMO Interference Channel In the overlay paradigm, primary and secondary collaborate. This collaboration could be interpreted at multiple levels, at the level of an exchange of Tx signals (as in network MIMO), or just at the level of CSIT, which in the single antenna case translates to coordinated power control. In the case of multiple antennas, if we limit cooperation to CSIT, this would lead to the exploitation of the multiple antennas for coordinated BF to achieve parallel interference-free channels. Coordinated BF applies to multiple antennas at the Tx side (MISO IC). In the case of multiple antennas at the Rxs, we can have coordinated Rxs. The case of the coordination of the multiple antennas on both sides corresponds to the (noisy) MIMO IC which was discussed earlier in the multi-cell setting. The recent Authorized Shared Access (ASA) proposal by Qualcomm and Nokia-Siemens Networks fits in the realm of overlay cognitive radio. Spatial Underlay: In the underlay paradigm, interference caused by a secondary Tx to a primary Rx is acceptable as long as the interference

L

remains under a maximum tolerance level. One possible definition of spatial underlay then would be that the primary Rx equipped with multiple antennas allows primary interference as long as it has enough antennas to handle it. Hence the primary Rx needs to be active. So, the primary Rx allows an interference subspace of maximum dimension equal to the excess of its number of antennas over the number of primary streams it needs to receive. The primary system is secondary-aware. Of course, the secondary Txs need to align the interference caused to primaries in subspaces of limited dimension. Spatial Interweave: In the interweave paradigm, the primary system should not be disturbed at all, and is not required to exhibit any cooperation with the secondary systems. So in a spatial interweave version, with multiple primary Rx antennas also, the secondary systems need to zero-force to all primary Rx antennas individually. In this case there is still room for secondary Tx if the secondary Txs have more antennas than the combined primary Rxs. The spatial interweave paradigm requires significant CSIT and can be reciprocity based in TDD, or location based in the case of LOS secondary-primary cross channels. In the LOS case, the number of primary Rx antennas becomes irrelevant (assuming they are in the far field from the secondary). In the case of NLOS, the secondary Tx needs to have more antennas than the number of propagation paths to all primary Rxs.

Define a discrepancy index as = Lap . Clearly, can be used to measure the inaccuracy of pap relative to p. When = 1, the a priori PDP is accurate. When > 1, the channel estimation algorithm developed in [26] will try to estimate more channel coefficients than necessary, which is prone to error due to channel noise. The related performance is demonstrated by the numerical results in Fig. 12. We can see from Fig. 12 that the performance degrades moderately as increases. When < 1, the channel estimation algorithm developed in [26] will try to estimate less channel coefficients than necessary. The signals transmitted on un-estimated paths become pure interference, which cause serious performance loss as sown in Fig. 12.

XI. C OGNITIVE R ADIO : L OCATION - AIDED C HANNEL E STIMATION

From the results above, we observe that the a priori information should be used carefully. It is preferable to overestimate the PDP length rather than to under-estimate it. This provides a useful guideline for the application of positioning information in communication systems.

Channel state information (CSI) is crucial for orthogonal frequency division multiplexing (OFDM) systems. Channel statistic information, e.g., power delay profile (PDP), can be exploited to enhance the estimation performance. Such PDPs can be obtained from positioning information. Alternatively, the PDPs could also be measured from past channel estimates. In cognitive radio systems, secondary users can only enter the primary network opportunistically. Since the latter method needs relatively longer time to converge, the location-aided approach is preferable in this regard. In WHERE2, we developed a fast channel estimation algorithm based on the so-called dual diagonal LMMSE (DDLMMSE) principle. This algorithm can achieve excellent performance with complexity of only O(N log N ), where N is the number of sub-carriers. The details are reported in [26]. We also investigated the effect of PDP mismatch on the system performance in [27] based on the DD-LMMSE algorithm. Let p be the true channel PDP and pap be the available a priori PDP. L and Lap be the true and a priori maximum delay spread respectively. We focus on the PDPs in the following form, p = [1/L, 1/L, . . . , 1/L, 0, . . . , 0] | {z } L

pap = [1/Lap , 1/Lap , . . . , 1/Lap , 0, . . . , 0]. | {z } Lap

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Fig. 12. BER Performances for an OFDM system with different . N = 1024, L = 8. Rate-1/2 (23, 35)8 convolutional coding and Gray 16-QAM modulation are used.

XII. S PECTRUM S ENSING T ECHNIQUES FOR L OCATION -A IDED C OGNITIVE R ADIO N ETWORKS Spectrum sensing is one of the prominent techniques to enable cognitive users’ opportunistic access into temporarily unused parts of the spectrum. Major challenging requirements preventing practical application of spectrum sensing are • High sensitivity to very weak signals. For instance the signal-to-noise ratio (SNR) is required to be as small as 20 dB. • Short observation time for measuring the spectrum. For instance the observation time is required to be as small as 1 or 2 OFDM symbols. Spectrum sensing is an important technique that is complementary to geo-location database techniques for the opportunistic reuse of TV White Space or Authorised Shared Access (ASA). We have developed fast and high-sensitivity spectrum sensing schemes for detecting OFDM signals. The non-dataaided scheme proposed in [28], [29] offers 90% Probability of Detection and 10% Probability of False Alarm for a SNR as low as 21 dB and the observation time as short as 2 OFDM symbols. Moreover, the work presented in [30] turns out to be the best pilot-assisted spectrum sensing scheme, offering acceptable performance for a SNR as low as 10 dB.

The above results have been recently extended by considering new elements such as time/frequency diversity combining, timing and frequency synchronisation, and computational complexity. The comprehensive results can be found in [31], [32]. It has been shown that time/frequency diversity combining facilitates the non-data-aided scheme with additional 4 dB gain and the pilot-assisted scheme with additional 7 dB gain. It is worth highlighting that the proposed non-data-aided scheme outperforms the state-of-the-art (i.e. the eigenvaluebased scheme) by 15 dB gain; and the proposed pilot-assisted scheme offers more than 5 dB gain compared to existing schemes. Such large gains come from the a-priori knowledge of OFDM waveforms including the length of cyclic prefix, number of subcarriers, pilot placement, etc. The knowledge of the OFDM waveforms can be obtained by employing locationassisted techniques with the following flowchart description: 1. 2.

3.

The CR obtains its position coordinates (x0 , y0 ), by employing GNSS and other available positioning systems. Look up the geo-location database: ID of available access points within a range r of (x0 , y0 ); what are the waveforms and relevant parameters employed by those access points? Employ the proposed spectrum sensing schemes based on the location-related waveform parameters.

Since wireless systems (such as Wi-Fi and cellular networks) normally have a large coverage (50 meter to 500 meter), the proposed spectrum sensing schemes are not demanding in terms of positioning accuracy as long as the positioning error is smaller than the coverage of the wireless systems. ACKNOWLEDGMENT This work has been performed in the framework of the ICT248894 FP7 project WHERE2, funded by the European Union. R EFERENCES [1] “WHERE2 Project,” http://www.kn-s.dlr.de/where2/index.php. [2] M. Guillaud, D. Slock, and R. Knopp, “A Practical Method for Wireless Channel Reciprocity Exploitation Through Relative Calibration,” in Proc. IEEE Int’l Symp. on Signal Processing and its Applications (ISSPA), Sydney, Australia, Sept. 2005. [3] D. Astely and B. Ottersten, “The Effects of Local Scattering on Direction of Arrival Estimation with MUSIC,” IEEE Trans. on Signal Processing, Dec. 1999. [4] W. Guibene and D. Slock, “Degrees of Freedom of Downlink Singleand Multi-Cell Multi-User MIMO Systems with Location based CSIT,” in Proc. IEEE Veh. Tech. Conf. (VTCspring), Dresden, Germany, Jun. 2013. [5] Y. Zhao, R. Adve, and T. Lim, “Improving amplify-and-forward relay networks: optimal power allocation versus selection,” Wireless Communications, IEEE Transactions on, vol. 6, no. 8, pp. 3114 –3123, 2007. [6] M. Abdizadeh, H. Rad, and B. Abolhassani, “Joint Optimization of Power Allocation and Relay Deployment in Wireless Sensor Networks,” in Proc. IEEE Wireless Communications and Networking Conf. (WCNC), Apr. 2010. [7] S. Atapattu, Y. Jing, H. Jiang, and C. Tellambura, “Opportunistic Relaying in Two-Way Networks,” in Proc. Int’l ICST Conf. Comm’s and Networking in China (CHINACOM), Aug. 2010. [8] G. TR 36.814 V9.0.0, “Further advancements for E-UTRA physical layer aspects,” Tech. Rep., 2010.

[9] N. Krishnan, R. Yates, and N. Mandayam, “Bandwidth Sharing for Relaying in Cellular Systems,” IEEE Transactions on Wireless Communications, vol. 11, no. 1, pp. 117–129, 2012. [10] E. Hahne, “Round-robin scheduling for max-min fairness in data networks,” Selected Areas in Communications, IEEE Journal, vol. 9, no. 7, pp. 1024–1039, 1991. [11] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity in wireless networks: Efficient protocols and outage behavior,” IEEE Trans. Inf. Theory, vol. 50, no. 12, pp. 3062–3080, Dec. 2004. [12] N. Yi, Y. Ma, and R. Tafazolli, “Incremental decode-forward relaying over asymmetric fading channels: Outage probability and location-aided relay selection,” in Proc. IEEE SSP’11, 2011, pp. 181–184. [13] C. Qian, H. Chen, Y. Ma, and R. Tafazolli, “A novel adaptive hybridARQ protocol for machine-to-machine comm’s,” in Proc. VTCspring, 2013. [14] Y. Ma, R. Tafazolli, Y. Zhang, and C. Qian, “Adaptive modulation for opportunistic decode-and-forward relaying,” IEEE Trans. Wireless Commun., vol. 10, no. 7, pp. 2017–2022, Jul. 2011. [15] C. Qian, Y. Ma, and R. Tafazolli, “Relay selection for modulationadaptive opportunistic df relaying using mixed channel knowledge,” in Proc. IEEE WCNC, Apr. 2012, pp. 2429–2433. [16] A. Dammann and R. Raulefs, “Exploiting Position Information for Synchronization in Coordinated Multipoint Transmission,” in Proc. 77th Vehicular Technology Conf. (VTC Spring), Dresden, Germany, Jun. 2013. [17] LTE; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical channels and modulation (3GPP TS 36.211 version 8.7.0 Release 8), ETSI, Jun. 2009, ETSI TS 136 211 V8.7.0. [18] “WINNER II Channel Models,” Sep. 2007, IST-4-027756 WINNER II Deliverable D1.1.2, http://www.ist-winner.org/deliverables.html. [19] J. Guillet, L. Brunel, and N. Gresset, “Downlink femto-macro icic with location-based long-term power setting,” in Proceedings IEEE CAMAD, Barcelona, Spain, Sept. 2012. [20] H. Zhu and G. Cao, “rDCF: A relay-enabled medium access control protocol for wireless ad hoc networks,” IEEE Trans. on Mobile Computing, 2006. [21] P. Liu, Z. Tao, S. Narayanan, T. Korakis, and S. Panwar, “CoopMAC: A cooperative MAC for wireless LANs,” IEEE Journal on Selected Areas in Communications, 2007. [22] J. Nielsen, R. Olsen, T. Madsen, and H.-P. Schwefel, “On the Impact of Information Delay on Location-based Relaying: A Markov Modeling Approach,” in Proc. IEEE Wireless Comm’s and Networking Conf. (WCNC), 2012. [23] P. Papadimitratos, M. Poturalski, P. Schaller, P. Lafourcade, D. Basin, S. Capkun, and J.-P. Hubaux, “Secure neighborhood discovery: a fundamental element for mobile ad hoc networking,” IEEE Communications Mag., Feb. 2008. [24] M. Garc´ıa-Otero and A. Poblaci´on-Hern´andez, “Secure Neighbor Discovery in Wireless Sensor Networks Using Range-Free Localization Techniques,” Int’l Journal of Distributed Sensor Networks, 2012. [25] D. Slock, “Location Aided Wireless Communications,” in Proc. IEEE Int’l Symp. on Control, Comm’s and Signal Proc. (ISCCSP), Rome, Italy, May 2012. [26] N. Geng, X. Yuan, and L. Ping, “Dual-Diagonal LMMSE Channel Estimation for OFDM systems,” IEEE Trans. Signal Process., Sep. 2012. [27] J. Ma, N. Geng, and L. Ping, “Impact of the a priori channel state information on the performance of OFDM systems,” in 8th Int’l Workshop Multi-Carrier Systems Solutions (MC-SS), May 2011. [28] P. Cheraghi, Y. Ma, and R. Tafazolli, “Frequency-Domain Differential Energy Detection Based on Extreme Statistics for OFDM Source Sensing,” in Proc. IEEE VTC Spring, 2011. [29] P. Cheraghi, Y. Ma, Z. Lu, and R. Tafazolli, “A novel low complexity differential energy detection for sensing OFDM sources in low SNR environment,” in Proc. IEEE GLOBECOM Workshops, 2011. [30] Z. Lu, P. Cheraghi., Y. Ma, and R. Tafazolli, “Extreme statistics based spectrum sensing for OFDM systems by exploiting frequency-domain pilot polarity,” in Proc. IEEE Globecom, 2011. [31] P. Cheraghi, Y. Ma, R. Tafazolli, and Z. Lu, “Cluster-Based Differential Energy Detection for Spectrum Sensing in Multi-Carrier Systems,” IEEE Trans. Signal Process., Dec. 2012. [32] Z. Lu, Y. Ma, P. Cheraghi, and R. Tafazolli, “Novel Pilot-Assisted Spectrum Sensing for OFDM Systems by Exploiting Statistical Difference Between Subcarriers,” IEEE Trans. Communications, 2013.

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Location Aided Wireless Communications Armin Dammann∗ , Joaquim Bastos¶ , Lo¨ıc Brunelk , Miguel A. Garc´ıa†† , Mariano Garc´ıa†† , Julien Guilletk , Junjie Ma‡‡ , Jimmy J. Nielsen∗∗ , Li Ping‡‡ , Ronald Raulefs∗ , Jonathan Rodriguez¶ , Dirk Slock‡ , Du Yang¶ , Santiago Zazo†† , ∗ German Aerospace Center (DLR), Germany, Email: {Armin.Dammann, Ronald.Raulefs}@DLR.de ‡ EURECOM, Sophia-Antipolis, France, Email: [email protected] ¶ Instituto de Telecommunicac ¸ oˆ es, Aveiro, Portugal, Email: {duyang, jbastos,jonathan}@av.it.pt k Mitsubishi Electric R&D Centre Europe, Rennes, France, Email: {l.brunel, j.guillet}@fr.merce.mee.com ∗∗ Dept. Electronic Systems, Aalborg University, Denmark, Email: [email protected] †† ETSI Telecom., Universidad Polit´ ecnica de Madrid, Spain, Email: {miguel,mariano,santiago}@gaps.ssr.upm.es ‡‡ Dept. of EE, City University of Hong Kong, Email: {junjiema2-c@my., eeliping@}cityu.edu.hk Abstract—This paper presents a subsampled overview of the results of investigations within the WHERE2 Project [1] on identifying promising avenues for location aided enhancements to wireless communication systems. The wide ranging contributions are organized according to the following targeted systems: cellular networks, mobile ad hoc networks (MANETs) and cognitive radio (CR). Location based approaches are found to alleviate significant signaling overhead in various forms of modern communication paradigms that are very information hungry in terms of channel state information at the transmitter(s) (CSIT). And this at a reasonable cost given the ubiquitous availability of location information in recent wireless standards or smart phones. Location tracking furthermore opens the new perspective of slow fading prediction.

I. I NTRODUCTION The main goal of the WHERE and WHERE2 projects [1] was to explore wireless network based location estimation to offer an alternative and/or complement to GNSS based localization. Satellite connectivity may pose problems in urban canyons and indoor, and not all mobile terminals (MTs) are GNSS equipped. Wireless network based localization is now part of LTE-A, based on the following techniques: Enhanced Cell Id = Cell Id + RSS (Received Signal Strength), O-TDoA (Observed Time Difference of Arrival), and DoA (Direction of Arrival at the base station (BS)). The availability of location information, which has become widespread with smartphones, offers in turn opportunities to enhance the wireless communication. Especially for the more critical design of the transmitters, which esp. in multiuser settings require Channel State Information at the Transmitter (CSIT). Position information by itself of transmitter and receiver provides information about the Line of Sight (LoS) component of the channel response, such as delay and attenuation and, in the multi-antenna case, the LoS antenna array response. The evolution of a position leads to information about Doppler shift and maximum Doppler spread. More channel information can be obtained if we assume the availability of a database per BS in which (multipath) propagation characteristics are stored as a function of the MTposition. The idea of using such databases is starting to spread in wireless system design, expecially in the context of cognitive radio and white spaces. With such a database, the position based information that can be exploited comprises slow fading channel characteristics of various links such as:

LoS/NLoS ((Non) Line of Sight), attenuation, • delay spread, frequency selectivity and diversity, • angular spreads, MIMO channel characteristics (rank profile), dominant paths for Massive MIMO. The observation of a sequence of past channel estimates may allow the prediction of the fast fading, but not the slow fading. However, the availability of a database and MTtrajectory information leads to position prediction and hence the prediction of not only fast fading characteristics (e.g. power delay Doppler space profile (PDDSP)) but also various slow fading characteristics (such as the birth and death of multipath components, shadowing). What can not be inferred on the basis of position (as generally believed) is the fast fading state, the instantaneous complex channel impulse response. In what follows, we consider a number of problem formulations in which fast fading state information can essentially be avoided. In general, these location based approaches are complementary to feedback based instantaneous CSIT and help reduce feedback overhead or improve performance. In this paper, Tx may denote transmit/transmitter/transmission and Rx may denote receive/receiver/reception. This paper is a futher evolution of and complement to [2] where some other related approaches can be found. See also [3] for e.g. the exploitation of location information at the receiver side or in the single user case, and also [4], [5] for more elaborate discussions and references. • •

II. L OCATION A IDED C ELLULAR C OMMUNICATIONS A. Location Aided CSI Feedback for LTE-A Relay Network The deployment of fixed relay nodes (RNs) has been standardized in LTE-A networks since Rel-10 for its capability of range extension, throughput enhancement, energy reduction, etc. To fully exploit these benefits, it is important to acquire downlink channel state information (CSI), which facilitates adaptive transmission and scheduling leading to efficient resource utilization. For a FDD network, the downlink CSIs are usually estimated at the mobile terminals (MTs) and then fed back to BSs. Considering the time-variant and frequencyselective nature of the wireless channel, the amount of CSI information is significant, which results in the adoption of CSI quantization, frequency-domain compression (known as wideband/sub-band mode), and periodic/aperiodic feedback mode.

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The involvement of multiple relay nodes further increases the amount of CSI by several folds, since more than one link – BSto-MT and RN(s)-to-MT – requires monitoring. We propose a location-aided mechanism [3] to reduce the CSI feedback overhead by exploiting location-dependent long-term channel properties.

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An example scenario is illustrated in Fig. 1, where a user moves through an area covered by 1 BS and 2 RNs. Without location information, this MT periodically reports the instantaneous SNR from these three nodes so as to connect to the one having the highest value. In our scheme, the BS consults the target user’s location from the Evolved Serving Mobile Location Centre (E-SMLC), which is a standardized network element responsible for MT positioning. Then it searches the current location’s averaged-SNRs in a dedicated database (or computes from the positions). If the averagedSNR of one node (e.g. RN1) is significantly higher than those of others (e.g. in area A or B), it would be confident to associate the MT with this node. The MT could stop monitoring signals from other nodes until it enters an uncertain area, so as to save energy and reduce feedback overhead. Besides node selection, the database also provides location dependent coherence bandwidth (roughly an inverse of the delay spread value) to the BS. For example, the residential area C has low coherence bandwidth because of its rich scattering environment, while the park area D is the opposite. Aided with this information, the MT is required to operate in subband mode in area C, to feedback multiple CSIs characterizing the frequency-domain fluctuations. While wide-band mode, with one compressed CSI for the entire frequency band, is adopted in area D. In the absence of location information, the appropriate choice of wide-/sub-band mode can not be achieved unless some resources are spent on learning the environment. The signalling overhead of MT positioning is much less than that for CSIs, considering the low spatial resolution requirement, the practical constraints such as road boundaries, and the possibility of exploiting users’ mobility patterns. The database can be constructed using trial field-test data, accumulated user measurements, or propagation models. The proposed mechanism is applicable not only to relay networks but also in other networks having cooperative multiple access points, exploiting an accessible database managing the user location as well as location dependent channel information.

B. Location Aided Relay Node Planning Employing fixed RNs in dense population areas allows enhancing the cellular system capacity. The locations for installing a RN usually need sufficient power supply, Light-ofSight (LoS) connection with the closest BS, etc. Despite these constraints, optimizing RN locations according to spatial data demand distribution is crucial to the achievable performance. Taking advantage of today’s modern smartphones and their location awareness, we propose a new scheme to obtain the spatial data demand distribution of a certain area, and to optimize the location of relay nodes accordingly [3]. More explicitly, in the network planning phase, the BS and ESMLC take a period of time (e.g. weeks) to learn the spatial user distribution by periodically requesting and recording the precise positions of its connected MTs, from which user mobility patterns could be obtained. In the meantime, the BS monitors and records the associated MT traffic demand, so as to derive user data consumption patterns. Combining these two patterns, one can model the spatial distribution of a certain area’s traffic demand. Based on this knowledge, optimal locations for installing RNs can be selected from a candidate set of positions using linear programming. As an example scenario, Fig. 2 (left) shows a non-uniformly spatially distributed downlink traffic demand in a square shaped area, which is constructed using a simple ”home-officehome” mobility pattern and assuming every MT consumes equal amount of data. Areas denoted in brighter grey tones demand large volume of data service, while areas denoted in darker tones require smaller volume. For simultaneously satisfying all downlink data demand, using the central BS alone requires a 320 MHz frequency band under the assumption of typical LTE-A parameters in an urban outdoor environment. As demonstrated in Fig. 2 (right), the required bandwidth reduces from 320 to 160 MHz using 2 additional relays placed in high-demand areas, which achieves 160 MHz (50%) bandwidth reduction. An additional 20 MHz frequency resource reduction can be achieved by employing 5 more relay nodes. In future work, this mechanism could be extended to model real-time spatial traffic demand distribution, based on which it would be possible to further dynamically optimize the resource utilization via power adaptation, relay node activation/deactivation, etc.

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C. Location Based MU-MIMO Downlink In the Multi-User (MU) Multi-Input Single Output (MISO) downlink (DL), all zero-forcing (ZF) can only done by the Tx. In MU MIMO however the ZF can be shared between Tx (BS) and Rx (MT). All possible distributions of the ZF task between Tx and Rxs lead to many possible local optima of the sum rate at high SNR, hence providing potential for improved performance while complicating the task of Tx/Rx design. Assume now that in the multipath channel for any user, one of the paths is the LoS path which is known by the BS (location aided). The situation that arises now is similar to chip equalization in the 3G downlink: due to the synchronicity of the downlink, 3G systems use CDMA with orthogonal codes such that a simple correlator at the Rx would suffice to suppress all intracell interference. This ideal scenario is perturbed by the multipath propagation channel whose frequencyselectivity perturbs the orthogonality of the spreading codes. However, since in the downlink from the BS to a particular user all intracell signals pass through the same channel of that user, it suffices for the user to equalize that channel to restore the code orthogonality and to allow a correlator to suppress the interference. In Spatial Division Multiple Access (SDMA), the temporal spreading of CDMA is replaced by spatial filtering at the BS. This spatial filtering is based on the hypothesis of a LoS channel. Hence, for the reception at the user through the LoS path, all interference will be supressed. But the interference arrives at the user through the multipath components also. However, regardless of the beamforming employed at the BS, all interference received by a user passes through the same multipath components of the channel of that user. Now, if the user has as many Rx antennas as number of (distinct) multipath components, the user can employ Rx spatial filtering to suppress all paths, except for the LoS path, so that the MISO cascade of MIMO channel and Rx only contains the LoS path. Combined with the LoS based BF design, this allows to suppress all interference. For the previous reasoning to work, it would have been sufficient (in terms of Degrees of Freedom (DoF)) that the Bs knows any vector in the row space of the MIMO channel, but clearly the LoS path is typically much stronger than the other paths. Hence the knowledge of the LoS path leads to better performance at finite SNR. When there is no LoS path, it suffices to use another path, preferably the strongest path. Whereas the LoS path can be computed on the basis of only the user position (and a calibrated antenna array), in case another (and hence single- or multi-bounce) path needs to be used, this will typically require a database containing the information of the DoA of the strongest path, as a function of the position of the user. Related work appears in [6], [7] where a not so rich propagation environment leads to subspaces (slow CSIT) for the channel vectors so that the fast CSIT can be reduced to the smaller dimension of the subspace, which is especially crucial for Massive MIMO. One remark is in order here about antenna spacing. For the purpose of DoA estimation, and considering a uniform linear array (ULA) of antennas, it is generally considered

that an antenna spacing of λ/2 (half a wavelength) is good. However, for the purpose of SDMA, in which we would like the antenna array responses between different angles to be easily orthogonal, it is preferable that the antenna spacing is larger. Indeed, the larger the antenna spacing, the larger the number of angles within a sector for which the array response is orthogonal to the array response at a given angle in the same sector. This multiplicity of ”orthogonal” angles on the other hand leads to ambiguities in the DoA estimation problem. In the case where the DoA is not estimated from received signal data but is computed on the basis of the position, these ambiguity problems are irrelevant and then antenna spacing should indeed be as large as possible (although not too large to invalidate the far field and narrowband assumptions). D. Location Aided Synchronization In order to achieve high service coverage, terrestrial mobile communication systems are based on a grid of base stations, where each base station is serving mobile terminals located in the surrounding area, the cell. In order to use the available spectrum efficiently, such systems usually target a frequency reuse factor of one. Adjacent cells are accessing the same resources in time and frequency. At the cell border, downlink signals from adjacent base stations are received with similar power levels. This results in severe interference and makes it extremely difficult to achieve high data rates at cell edges if there is no coordination at all between the serving and interfering base stations. To overcome this problem, concepts like interference coordination, which reduce interference by coordinated resource management at the cell border, have been proposed. Macro diversity methods even exploit the presence of signals received from several adjacent base stations. Such coordinated multipoint (CoMP) transmission technologies require synchronized transmission at the base stations and sufficiently accurate mobile terminal synchronization, especially at cell edges, where CoMP transmission is expected to improve system performance metrics like throughput. In order to improve mobile terminal synchronization at cell borders, macro diversity can be exploited as well. Fig. 3 shows a mobile terminal (MT) located close to the cell edge between three adjacent base stations (BSs). At the MT we receive a superposition of the BS synchronization signals s1 , s2 and s3 . However, these signals arrive at the MT with different signal propagation delays τ1 , τ2 and τ3 . Therefore, we can improve the MT synchronization performance with respect to the serving BS1 if there is information about the interrelation of the synchronization signals’ delays. This information can be inferred from the positions of the BSs and the MT. It is reasonable to consider the BSs positions as known. The MT terminals position might be obtained from a positioning entity using GPS for instance. The accuracy of the MT position estimation as well as knowledge about potential non lineof-sight biases is essential for exploiting the synchronization signal energy of the non serving BS2 and BS3 . A detailed study about achievable gains for CoMP synchronization based on the Cramer-Rao lower bound can be found in [2], [3], [8]. As a rule of thumb we can expect benefit from CoMP

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synchronization if the MT position error is at most of the same order of magnitude as the target synchronization error standard deviation, multiplied by the speed of light. For a target synchronization accuracy of 470 ns, which is about 10 % of the LTE guard interval length, we need a MT position estimation accuracy (including potential non line-of-sight biases) of about 470 ns · 3 × 108 m/s = 141 m. Significant performance improvements can typically be obtained if the diversity order of the signal propagation fading processes are low, as in e.g. Rayleigh flat fading. E. Location-Based Long-Term Power Setting in ICIC In heterogeneous co-channel deployments of macro base stations (MBS) and femto base stations (FBS), inter-cell interference coordination (ICIC) appears as a proper way to secure the MBS traffic. Priority should be put on minimizing the interference created by FBSs on MBSs while maintaining a reasonably high FBS throughput. Besides, due to the high number of FBSs, ICIC minimizing the MBS-FBS signaling exchanges is desirable. In the downlink, the impact of the interference generated by a FBS on mobile terminals served by a MBS (MMTs) depends on the power received by each MMT around the FBS from its serving MBS and surrounding base stations. Based on this received power information, locationbased long-term power setting [9] ensures that the FBS impact on surrounding MMTs is independent of its location in the MBS coverage, as depicted in Fig.4. Using the MMT and FBS location information together with an appropriate georeferenced database benefits to the ICIC power setting by enabling a precise knowledge of received powers at MMTs in a high interference reference zone (HIRZ) surrounding a given FBS. The geo-referenced database is built from MMT reports to their serving MBS, containing received power from neighboring MBSs and FBSs and the MMT location. Upon installation or reinitialization, a FBS transmits its location information to the server maintaining the database, which transfers in response information about MMTs located in HIRZ. This information allows more accurate power setting

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at FBS, compared to the non-location-based approach in which the FBS sets its transmit power without any external knowledge, measuring received powers from neighboring base stations and assuming that they properly approximate received powers at surrounding MMTs. For a reasonable 10% macro spectral efficiency loss compared to the case without FBSs, the location-based approach, even with location errors, largely outperforms the non-location-based approach, especially if the FBS power measurement is erroneous due to the decorrelation between indoor and outdoor shadowing [9]. Indeed, for a medium FBS density of 125 FBS/km2 , the location-based approach with a positioning root mean square error (RMSE) lower than 30 m outperforms the non-location-based approach with a typical FBS power measurement RMSE of 3 dB. Furthermore, the location-based approach has lower sensitivity to errors in wall penetration loss estimation, which is needed in order to evaluate the impact of the FBS outside a building. F. MIMO Interference Channel (IC) with Decoupled Tx/Rx and Location Aided Designs Consider cell edge users in mutually interfering (neighboring) cells. Either uplink or downlink are modeled by the Interference Channel (IC) paradigm. In [10] we study interference alignment (IA) (the number of spatial signal streams for which the interference can be zero forced (ZF’d)) first for the case of rank reduced MIMO channels in which the channel matrices can be written with reduced dimension factors of the form Hik = Bik Aik and then for the case in which we require the design of Tx and Rx filters to be decoupled. Indeed, the big problem of MIMO IFC is that the design of the Tx filter gk at any BS k depends on all the MT Rx filters fi and vice versa, in the ZF conditions fi Hik gk = 0. As a result, for the design of its Tx filter, any BS needs to know the channels from all BSs to all MTs (global CSIT). A decoupled design would in a first instance only require local CSIT (knowledge of the channels from that BS only). In what follows, we shall focus on the LoS limit for considerations of location based processing. Consider an IC (multi-cell) with K cells in which all BS have M antennas and all MThave N antennas. The LoS case is an ultimate reduced rank case and leads to the requirement M +N ≥ K +1 for IA feasibility with a single stream per user. In the MISO or SIMO cases this becomes M ≥ K or N ≥ K resp. The meaning of M + N ≥ K + 1 is: (M − 1) + (N − 1) ≥ K − 1: that each BS performs ZF towards M − 1 MTs. As a result, each UE still receives interference from (K − 1) − (M − 1) cross

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links but with its N antennas it can ZF N − 1 streams while receiving its own stream. In the decoupled approach, in which the conditions fi Hik gk = 0 = fi Bik Aik gk get replaced by either fi Bik = 0 or Aik gk = 0, the design of any Tx only depends on the Tx side channel factors Aik of the channels connected to it and in general even only on a subset of this local CSIT (e.g. in the LoS case, only M − 1 cross link Aik are required to be known for any given BS). In the LoS case, the factors (vectors) Aik are clearly only a function of the positions of the BS and MTs (and the BS antenna array response). In the multipath case, to infer Aik from M T position information, a database is required. Even in the general non-low rank case, Hik = Bik Aik represents the pathwise channel contributions and Aik gk = 0 represents a number of conditions equal to the number of significant paths. However, this augmented number of ZF conditions in a propagation pathwise processing approach can easily be handled in Massive MIMO. III. L OCATION A IDED MANET S A. Location Assisted Handover for Heterogeneous Networks The widespread deployment of Wifi hotspots in urban areas constitutes a potential possibility for offloading mobile users’ data from cellular network connections to Wifi networks. Such offloading techniques will most likely be needed, given the expected quadratic growth of mobile data in the coming years. A key challenge in getting cellular users to use Wifi hotspots is to ensure that their experience is as seamless as possible. Currently, mobile devices do not provide very seamless handover experiences, partly because the handover is determined only from the observed signal strengths and threshold values. In this WHERE2 contribution, which is described in detail in [4], we add the dimension of users’ geographical movements to the handover decision and show how the optimal handover sequence for a finite time horizon can be computed efficiently. An example scenario is shown in Fig. 6, where a mobile user moves through the range of three Wi-Fi access points (APs). Here, a conventional signal strength based handover algorithm would most likely connect first to B, then when the signal becomes too weak it hands off to A and then finally C. The location based algorithm uses movement prediction and knowledge about available networks to foresee that it is better

B

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Fig. 6. Example scenario: which of the Wi-Fi APs A, B or C to connect to along the MT trajectory?

The operation of the location based algorithm is based on the assumption that the performance (e.g. throughput) a mobile user can expect from nearby networks can be estimated for the mobile’s predicted movement trajectory. In practice this is determined not only by the APs geographical location, propagation conditions and the mobile user’s movement trajectory, but also by the interference and capacity reductions in APs and BSs that data transmissions from other users cause. As the work in [4] has only considered the single mobile user handover problem, future work should look into how interference to/from and resource allocations for other users can be incorporated efficiently into the handover decision process. B. Location Aided MANET Security When deployed in uncontrolled environments, MANETs are particularly vulnerable to different threats. But the so-called wormhole or relay attack is one of the most devastating. A wormhole is a direct, high-speed communication link between two distant malicious nodes, which use it to transparently forward data packets from one point to another. Wormholes distort the network topology and jeopardize location and neighbor discovery protocols, because they make distant nodes appear as local for a compromised node trying to obtain its own position or looking for its neighbors [11]. Wormhole attacks challenge cryptographic protocols because the wormhole nodes act as simple relays and do not manipulate the information contained in the packets. Hence the most effective procedures to detect them are based on looking for inconsistencies in measurements performed at the physical layer level. For instance, in [12], [4] we present a general framework called Detection of Wormhole Attacks using Range-Free (DWARF) methods, which consists of a set of strategies based on checking the received signal strength

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IV. L OCATION A IDED C OGNITIVE R ADIO (CR) A. Cooperative Spectrum Sensing and Localization using Compressed Sensing (CS) In [13] we propose to fuse two main enabling features in CR systems: spectrum sensing and location awareness in

BP OMP CoSaMP

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(RSS) values measured by the nodes interacting in the localization and/or neighbor discovery procedures; these approaches perform nonparametric statistical inferences and, therefore, are not tied to any particular radio propagation model (i.e., they are range-free procedures). Two different DWARF schemes are briefly described below: 1) Simultaneous Localization and Attack Detection: In this mode of operation, a set of trusted anchor nodes (ANs) broadcast their positions; then, every other network node tries to obtain a nonparametric estimation of its own location using the RSS values of its links with the ANs. However, if a compromised node is under a wormhole attack, it will not receive packets directly from some of the anchors, but from a neighbor wormhole node instead, thus resulting in significant errors in the estimated position. To detect such attack, the node obtains a measure of the “quality” of the computed position estimation and uses it as a test statistic to validate the localization process. 2) Attack Detection after Localization: Once a node has obtained its (possibly wrong) position, it begins to broadcast its estimated coordinates, and then asks the ANs to check their accuracy using RSS measurements. To detect a wormhole attack, the ANs use those RSS values to validate the node position using a nonparametric test. Both nonparametric wormhole attack detection strategies have been tested and compared with parametric approaches based on the likelihood ratio test (LRT) using simulated measurements provided by a database developed in WHERE2 [4]. Some results are represented in Fig. 7, showing the attained probability of detection for a fixed probability of false alarm (PFA) and different number of ANs. We observe that the parametric LRT-based approach for simultaneous wormhole detection and localization performs better than the nonparametric procedure, although the differences between them tend to disappear as the number of ANs increases. On the other hand, we can see that the situation is reversed if we perform detection after localization, because parametric methods rapidly degrade in the presence of significant shadowing effects.

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Fig. 8. Joint localization and spectrum sensing simulations: CR system topology with five primary users and three secondary users and impact of sparsity on spectrum reconstruction MSE at 0 dB SNR for 3 compressive sensing methods: Basis Pursuit (BP), Orthogonal Matching Pursuit (OMP) and Compressive Sampling Matching Pursuit (CoSaMP).

a single compressed sensing based formalism. In this way we exploit 2D sparse characteristics of the primary units to be detected, both in terms of spectrum used and location occupied. The compressed sensing approach also allows to overcome hardware limitations, in terms of the incapacity to acquire measurements and signals at the Nyquist rate when the spectrum to be scanned is large. Simulation results in Fig. 8 for realistic network topologies and different compressed sensing reconstruction algorithms testify to the performance and the feasibility of the proposed technique to enable in a single formalism the two main features of cognitive sensor networks. Nevertheless, the approaches in [13] are just a first attempt at exploiting double sparsity, in spectrum and space, leaving room for improvements. B. Location based Improved Spectrum Resource Use in CR This section explores the idea of opportunistically reusing spectrum resources assigned to a primary network by a secondary network that has information about the locations of the nodes. In order to achieve this objective, smart secondary devices scan the band and cooperatively decide which are the most appropriate frequencies to use in their communications, taking into account positioning knowledge and applicable restrictions (such as interference to primaries, connectivity, energy consumption, etc.). 1) Cooperative detection and identification of primary users: exploiting location information by a network of secondary users (SUs) to cooperatively detect activity of the primary users (PUs) and identify which of the PUs is transmitting at a given time or frequency. Both distributed and centralized schemes use estimations of the received power at the SUs to detect a PU transmission; once detected, a procedure to identify the active PU is triggered. The detection phase is formulated as a binary hypothesis testing problem, while the PU identication is considered as a multiple hypothesis testing (i.e. pattern classication) problem. A fully detailed formulation, models and extensive results can be found in [14]. As an example, Figures 9(a), 9(b) illustrate the minor differences in identification performance between the distributed and centralized schemes when applied to a non-LOS, multipath

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scenario. It is also remarkable that the curves of probability of identification tend to limits less than 1 as the SNR increases, an effect attributable to the impredictable nature of shadowing losses that frequently confuse the PU identification process when the number of cooperating SUs is low. 2) Optimal channel allocation for secondary users: all information concerning PUs (namely, locations and activity) is exploited to establish an optimized allocation of available radio channels to SUs, by reusing frequencies as much as possible without causing interferences with PUs. After successive repetitions of the detection and identification procedures referred to above for every allowable frequency band, the SUs reach an agreement concerning the PU use of the spectrum resources. Then, they take into account available location information and coverage maps to optimally allocate frequency channels to the SUs so as to maximize a predefined quality criterion. The figure of merit we have considered is a linear combination of the following desired features, a) Require full connection, b) Penalize the energy consumption, c) Reward reusing the primary’s frequencies, and d) Reward a high number of average neighbors. Finally, after applying the algorithm, every pair of nodes has decided which frequency to use, reusing frequencies of the primary nodes but not interfering them. The coverage of secondary users is optimized according to the mentioned figure of merit achieving a significant data rate gain in comparison EUR/IFX Spatial where Interweave TDD Cognitive Radio Systems 3 with the case location information is Brussels not available [5]. 1 S-BS1

h11

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Underlay Cognitive Radio (CR) is a popular CR design problem, in which a secondary network is allowed to operate in the presence of a primary system with interference limits at the primary Rxs, and this without any collaboration or even awareness of the primary system. To make underlay feasible, the exploitation of position information to determine attenuations from secondary transmitters to primary receivers constitutes probably the only realistic approach. In the MultiInput Single Output (MISO) case, the location information could also be translated to Direction of Departure (DoD) based ZF beamforming, esp. in the LoS case. In [5] we consider multiple parallel interfering secondary links as in Fig. 10, in which the communication can be optimized via the use of transmit beamforming (BF) and power control. We study a CR MISO Interference Channel (IC) with K secondary user (SU) MISO BS-MT pairs and an additional set of L single-antenna Primary Users (PUs). This setting is relevant in the case of a network of two or more cognitive small cells, that represent the SU system, where each small cell BS is serving a single user in the time-frequency unit of interest. The small cells are deployed in the same area of a macro cell (primary system) and they want to coexist with L mobile PUs that belong to one or more macro cells. In [5] the objective is to find the set of BF vectors that maximize the Weighted Sum Rate (WSR) of the secondary IC network, under transmit (Tx) power constraints for the secondary BS, and interference level constraints at the PU Rxs. The critical ingredient in such an underlay design is to realistically guarantee the satisfaction of the interference levels at the PU Rxs. For this, the attenuation of the links from SU Txs to PU Rxs needs to be known, and to infer this on the basis of the information of the respective locations appears to be one of the few realistic possibilities. The alternative problem formulation of SINR balancing is also considered in [5], to minimize sum transmit power subject to SINR guarantees on the SU links, and of course PU intererence level upper bounds. Spatial extensions for the CR paradigms of overlay (which corresponds to section II.F), underlay and interweave have been introduced in [5], in which the Rxs are also equipped with multiple antennas. E.g. ZF (IA) feasibility for the MIMO underlay IC has been investigated. In spatial interweave, the SU has to ZF to all primary Rx antennas or Rx filter outputs. In spatial underlay, the primary Rx uses its excess antennas to cancel SU interference. In spatial overlay, not only the primary Rxs but also the primary Txs coordinate their beamforming with the secondary system.

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Fig. 10. links).

MISO underlay CR IC system (all slanted lines are interfering

D. Distributive Power Allocation for Multi-SU CR In a conventional ALOHA type random access system, simultaneous transmission by two or more users will lead to unresolvable collisions, which seriously affect system throughput. We developed a random power control (RPC) scheme that leads to significantly improved throughput [15]. With RPC, each user randomly selects its transmitted power level according to a certain distribution. Our objective is to maximize the probability to resolve collisions using successive

8

interference cancelation (SIC). We studied the RPC techniques for multiple-input multiple-output systems. We show that system performance can be enhanced based on partial channel information. In particular, the slow fading factor of each user can be used for throughput maximization [5]. In practice, the knowledge of the (attenuation and) slow fading factors at the users can be obtained from their location information (i.e., through the use of databases). Intuitively, a user in a good location (i.e., a larger average channel gain) can expect a high received power level and vice versa, so that power consumption can be minimized. 1

RPC, 2 users

•

Location aided multi-user systems (Broadcast and Interference Channel, Cellular and HetNets): the CSIT issue a very hot non-trivial topic, leading to a proliferation of schemes: Blind IA, Ergodic IA, Retrospective IA, MAT, etc. Also the coupled Tx/Rx design is highly non-trivial. Location aided alternative: pro: replaces most CSIT needs, simplifies (enormously) Tx/Rx design, allows to handle interference strength (mostly ignored so far, ”topological” interference management), con: may not be well applicable to any environment (requires dominant propagation paths), but appears to be well matched to Massive MIMO.

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Fig. 11. Throughput comparisons of the RPC and conventional ALOHA schemes. Each transmitter is equipped with 2 antennas, so is the common receiver. The (3, 6, 32, 4) spatially coupled LDPC code is employed with QPSK modulation. The channel consists of Rayleigh fading and lognormal shadowing with standard deviation σ = 8.

The proposed scheme is suitable for a CR system in which the SUs are only allowed to access the channel opportunistically. Due to the opportunistic nature, decentralized power control is very desirable, as setting up coordination among the secondary users may not be practical. Fig. 11 compares the throughputs of the proposed RPC and the conventional ALOHA schemes under the same sum-average power constraint. We can clearly see the throughput gain of RPC which exploits the location aided CSI. V. C ONCLUSIONS The work in the WHERE2 project has allowed to identify a number of genuine location aided wireless communications opportunities (non exhaustively): • Selection of relays: non location aided alternatives represent very high signaling overhead. In the usual case of fixed relays, their position as well as that of base stations is known and fixed, only the MT position is a varying parameter. • Location aided power control to minimize interference: e.g. ICIC with very convincing results. • Location aided underlay cognitive radio: location information allows to predict the attenuation to and hence the interference level at primary locations (if known). • Location aided random access schemes: illustrates how location aided slow fading statistics knowledge can be useful.

[1] “WHERE2 Project,” http://www.kn-s.dlr.de/where2/index.php. [2] A. Dammann, G. Agapiou, J. Bastos, L. Brunel, M. Garc´ıa, J. Guillet, Y. Ma, J. Ma, J. J. Nielsen, L. Ping, R. Raulefs, J. Rodriguez, D. Slock, D. Yang, and N. Yi, “WHERE2 location aided communications,” in Proc. European Wireless (EW), Guildford, UK, Apr. 2013. [3] “Final: Coordination and cooperation between network nodes,” Tech. Rep., 2013, FP7-ICT-2009-4 WHERE2 Deliverable D3.4. [Online]. Available: http://www.ictwhere2.eu/documents/Deliverables/Deliverable-D3.4.pdf [4] “Final: Realization and usage of geo-location based clustering and mobile relaying,” Tech. Rep., 2013, FP7-ICT-2009-4 WHERE2 Deliverable D3.5. [Online]. Available: http://www.ictwhere2.eu/documents/Deliverables/Deliverable-D3.5.pdf [5] “Final: Location-aided PHY/MAC layer design for advanced cognitive radios,” Tech. Rep., 2013, FP7-ICT-2009-4 WHERE2 Deliverable D3.6. [Online]. Available: http://www.ictwhere2.eu/documents/Deliverables/Deliverable-D3.6.pdf [6] H. Yin, D. Gesbert, M. Filippou, and Y. Liu, “A coordinated approach to channel estimation in large-scale multiple-antenna systems,” IEEE J. on Sel. Areas in Comm’s (JSAC), Special Issue on: Large Scale Antenna Systems, Jan. 2013. [7] A. Adhikary, J. Nam, J.-Y. Ahn, and G. Caire, “Joint Spatial Division and Multiplexing,” 2012, arxiv1209.1402. [8] A. Dammann and R. Raulefs, “Exploiting Position Information for Synchronization in Coordinated Multipoint Transmission,” in Proc. 77th Vehicular Technology Conf. (VTC Spring), Dresden, Germany, Jun. 2013. [9] J. Guillet, L. Brunel, and N. Gresset, “Downlink femto-macro icic with location-based long-term power setting,” in Proc. IEEE CAMAD, Barcelona, Spain, Sept. 2012. [10] W. Guibene and D. Slock, “Degrees of Freedom of Downlink Singleand Multi-Cell Multi-User MIMO Systems with Location based CSIT,” in Proc. IEEE Veh. Tech. Conf. (VTCspring), June 2013. [11] P. Papadimitratos, M. Poturalski, P. Schaller, P. Lafourcade, D. Basin, S. Capkun, and J.-P. Hubaux, “Secure neighborhood discovery: a fundamental element for mobile ad hoc networking,” IEEE Communications Mag., Feb. 2008. [12] M. Garc´ıa-Otero and A. Poblaci´on-Hern´andez, “Secure Neighbor Discovery in Wireless Sensor Networks Using Range-Free Localization Techniques,” Int’l Journal of Distributed Sensor Networks, 2012. [13] W. Guibene and D. Slock, “Cooperative Spectrum Sensing and Localization in Cognitive Radio Systems using Compressed Sensing,” Hindawi Journal of Sensors, July 2013. [14] P. Belanovic, S. Macua, and S. Zazo, “Location-aided distributed primary user identification in a cognitive radio scenario,” in IEEE Conf. Acoustics, Speech and Signal Processing (ICASSP), 2012. [15] C. Xu, L. Ping, P. Wang, S. Chan, and X. Lin, “Decentralized power control for random access with successive interference cancellation,” Selected Areas in Communications, IEEE Journal on, vol. PP, no. 99, pp. 1–10, 2013.

A.2

Adaptive location-aided cooperative relaying

This appendix includes the following papers, already published or accepted for publication: • N. Yi, Y. Ma, and R. Tafazolli, ”Incremental decode-forward relaying over asymmetric fading channels: Outage probability and location-aided relay selection”, in IEEE SSP´11, pp. 181-184, 2011. • Y. Ma, R. Tafazolli, Y. Zhang, and C. Qian, ”Adaptive modulation for opportunistic decode-andforward relaying”, IEEE Trans. Wireless Commun., 10(7):2017-2022, July 2011. • C. Qian, Y. Ma, and R. Tafazolli, ”Relay selection for modulation-adaptive opportunistic df relaying using mixed channel knowledge”, In Proc. IEEE WCNC, pp. 2429-2433, April 2012. • C. Qian, H. Chen, Y. Ma, and R. Tafazolli, ”A novel adaptive hybrid-ARQ protocol for machineto-machine communications”, in IEEE VTC’13 Spring, Dresden, Germany, June 2013. • N. Yi, Y. Ma, and R. Tafazolli, ”Joint rate adaptation and best-relay selection using limited feedback”, IEEE Trans. Wireless Commun., 12(6):2797-2805, June 2013. • C. Qian, Y. Ma, and R. Tafazolli, ”On Spectral Efficiency of Using Relay with Opportunistic Channel Assignment”, in Proc. IEEE GLOBECOM’13, December 2013.

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2011 IEEE Statistical Signal Processing Workshop (SSP)

INCREMENTAL DECODE-FORWARD RELAYING OVER ASYMMETRIC FADING CHANNELS: OUTAGE PROBABILITY AND LOCATION-AIDED RELAY SELECTION Na Yi, Yi Ma and Rahim Tafazolli Centre for Communication Systems Research University of Surrey, UK, GU2 7XH. e-mail: {n.yi, y.ma, r.tafazolli}@surrey.ac.uk ABSTRACT This paper presents two contributions towards incremental decode-forward relaying over asymmetric fading channels. One is about the outage probability of incremental relay network accommodating i.n.d. cooperative paths. Our contribution is mainly on formulating a closed-form of the outage probability through employment of the Inverse Laplace Transform and Eular Summation. The other is about the proposal of transmit-power efficient relay-selection strategy through exploitation of the relationship between position of relays and the outage probability. Index Terms— Asymmetric fading channel, decodeforward, incremental relay, location, outage probability. 1. INTRODUCTION Incremental relaying (IR) refers to a special distributed retransmission protocol, which combines the principle of Type II HARQ with multi-hop communications. By adapting the transmission redundancy, it can effectively improve the energy and spectral efficiencies in comparison with other fixed relaying protocols. The first IR concept was introduced in [1], which combined the request-based re-transmission scheme with the amplify-forward (AF) relaying protocol. The AF-IR scheme has been recently extended from the single-relay scenario to the multiple-relay scenario combined with adaptive protocols [2]. In [3], the AF-IR scheme was combined with the best-relay selection policy in order to achieve the energy optimality. Moreover, the IR scheme can be combined with other classical relaying protocols such as decode-forward (DF) and compress-forward (CF). For example in [4], the performance of outage probability and bit-error-probability (BEP) has been studied for single-relay networks in Rayleigh fading channels. This work has been extended to multiplerelay networks with the consideration of best-relay selection and independent non-identical Rayleigh channels [5]. Those This work has been performed in the framework of the FP7 projects ICT248577 C2POWER and ICT-248894 WHERE2 (Wireless Hybrid Enhanced Mobile Radio Estimators - Phase 2) and ICT-257626 ACROPOLIS, which are partly funded by the European Union.

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research outputs, in particularly closed-form formulas, serve as an important role in the design of relay networks. The focus of this paper is mainly on the outage probability of the DF-IR scheme, where communication links experience asymmetric fading mixed with Rayleigh and Rician distribution. This work is motivated by the fact that practical relay networks often operate in complex mobile environments. For example communications between closely located devices may experience Rician channels due to the line-ofsight (LoS) radio propagation, while communications without the LoS propagation path may experience Rayleigh channels. Recent research progress towards the IR scheme in the asymmetric channel includes Katz and Shamai’s work in [6] about the mixture of Rayleigh and Gaussian channels as well as those contribution (e.g. [7]-[8]) about the fixed AF scheme over dual-hop asymmetric fading channels. Instead, our contribution is mainly in two folds: 1) we intend to find the closed-form of outage probability for two types of asymmetric channels as depicted in Fig. 1. The complex mathematical problem is solved in an approximate form through employment of the Inverse Laplace Transform and Eular Summation; 2) A new relay-selection policy is proposed for the DFIR network. The proposed scheme can improve the transmitpower efficiency through exploitation of the relationship between position of relays and the outage probability. 2. DF-IR MODEL AND PROBLEMS 2.1. Brief Introduction of DF-IR Protocol Fig. 1 illustrates a DF-IR network accommodating one source (S), one destination (D), and many relays (Rs). The communication procedure consists of two phases. At the first phase, the source sends signals to the destination at the rate of Rs . Due to the broadcasting nature of wireless communications, there are several relays who can successfully re-produce the original signals. Those are called well-informed relays (WIRs) in this paper. At the second phase, WIRs sequentially retransmit the original signals only when a negative acknowledge (NAK) is received from the destination. Otherwise, the source will send new signals. In the case of NAK, the des-

3. KEY RESULTS OF OUTAGE PROBABILITY The outage probability often refers to the probability of an event when the transmission rate exceeds the channel capacity [9]. Using the maximum-flow min-cut principle, the outage probability of DF-IR, denoted by Pout , can be generally computed by h i h i Pout = Pr γ (SD) < γt Pr γ (MRC) < γt |γ (SD) < γt , (1) where γ (SD) denotes the instantaneous signal-to-noise ratio (SNR) of the S-D link, γ (MRC) the effective SNR after the MRC at the destination, and γt the SNR threshold which has a direct relationship with the transmission rate Rs (see Sec. 2.1). We assume the DF-IR network accommodating M relays in total, and N out of which are WIRs. The outage probability (1) can be expressed by

Fig. 1. Two types of asymmetric fading channels. (a) Type I SD/SR (Rayleigh) and RD (Rician); (b) Type II - SD/RD (Rayleigh) and SR (Rician).

tination employs the maximum-ratio combine (MRC) of all signals received at both phases to attain the achievable cooperative diversity gain. It is worthy to note that the above description shows only a special paradigm of the DF-IR scheme. A more general case would be the combination of DF-IR and coded cooperation, which would considerably complicate the analysis of outage probability. In this paper, our contribution is on the re-transmission based paradigm of the DF-IR scheme.

h

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=

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Type I: The S-D link and all S-R links obey the Rayleigh distribution, while all R-D links obey the Rician distribution. This model is suitable for the scenario where relays have LoS links with the destination and NLoS links with the source.

where Φi denotes the set of WIRs, Φi the complementary set of Φi , γ (SRα ) the SNR at the α th relay, and γ (RDα ) the SNR of the corresponding relay to the destination link. Next, we will use the equation (2) to analyze the outage probability of Type I &II asymmetric channels.

Type II: The S-D link and all R-D links obey the Rician distribution, while all S-R links obey the Rayleigh distribution. This model is suitable for the scenario where relays have NLoS links with the destination and LoS links with the source.

3.1. Type I Asymmetric Fading Channel In this channel, all S-R links experience the Rayleigh fading. We can readily obtain the terms A and B by following the derivation in [9] µ ¶ Y γt exp − (SR ) , (6) A = γ α α∈Φi ¶¶ µ Y µ γt , (7) 1 − exp − (SR ) B = γ β

Surely, there are several other combinations of Rayleigh and Rician channels. We would argue that those channel models can be easily extended from the above two types.

β∈Φi

2.3. Research Problems and Challenges

where γ stands for the average SNR. In (5), the term γ (MRC) is the sum of multiple random variables obeying two different distributions. We use the inverse Laplace Transform to compute the term C as à ! Y 1 C = L−1 M (SD) (−s) Mγ (RDα ) (−s) (8) s γ

The key research issue is to find the outage probability of multiple i.n.d. cooperative paths. This issue once resolved can easily enable the location-aided relay selection strategy. The challenges are mainly in two folds: 1) randomness of the number of WIRs; 2) combination of multiple Rayleigh and Rician random variables.

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where L−1 denotes the inverse Laplace transform, Mγ (s) the moment generating function (MGF) associated with γ. Employing the Eular Summation [9, Appendix 9B], (8) is computed as C

=

as (proof abbreviated) µ ¶ X ¶ µ γt γt C = 1 + F exp − (SD) + H exp − (RD ) , α γ γ α∈Φi (17) where

L µ ¶ G+l 2(−L) eD/2 X L X (−1)g γt l g=0 θg l=0 ´ ³    Mγ (MRC) − D+2πgj 2γt + E(D) + E(G, L), (9) < D+2πgj  

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α∈Φi

2γt

where Pt . 2) Criterion II: Since the statistic channel knowledge is available, the relays can be ordered according to the average SNR of S-R links, then the best k relays with better average SNR are included in S for the second stage of the selection process. After determining S, all the relays in S send their instantaneous S-R channel quality knowledge to the destination in the second stage, meanwhile training symbols from those relays are sent to the destination to provide the instantaneous channel quality information of R-D links to the destination to perform the best-relay selection and adaptive modulation. These two criteria introduce a problem that the actual best relay with the highest instantaneous channel quality may not be included in S in the first stage of the process then be missed in the second stage, which results in a loss of performance. Thus an important metric as the probability of missing the best relay (PMBR) is introduced to analyse the two selection criteria. Then the problem addressed in (6) can be developed into ηr = arg max{ηi } s.t. BERup i ≤ BERtarget and PMBR = Cm , (9) where Cm ∈ [0, 1] is a constant value determined by the system set-up such as the values of the threshold and the size of S. For Criterion I, the advantage is that the size of S changes dynamically according to the channel quality, which is more efficient in relay selection compared with Criterion II with a fixed size of S. On the other hand, Criterion II can significantly reduce PMBR by setting the size of S to a reasonable number. B. Statistic of The Candidate Set S The first stage of the proposed relay selection scheme is to determine the candidate set S, so it is important to obtain

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the statistic behaviour of S in terms of c.d.f. and p.d.f.. These results can be used to analyse the system spectral efficiency and signalling overhead. Although the proposed scheme is applicable to various channel models, to make analysis more tractable, it is assumed that each device-to-device link experiences frequency-flat Rayleigh-fading channel. Let γab and γ¯ab denote the instantaneous and average received SNR of the a-b link respectively, then γab follows the exponential distribution, with common p.d.f. and c.d.f. given as in [8]. The condition in (8) then can be expressed as γth

Pr(γSRi > γth ) = 1 − FγSRi (γth ) = e

− γ¯

SRi

> Pt ,

where i1 , i2 , . . . , iN −1 ∈ {1, 2, . . . , N } − l. Thus the probability that the ith relay has the best S-R link channel quality can be expressed as Z ∞Z x (15) Pi = fZr1 (z)fγSRi (x)dzdx, 0

where fγSRi (x) is the p.d.f. of ith S-R link with mean γ¯SRi . For Criterion I, as γSD and γSRi are independent, the probability of ith relay being the best relay and included in S can be simply expressed as multiplication of (11) and (15). Finally PMBR can be written as

(10) PMBR = 1 −

where FγSRi denotes the c.d.f. of γSRi . According to (7) and (10), the probability of the ith relay Ri being in the candidate set S can be expressed as Pr(Ri ∈ S) = FγSD (−

γ ¯SR i γ¯SRi Pt ln ) = 1 − e C γ¯SD C

lnPt

.

(11)

Let |S| denote the number of relays in S, defined by |S| = card{k, such that Pr(γSRi k ≥ γth ) > Pt }, where card is the cardinal operator. When |S| = 0, the system works in DT mode. When |S| > 0, the system will perform the selection as (6) within the relays in the set of S only. Then the probability that no relay being selected in the first stage and the system switches to DT mode can be given as PrDT =

N Y

n=1

(1 − Pr(Rn ∈ S)),

(12)

where N is the number of relays. In the other hand, the probability that the number of relays in S is not zero and relays participating in the second stage of selection can be obtained PrDF =

−k N X !N
NY k

k=1

n=1

(1 − Pr(Rn ∈ S)) ×

k Y

n=1

0

Pr(Rn ∈ S). (13)

fZr1 (z) =

N X l=1

fl (z)

X

N −1 Y

i1 ,i2 ,...,iN −1 j=1

Fij (z),

(14)

i=1

Pi · Pr(Ri ∈ S).

(16)

Similarly, for Criterion II, PMBR can be expressed as PMBR = k Z ∞Z X 1− i=1

0

(17)

0

N xX

X

fl (z)

N −1 Y

Fij (z)fγSRi (x)dzdx.

i1 ,i2 ,...,iN −1 j=1

l=1

(18)

D. Spectral Efficiency and Signalling Overhead In [6], all channel information needs to be signalled to the destination, which results in a total signalling overhead of 2N +1 frames for every block of information transmitted in the network, where N is the number of relays. With the proposed relay selection scheme, the average signalling overhead can be reduced to ¯ × PrDF + 1, F = 2|S| (19) ¯ is the average number of relays in set S, which can where |S| be expressed as ¯ = |S|

N −k k X Y !
NY k N (1−Pr(Rn ∈ S)) Pr(Rn ∈ S). (20) k

k=1

n=1

n=1

The average spectral efficiency of a point-to-point adaptive modulation system applying L modulation schemes, η, can be calculated as [3]

C. Probability of Missing The Best Relay PMBR can be interpreted as that the relay with the best instantaneous S-R channel quality is not included in S. The following results for the p.d.f. of the order statistic for a set of independent random variables can be used in determining the statistics of PMBR. Let X1 , X2 , . . . , XN denote N independent random variables. The corresponding order statistic are obtained by arranging them in a non-increasing order, denoted by Xr1 , Xr2 , . . . , XrN . Thus, Xr1 denote the largest of all the N variables. Let fj (z) and Fj (z) denote the p.d.f. and c.d.f. of random variable Xj . The p.d.f. of maximum statistic, Z = Xr1 , is then given by [9]

N X

η=

L X

(Mn )

log2

n=1

Pn ,

(21)

where Mn is the constellation size of nth modulation scheme and Pn is the probability that nth modulation scheme is chosen for transmission. When the relay comes to help the average spectral efficiency can be rewritten as η=

L X

n=1

ηn Pks Pir ,

(22)

where ηn is the overall spectral efficiency when nth relay is selected, and Pks , Pir are the probabilities that the source and the relay transmit with corresponding rate respectively. Compared with conventional opportunistic relaying system, a loss of performance in terms of spectral efficiency is introduced by missing the best relay in the first stage of

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4

selection. Let ηCSI denote the average spectral efficiency of the adaptive modulation for opportunistic relaying with full channel quality knowledge. Then the average spectral efficiency of the proposed selection scheme can be written as ηAVG = ηCSI · (1 − PMBR). (23)

IV. S IMULATION R ESULTS In this section, computer simulations are carried out to evaluate the performance of the proposed scheme. The benchmark of comparison is the adaptive direct transmission as well as adaptive DF relaying with full channel knowledge. All the channels in the network are modelled as independent Rayleigh block fading channels. The block length is set to be B = 96, BERtarget = 10−3 , Pt = 0.9 and QPSK, 16-QAM, 64QAM, 256-QAM are used for adaptive modulations and relay selection. Experiment 1: The objective of this experiment is to examine the proposed scheme with discrete-rate adaptation for Criterion I. The performance of spectral efficiency for the proposed scheme is illustrated with that of the full channel knowledge scheme. In Fig.1, the system is configured as: Relay 1 is placed at the middle between the source and destination; Relay 2 is placed closer to the source and Relay 3 is placed closer to the destination. This system configuration results in that the average SNR of S-R link to be 6 dB, 12 dB and 2.5 dB higher than that of the S-D link for Relay 1, Relay 2 and Relay 3 respectively. In 1-relay case, only Relay 1 is considered. In 2-relay case, Relay 1 and Relay 2 are used. Fig.1 shows that the performance of full channel knowledge servers as an upper bound. It also can be observed that a looser SNR selection threshold (i.e. C=1) has better performance than that of a tighter SNR selection threshold (i.e. C=2). It is mainly because that a looser selection threshold includes more relays in S than a tighter one, which reduces PMBR. However, more relays in S cause more signalling overhead since more channel knowledge of S-R links need to be sent to the destination. It is illustrated in Fig.2 that the average number of relays selected in S is reduced as the selection threshold increases. A reduction of signalling overhead can be easily observed from Fig.2, compared to the conventional adaptive modulation relay network. With Pt being set to 0.9, the signalling overhead can be reduced by half. Also, it is shown by the simulation results that there is a trade-off between the signalling overhead and spectral efficiency, which is affected by the selection thresholds. Higher threshold further reduces the signalling overhead meanwhile increases the loss in spectral efficiency.

Spectral Efficiency (Bits/s/Hz)

3 2.5 2 1.5 1 0.5 0

0

2

4

6

8

10 12 SNR (dB)

14

16

18

20

Fig. 1. Spectral efficiency of the modulation-adaptive cooperation scheme with relay selection Criterion I as a function of the average SNR of S-D link. The average SNR of the S-R links are 6 dB, 12 dB and 2.5 dB higher than the S-D link respectfully. 10 2 relays 3 relays 10 relays

9

Average Number of Relays

Referring to (11), it is shown that the value of |S| depends on the set up of thresholds γth and Pt . If γth and Pt are increased, the size of S will be decreased which leads to a reduction in signalling overhead. However, the pay is that with decreased number of relays in S, the probability of missing the best relay increases and causes more loss in the spectral efficiency. In the next section, the simulation results show the trade-off between the overall spectral efficiency and the signalling overhead.

Adaptive DT 1−relay Partial CSI C=2 2−relay Partial CSI C=2 3−relay Partial CSI C=2 1−relay Partial CSI C=1 2−relay Partial CSI C=1 3−relay Partial CSI C=1 1−relay full CSI 2−relay full CSI 3−relay full CSI

3.5

8

7

6

5

4

3

2

1

0

0.1

0.2

0.3

0.4

Pt

0.5

0.6

0.7

0.8

0.9

Fig. 2. Average number of relays used for relay selection criterion I as a function of the threshold probability, with totally 2, 3 and 10 relays in the system.

Experiment 2: The objective of this experiment is to examine the proposed scheme for Criterion II, the total number of relays is 10 and the average SNR of S-D link is fixed to 10 dB. The relays are ordered in a decreasing manner according to the average SNR of S-R link, such that γ¯1 > γ¯2 > · · · > γ¯N . All the relays are placed in different positions close to either the source or the destination. In such a scenario, the average S-R SNR increases in the step of 1 dB for differently placed relays and the minimum average SNR of S-R γ¯N varies from 0 dB to 20 dB. Fig.3 shows the spectral efficiency of criterion II with different sizes of S. It can be observed that as the size of S is increased the performance is improved. Also it is shown that the performance achieves almost the same level as the scheme with full channel information, when k is large enough to make PMBR negligible. This observation is illustrated in Fig.4. It is shown that a reasonable number of relays (i.e. 3) is enough to achieve almost the same performance as the scheme with full channel knowledge. Experiment 3: The objective of this experiment is to investigate PMBR for both Criterion I and II. As mentioned in the above sections, the statistic behaviour of S affects PMBR. The case with 10 relays for Criterion I is investigated as shown in Fig.2 and Fig.5, the average S-R SNR of the 10 relays range from 1 dB to 10 dB higher than the S-D SNR with an increasing step of 1 dB. For the cases of 2 relays and 3 relays, the system is configured as mentioned in Experiment 1. It is observed that increasing the threshold can reduce the

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3.5

0.7

Full CSI Proposed k=3 Proposed k=2 Proposed k=1

Spectral Efficiency (Bit/S/Hz)

3

0.6

0.5

PMBR

2.5

2

0.3

1.5 0.2

1

0.5

0.1

0

0

2

4

6

8

10 12 SNR (dB)

14

16

18

20

γ =20 dB N

γN=10 dB γ = 16 dB

Spectral Efficiency (Bit/S/Hz)

3

N

2.8 2.6 2.4 2.2 2 1.8 1.6 1.4

1

2

3

4

5

6

7

8

9

10

Number of Relays

Fig. 4. Spectral efficiency of selection criterion II as a function of the number of relays in S. The minimum average SNR of the S-R links are 10 dB, 16 dB and 20 dB and the average SNR of the S-D link is fixed to 10 dB .

0.35 10 Relays 3 relays 2 relays

0.3

0.2

0.15

0.1

0.05

0

0.1

0.2

3

4

5

6

7

8

9

10

Fig. 6. PMBR for Criterion II as a function of the number of relays in S with totally 10 relays in the system.

ACKNOWLEDGEMENT The work has been performed in the FP7 project ICT248894 WHERE2, which is partly funded by the European Union. R EFERENCES

0.25

0

2

using mixed channel knowledge. The proposed scheme aims at reducing signalling overhead of modulation-adaptive opportunistic DF relaying through exploitation of mixed channel knowledge. A novel semi-deterministic approach is proposed for performing joint rate adaptation and best relay selection. Two selection criteria using mixed channel knowledge are proposed. A new metric namely the probability of missing the best relay is introduced to illustrate the relationship between the spectral efficiency and signalling overhead. It is shown that the proposed approach can achieve a good trade-off between the spectral efficiency and signalling overhead.

3.4 3.2

1

No of Relays

Fig. 3. Spectral efficiency of the modulation-adaptive cooperation scheme with relay selection Criterion II as a function of the average SNR of S-R link. The average SNR of the S-D link is fixed to 10 dB, and the average SNR of the R-D link is the same as that of the S-R link.

PMBR

0.4

0.3

0.4

Pt

0.5

0.6

0.7

0.8

0.9

Fig. 5. PMBR for Criterion I as a function of the threshold probability, with totally 2, 3 and 10 relays in the system.

number in S and increase PMBR. Also the position of relays can affect PMBR, which means that more sparse the relays are, higher PMBR is introduced. For the case of 3 relays, since the relays are placed in a more sparse way compared to the case of 2 relays, higher PMBR is observed although more relays are involved in the selection. For Criterion II, it is shown in Fig.6 that when the size of S is large enough, PMBR can be negligible and the same performance can be achieved as the scheme with full channel knowledge.

[1] A. Bletsas, A. Khisti, D. P. Reed, and A. Lippman, “A simple cooperative diversity method based on network path selection”, IEEE Journal on Selected Areas in Communications, vol. 24, no. 3, pp. 659–672, 2006. [2] A. Goldsmith, “Adaptive modulation and coding for fading channels”, in Proc. IEEE Information Theory and Communications Workshop, 1999, pp. 24–26. [3] M. Alouini and A. Goldsmith, “Adaptive modulation over nakagami fading channels”, Wireless Personal Communications, vol. 13, pp. 119– 143, 2000. [4] K. S. Hwang, Y. C. Ko, and M. S. Alouini, “Performance analysis of incremental relaying with relay selection and adaptive modulation over non-identically distributed cooperative paths”, in Proc. IEEE International Symposium on Information Theory ISIT 2008, 2008, pp. 2678–2682. [5] Y. Zhang, Y. Ma, and R. Tafazolli, “Modulation-adaptive cooperation schemes for wireless networks”, in Proc. IEEE Vehicular Technology Conference VTC Spring 2008, 2008, pp. 1320–1324. [6] Y. Ma, R. Tafazolli, Y. Zhang, and C. Qian, “Adaptive modulation for opportunistic decode-and-forward relaying”, IEEE Transactions on Wireless Communications, vol. 10, no. 7, pp. 2017–2022, 2011. [7] M.-S. Alouini, X. Tang, and A. Goldsmith, “An adaptive modulation scheme for simultaneous voice and data transmission over fading channels”, IEEE Journal on Selected Areas in Communications, vol. 17, no. 5, pp. 837–850, 1999. [8] D. Tse and P. Viswanath, Fundamentals of wireless communication, Cambridge University Press, New York, NY, USA, 2005. [9] A. Papoulis, Probability, Random Variables, and Stochastic Processes, Mc-Graw Hill, fourth edition, 1984.

V. C ONCLUSION In this paper, we have presented a novel joint rate-adaptation and best-relay selection scheme for opportunistic DF relaying

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A Novel Adaptive Hybrid-ARQ Protocol for Machine-to-Machine Communications Chuyi Qian, Hong Chen, Yi Ma and Rahim Tafazolli Centre for Communication Systems Research, University of Surrey, UK, GU2 7XH Emails:{c.qian, hong.chen, y.ma, r.tafazolli}@surrey.ac.uk Abstract—Emerging low date-rate Machine-to-Machine (M2M) communications call for promising Hybrid Automatic Repeat-reQuest (HARQ) schemes with improved link reliability and feedback efficiency. This motivates us to develop a novel adaptive HARQ scheme by exploiting the knowledge of Channel Quality Information (CQI), which can be obtained through either channel estimation techniques or location-aided technology. The proposed adaptive HARQ scheme will determine the suitable transmission mode to guarantee a specific Frame Error Rate (FER) during the first transmission with the aid of location information. Simulation results demonstrated that our proposed scheme can achieve more attractive throughput performance, while maintaining a similar FER, compared to conventional HARQ schemes. Index Terms—Hybrid automatic retransmission request (HARQ), incremental redundancy, rate adaptation, machine-tomachine, channel information, location aided.

I. I NTRODUCTION Machine-to-Machine (M2M) communications are emerging as an important area in cellular networks, when the service demands increased dramatically [1]. Certain services in M2M communications require better transmission reliability. For example, the reliability of data transmission in a sensor network for medical monitors is critical to maintain the functionality of the entire system. Furthermore, the power-limited M2M devices are expected to work for a long life-time, especially for those un-chargeable ones. Therefore, energy efficiency and reliability become two key design requirements for M2M communications [2]. Hybrid Automatic Repeat-reQuest (HARQ) [3] [4] combines Forward Error Correction codes (FEC) and Automatic Repeat-reQuest (ARQ) to improve the reliability of data transmission and achieves a better throughput performance, which neither of the two methods can achieve alone. The simplest version of HARQ scheme is Type-I HARQ, which straightforwardly combines FEC with ARQ [5]. With the aid of soft combining, more sophisticated HARQ schemes may achieve higher throughput, since all corrupted replicas from different (re)transmissions are combined to recover the original frame. Namely, Type-II HARQ with Chase Combining (CC), Type-II HARQ with Incremental Redundancy (IR) and TypeIII HARQ [6]-[8]. More explicitly, CC adds the soft information of retransmitted identical bits, which is represented by the Log-Likelihood Ratios (LLRs) during decoding [9]. However, IR indicates that new parity bits will be transmitted

in each retransmission. The probability of successful decoding increases, due to the lower-rate codeword after combining the additional parity information from each retransmission. Like Type-II HARQ, Type-III HARQ may also use CC or IR for its retransmission strategy, while each of (re)transmissions is self-decodable. Both CC and IR may be adopted in a practical HARQ scheme, e.g. Souza integrated CC and IR in his proposed HARQ scheme in [10]. Traditional rate-fix HARQ schemes have two disadvantages: long delay and throughput loss. Specifically, a number of retransmissions must be required for recovering the information bits for a specific channel condition. Since there is a gap between two transmissions, more retransmissions implies longer delay. Furthermore, the rate-fix HARQ may not match a specific overall coding rate, namely the minimum one which can be achieved by currently used codes for that channel condition. For example, if the fixed-rate of each transmission is 1, the overall coding rate decreases to 12 , 13 , · · · , 16 after one, two, · · · , six transmissions. However, the minimum overall coding rate for that channel condition lies between two boundary coding rates, e.g. between ( 15 , 61 ). In this case, the fixed-rate HARQ will suffer from a fraction of throughput loss. In order to improve the spectrum efficiency, link adaptation techniques have been proposed for HARQ, such as adaptive modulation and coding schemes [11]. Adaptive HARQ allows early termination of the transmission once sufficient information has been received, in this way the throughput loss can be compensated. In [12], a rate adaptation scheme was proposed for maximizing the average transmission rate while satisfying a target outage probability in Rayleigh block fading channels, where the selection of modulation and coding schemes for the initial frame transmission is usually determined by the channel quality information (CQI). The authors of [13] combined a truncated HARQ protocol with adaptive modulation and coding, in order to maximize spectral efficiency in a general Nakagami-m block-fading channel with delay and error constraints. Although a large amount of research on HARQ schemes has been carried out, the impact of signalling overhead and throughput in M2M scenarios has not been investigated yet. HARQ can still be polished in order to provide reliable transmission and efficient spectral employment for M2M communications. In this paper, we concentrate on designing a suitable HARQ mechanism for M2M communications. Rate-adaptive schemes

will be considered for the case of low data-rate and shortpacket communications for power-limited M2M devices. The main contribution of this work lies with a novel adaptive HARQ scheme, exploiting channel information to improve throughput, as well as maintaining a similar Frame Error Rate (FER). Compared to conventional fixed-rate HARQ schemes, better FER and throughput performance may be achieved. Remark: The M2M network is characterized with low mobility environment, where the communication channel is slowly time-varying. In such environment, the location information of M2M devices, if available, can be easily translated into the transmitter-side SNR knowledge, based on which the transmitter can optimize the code rate of the first transmission without need of the channel estimation at the receiver side. It is clear that such a location-aided technology can effectively reduce the pilot overhead and complexity paid for the channel estimation as well as the feedback overhead for code rate indication. Certainly, the location-aided SNR estimation is not as accurate as the receiver-side SNR estimation used in this paper, and it could be a good future work to further investigate the impact of SNR estimation error on the linklevel performance such as FER and throughput. II. S YSTEM M ODEL As shown in Fig.1, a point-to-point communication system including a transmitter and a receiver is considered, in which the transmitter sends coded message to the destination via a block fading channel [14]. Since the transmission period of M2M communications is rather short compared to the idle time of M2M devices, we may assume that the channel gain keeps constant within (re)transmissions for one packet, while varying independently from packet to packet. At the transmitter, the incoming message a having k equiprobable and independent information bits a = [a0 a1 . . . ak−1 ] is transmitted through the fading channel with one-side noise power spectral power density N0 . Prior to the transmission, each block of k-bit information sequence a is encoded by a rate- 1r turbo encoder, yielding a sequence of systematic and parity bits b, as seen in Fig. 1. The output codeword bj for the j th transmission is formed by puncturing b according to the decision of rate adaption, which will be detailed in Section III-A. Then, the modulated symbols are transmitted through the channel using the energy Es for each symbol. Assuming that the frame sent in time slot i experiencing a channel gain hi , the received ˜ j may be expressed as: symbols at the receiver b ˜ j (t) = hi bj (t) + ni , b

(1)

where t = 1 · · · l, and l is determined based on the coding rate kl of the current transmission from the rate adaptation in Fig.1. Furthermore, ni represents independent and identically distributed (i.i.d) N (0, 1) random variable with variance σ 2 = N0 2 . At the receiver, the turbo decoder in Fig.1 performs iterative decoding following the first reception. Cyclic Redundancy Check (CRC) is employed to detect errors after decoding. If

hi a

Turbo encoder

b

j

b Rate adaption

n ˜j b

Soft combining

Turbo decoder

˜ a

Feedback Channel

Fig. 1. System model: Hybrid ARQ protocols for the block-fading channel. The ACK/NACK feedback channel is error-free.

no error is detected, the receiver sends back an ACKnowledgement (ACK) message; otherwise, a Negative ACKnowledgement (NACK) message will be fed back to the transmitter. In our proposed HARQ scheme, only one retransmission is required due to the rate adaptive mechanism. The received frame from the second transmission will be soft combined with the previous one. Turbo decoding is then recommenced and may succeed in a high probability, based on the combined soft information. However, if CRC fails again, the packet will be discarded and no message will be sent back to the transmitter. All the signalling messages including the Channel Quality Information (CQI) indicator and ACK/NACK, are assumed to be transmitted over a perfect feedback channel and hence error-free. III. P ROPOSED A DAPTIVE HARQ S CHEME FOR M2M COMMUNICATIONS

With the aid of Rate Compatible Punctured Turbo (RCPT) codes [15], our proposed adaptive HARQ scheme allows two transmissions which are enough to achieve a desirable link level performance. During the first transmission, the coding rate may be adapted based on the CQI; while the whole codeword will be retransmitted during the second transmission. In the following sections, we will describe the working mechanisms of the transmitter and receiver in details in Sections III-A and III-B. Section III-C explains the generation of a Look-up table, which pre-stores the coding rates corresponding to the CQI. A. Transmitter mechanism The transmitter of our HARQ scheme employs a turbo encoder consisting of two parallel recursive convolutional encoders. Fig.2 illustrates the transmitter structure of our proposed HARQ scheme. Generally, the turbo encoder outputs a codeword with a specific coding rate. More specifically in our scheme, a 13 -rate codeword b may be obtained each time by invoking the turbo encoder, including the systematic bit sequence a and two parity bit sequences b1 , b2 , as seen in Fig.2. The coding rate for the j th transmission is determined by the rate adaptation strategy according to the CQI. Based on RCPT, the final transmitted bj with a coding rate higher than 13 may be obtained by puncturing from the initial rate codeword b. Usually, all systematic bits are contained in the output, while parity bits are evenly extracted from b1 and b2 . For example, if the current coding rate is decided to be 12 , apart from the systematic bits a, a half of parity bits are from

˜ a

CQI a a

1

RSC

b

2

Fig. 2.

RSC

˜a1 a ˜e1 a

BCJR1

˜a2 a ˜e2 a

BCJR2

˜1 b

1

π a

˜p a

rate selection

b

puncturing

bj

π−1

b

˜ b

combining and depuncturing

˜j b

π ˜2 b

2

The structure of the turbo encoder in our adaptive HARQ scheme.

the odd bits of b1 and the other half are from the even bits of b2 . The rate adaptation in Fig.2 plays an important role in our adaptive HARQ scheme. It returns a coding rate corresponding to the CQI by searching a look-up table, which pre-stores all coding rates corresponding to all 4 CQI messages for recovering the information bits at a probability of Pf . The CQI message can be obtained by two means: 1) using 2-bit CQI feedback from the receiver; 2) translating from the location information through employment of geo-location database. When the appropriate coding rate is found, the transmitter performs puncturing operation to obtain the codeword of b1 for the first transmission. ˜ 1 at the receiver may succeed at a probability Decoding on b of Pf and may fail at (1−Pf ), where Pf is the aforementioned specific FER that the coding rate may achieve. Then, the transmitter may receive an 1-bit ACK or NACK message respectively for successful or unsuccessful reception. If an NACK message is received, the transmitter will transmit the whole rate 13 turbo encoded packet b2 = b during the second transmission. If the decoding fails again, the packet will be discarded. B. Receiver mechanism ˜ 1 , it will When the receiver receives the first codeword of b perform the opposite de-puncturing and de-multiplexing operations to form the systematic LLRs of ˜ a and two parity LLR ˜ 1 and b ˜ 2 , as seen in Fig.3, which illustrates the sequences of b turbo decoder structure of our proposed HARQ scheme. Since only a part of parity bits of b1 and b2 may be transmitted in the first transmission when the coding rate is higher than 13 , the LLRs of those untransmitted bit positions will be padded with zeros during the de-puncturing. The iterative decoding is then executed by exchanging their extrinsic LLRs between two parallel components. After a number of iterations, the estimated information bits ˜ a are decoded by the hard decisions on the output a posteriori LLRs ˜ ap . In the case of an unsuccessful decoding during the first transmission, the second received packet will be soft combined with the previous one. More explicitly, the repeated systematic ˜ 2 are added with those LLRs in LLRs and parity LLRs in b ˜ ˜ 2 which are excluded in b1 . The new parity LLRs from b ˜ b1 replace the zeros padded in the de-puncturing for the first transmission. Turbo decoding is activated again, until the CRC succeeds or a number of iterations is reached. If the CRC still

Fig. 3.

The structure of the turbo decoder in our adaptive HARQ scheme.

indicator (00) (01) (10) (11)

SNR level (-∞, 2.1) dB [2.1, 5.1) dB [5.1, 6.2) dB [6.2,∞)dB

Coding Rate 1/3 2/5 1/2 2/3

TABLE I Look-up table for the coding rates and CQI messages. The SNR threshold (2.1, 5.1, 6.2) dB are corresponding to the coding rate (2/5, 1/2, 2/3) which satisfy the FER constraint of 10−3 .

fails, the packet will be discarded and nothing will be reported to the transmitter. C. Look-up table generation As mentioned before, the look-up table pre-stores all coding rates for all possible CQI messages. Considering the short packet length in M2M communications, a 2-bit CQI message indicating 4 channel statuses may not inflict a large number of extra overhead. Therefore, the look-up table contains 4 entries storing 4 coding rates. The criteria of selecting these coding rates is to ensure a successful transmission at a high probability, when using these coding rates. In other words, a potentially low FER may be achieved during the first transmission. In our implementation, we set this specific low FER to be Pf = 10−3 . In order to find the relationship between the coding rates and the channel statuses, we designed an off-line training based on a 13 turbo encoder and decoder. The same parameters are adopted as those used in the simulations of Section IV, such as 84-bit packet length, QPSK modulation and so on. However, the channel model for this training is an Additive White Gaussian Noise (AWGN) channel, instead of a quasistatic Rayleigh fading channel, since the channel gain keeps constant during the transmission of each block. Therefore, the transmission of each block may be viewed over an AWGN channel with the SNR corresponding to the current channel gain. Puncturing is also utilized to form the coding rate which is required to meet the target FER. Finally, Table I shows the resulted look-up table for four channel status, where the 2-bit CQI messages vary from 0 − 3 corresponding to four ranges of SNR values. The stored coding rates guarantee the FER of 10−3 in the corresponding SNR regions, as shown in Fig.4. The SNR thresholds of 2.1dB, 5.1dB and 6.2dB in Table I may be obtained by intersecting a horizontal line of 10−3 with three FER curves of coding rates 25 , 12 and 32 in Fig.4.

0

10

0

10

Rate 2/5 Rate 1/2 Rate 2/3 −1

−1

10 Frame Error Rate

Frame Error Rate

10

−2

10

−3

Non−HARQ

−2

10

10

Adaptive HARQ HARQ Type−III −4

10

−1

0

1

2

3 4 Es/N0 (dB)

5

6

7

HARQ Type−II CC

8 −3

10

Fig. 4. Frame error rate performance of Turbo codes over an AWGN channel with various coding rates.

−5

0

5

10

15

20

Es/N0 (dB)

Fig. 5. Frame error rate of the proposed adaptive HARQ schemes with instantaneous channel information.

IV. S IMULATION R ESULTS In this section, computer simulations are carried out to evaluate the performance of the proposed scheme. We chose non-adaptive HARQ schemes with a fixed coding rate, namely Type-II HARQ with CC and Type-III HARQ as benchmarks. Furthermore, a simple FEC scheme without retransmissions referred to as non-HARQ is employed as the benchmark to illustrate the improvement of HARQ schemes. All benchmarks in our simulations depend on the turbo encoder shown in Fig.2, which is able to produce a 13 -rate codeword b. Based on it, a 1 2 -rate encoded packet will be generated, which includes the whole systematic bits a and the parity bits punctured from the odd bits of b1 and the even bits of b2 . In Type-II HARQ with CC, this 12 -rate encoded packet will be (re)transmitted during each (re)transmission. At the receiver, only CC is performed before the iterative decoding. In order to maintain the same overall coding rate of 16 as our adaptive HARQ, we set the retry limit to be 3. For fair comparison, the non-HARQ scheme employ a simple FEC scheme with 61 coding rate which equals the lowest coding rate of the HARQ schemes. For the benchmark of Type-III HARQ, the same 12 -rate encoded packet is transmitted during the first transmission. However, a 21 -rate encoded packet including the systematic bits and the parity bits from the rest of b1 and b2 excluded in the first transmission will be sent to the receiver, where the soft combining of CC and IR will be executed for the iterative decoding. The same 1 2 -rate encoded packet in the first transmission is repeated for the third transmission. Likewise, only CC is performed by the receiver following the third reception. Finally, the non-HARQ scheme only transmits once the 21 -rate encoded packet as that in the first transmission of other two HARQ schemes. A statistically large number of packets were sent to calculate the throughput and FER for all above schemes, where the packet length is set to be k = 84 bits. Quadrature Phase Shift Keying (QPSK) modulated transmissions in all simulations are based on a quasi-static Rayleigh fading channel, as assumed before. Furthermore, the channel gain keeps constant for all (re)transmissions of a single packet, while varies independently packet by packet. The generator polynomials of the

turbo encoder may be octally presented by (13, 15)o . And the number of iterations during each turbo decoding is set to be 5. Experiment 1: The objective of this experiment is to examine the system reliability of the proposed adaptive HARQ scheme based on instantaneous channel information. The FER performance of the proposed scheme is illustrated with those of non-adaptive retransmission schemes in Fig.5, where the non-HARQ scheme without any retransmission serves as the upper bound for 16 coding rate. As is shown in Fig.5, the proposed adaptive HARQ scheme can almost achieve the same performance as Type-II HARQ with CC and slightly outperforms Type-III HARQ by 1 dB. In the low SNR range, the adaptive-HARQ scheme always transmits with the full coding rate due to the hostile channel situation and retransmission is always required resulting in a reduced throughput. In the high SNR range, rate-adaptation mechanism of the proposed scheme gains the benefit of the channel information and the throughput is improved which is shown in Fig.6. Experiment 2: The objective of this experiment is to examine the throughput for all HARQ schemes, which is defined as the successfully transmitted information bits over the total transmitted bits including retransmissions and the signalling overhead such as ACK/NACK and CQI indicator messages. As shown in Fig.6, the throughput is directly affected by the maximum number of transmissions for Type-II HARQ with CC and Type-III HARQ. Furthermore, the proposed HARQ scheme with instantaneous channel information outperforms the non-adaptive HARQ schemes, especially in high SNR regions. It may be observed in Fig.5 and Fig.6 that the FER performance goes in-line with the throughput. The proposed adaptive HARQ scheme strives to increase the probability of successful decoding for the first transmission and reduce redundancy information with the aid of the channel information. In this way, a better throughput performance may be achieved. Experiment 3: The objective of this experiment is to investigate the effect of the extra signalling overhead, namely the CQI indicator messages on the throughput when a shorter packet

Frame Length=32 Bits

0.7

0.7 Adaptive HARQ Type−II HARQ CC Type−III HARQ

Adaptive HARQ 0.6

0.6

HARQ Type−II CC HARQ Type−III Non−HARQ

0.5

0.4

Throughput

Throughput

0.5

0.3

0.2

0.3

0.2

0.1

0

0.4

0.1

−5

0

5

10

15

20

E /N (dB) s

0

0

−5

0

5 10 E /N (dB) s

15

20

0

Fig. 6. System throughput for the proposed adaptive HARQ schemes with instantaneous channel information, when the packet length is 84-bit.

Fig. 7. Throughput comparison of the proposed scheme of instantaneous channel feedback with non-adaptive HARQ scheme for frame length=32 Bits.

is implemented for the proposed scheme with instantaneous channel feedback. The threshold is obtained by simulation as mentioned in Section III-C. As shown in Fig.7 where the packet length is 32-bit, the proposed scheme outperforms the non-adaptive schemes in the low SNR regions, while suffering a throughput reduction due to the extra signalling overhead. However, the reduction becomes negligible as the SNR values increase. When the SNR values increase to those higher than 8dB, the throughput of our adaptive HARQ scheme becomes the largest one among all schemes, as seen in Fig.7. Additionally, it can be observed that as the packet length increases, the effect of channel feedback on throughput becomes negligible and the advantage of the proposed scheme over non-adaptive HARQ becomes more obvious.

[2] S. Parkvall, A. Furuska andr, and E. Dahlman, “Evolution of LTE toward IMT-advanced,” Communications Magazine, IEEE, vol. 49, no. 2, pp. 84 –91, february 2011. [3] S. Lin and P. Yu, “A hybrid ARQ scheme with parity retransmission for error control of satellite channels,” Communications, IEEE Transactions on, vol. 30, no. 7, pp. 1701 – 1719, july 1982. [4] S. Lin and D. Costello, Jr., Error Control Coding: Fundamentals and Applications. Prentice Hall, Englewood Cliffs, NJ., 1983. [5] R. Comroe and J. Costello, D., “ARQ schemes for data transmission in mobile radio systems,” Selected Areas in Communications, IEEE Journal on, vol. 2, no. 4, pp. 472 –481, july 1984. [6] D. Chase, “Code combining–a maximum-likelihood decoding approach for combining an arbitrary number of noisy packets,” Communications, IEEE Transactions on, vol. 33, no. 5, pp. 385 – 393, may 1985. [7] J. Cheng, “Coding performance of hybrid ARQ schemes,” Communications, IEEE Transactions on, vol. 54, no. 6, pp. 1017 –1029, june 2006. [8] D. Mandelbaum, “An adaptive-feedback coding scheme using incremental redundancy (corresp.),” Information Theory, IEEE Transactions on, vol. 20, no. 3, pp. 388 – 389, may 1974. [9] L. Hanzo, T. H. Liew, B. L. Yeap, R. Tee, and S. X. Ng, Turbo coding, turbo equalisation and space-time coding for transmission over fading channels, second edition. New York, USA: John Wiley & Sons, 2011. [10] R. Souza, M. Pellenz, and T. Rodrigues, “Hybrid ARQ scheme based on recursive convolutional codes and turbo decoding,” Communications, IEEE Transactions on, vol. 57, no. 2, pp. 315 –318, february 2009. [11] M.-S. Alouini, X. Tang, and A. Goldsmith, “An adaptive modulation scheme for simultaneous voice and data transmission over fading channels,” IEEE Journal on Selected Areas in Communications, vol. 17, no. 5, pp. 837–850, 1999. [12] P. Wu and N. Jindal, “Performance of hybrid-ARQ in block-fading channels: A fixed outage probability analysis,” Communications, IEEE Transactions on, vol. 58, no. 4, pp. 1129 –1141, april 2010. [13] Q. Liu, S. Zhou, and G. Giannakis, “Cross-layer combining of adaptive modulation and coding with truncated ARQ over wireless links,” Wireless Communications, IEEE Transactions on, vol. 3, no. 5, pp. 1746 – 1755, september 2004. [14] E. Biglieri, J. Proakis, and S. Shamai, “Fading channels: informationtheoretic and communications aspects,” Information Theory, IEEE Transactions on, vol. 44, no. 6, pp. 2619 –2692, october 1998. [15] D. Rowitch and L. Milstein, “On the performance of hybrid FEC/ARQ systems using rate compatible punctured turbo (rcpt) codes,” Communications, IEEE Transactions on, vol. 48, no. 6, pp. 948 –959, june 2000.

V. C ONCLUSION In this paper, we have presented a novel adaptive HARQ scheme for M2M communications using instantaneous channel information. The proposed scheme aims at achieving a better throughput-reliability performance through exploitation of channel information. The proposed scheme determines the suitable (re)transmission mode to guarantee a specific FER during the first transmission. The advantages of the proposed scheme in reliability and throughput are shown through simulations. It is shown that the proposed approach can outperform the conventional fixed HARQ schemes in reliability and throughput. ACKNOWLEDGEMENT The work has been performed in the framework of ICT project ICT-258512 EXALTED and ICT-248894 WHERE 2, which are partly funded by the European Union. R EFERENCES [1] Y. Chen and W. Wang, “Machine-to-machine communication in LTE-A,” in Vehicular Technology Conference Fall (VTC 2010-Fall), 2010 IEEE 72nd, september 2010, pp. 1–4.

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Joint Rate Adaptation and Best-Relay Selection Using Limited Feedback Na Yi, Member, IEEE, Yi Ma, Senior Member, IEEE, and Rahim Tafazolli, Senior Member, IEEE Abstract—This paper presents a novel joint rate adaptation and relay selection scheme for multi-relay networks adopting half-duplex best-relay decode-and-forward protocol. The proposed scheme aims to maximize the overall transmission rate when relays are allowed to forward messages using different rates from the source. It is shown that the proposed scheme outperforms the conventional adaptive scheme in terms of the spectral efficiency (e.g. by 10.1% improvement for SNR= 10 dB). Furthermore, in order to reduce signaling overhead of the proposed scheme, a number of joint discrete-rate adaptation and relay selection approaches are proposed for both non-reciprocal and reciprocal channels. The relay selection is basically a twostage scheme. At the first stage, a set of relays are selected based on mixed channel quality information (CQI), i.e., the knowledge of CQI varies for different links; at the second stage, the best relay within the set is selected based on instantaneous CQI, which is obtained through carefully designed signaling protocols. It is shown that the proposed discrete-rate adaptation schemes can offer comparable spectral efficiency to the conventional adaptive scheme with significantly reduced signaling overhead. Index Terms—Adaptive modulation, best relay, decode and forward, limited feedback, relay selection.

I. I NTRODUCTION

C

OMMUNICATION over wireless relay channels is one of fundamental problems in the area of network information theory. Since van der Meulen’s work in 1971 of three-terminal communication channel [1], numerous research efforts have been paid on capacity theorems (e.g. [2]-[4]), spatial multiplexing and diversity techniques (e.g. [5]-[7]), code design (e.g. [8]), etc. Moreover, it is also a fast developing area in mobile communication engineering. For example in European 3GPP long-term evolution (LTE-Advanced) [9], wireless relays are deployed to enhance coverage of cellular services. In LTE-Advanced machine-type communications [10], gateways serve as decode-and-forward (DF) relays to link capillary networks with core networks. Such mobile systems can be modeled as multi-source, multi-relay, and multi-destination networks. Certainly, this complex model can be reduced to a single-source, multi-relay, and single-destination network when sources transmit information over orthogonal medium. It is shown in [11] that the most spectrum efficient way of single-source multi-relay single-destination communication is allowing for only the best relay to forward the source’s

Manuscript received June 12, 2012; revised December 4, 2012 and February 8, 2013; accepted April 10, 2013. The associate editor coordinating the review of this manuscript and approving it for publication was M. Cenk Gursoy. This work has been performed in the framework of European Commission ICT project under grant agreement No. 298894 Wireless Hybrid Enhanced Mobile Radio Estimators - Phase 2 (WHERE2). This work was also partially supported by the UK 5G Innovation Centre. The authors are with the Centre for Communication Systems Research, the University of Surrey, United Kingdom, GU2 7XH (e-mail: {n.yi, y.ma, r.tafazolli}@surrey.ac.uk). Digital Object Identifier 10.1109/TWC.2013.050313.120884

message, which is named as the opportunistic relaying protocol in [12] or called the best-relay forward protocol in this paper1 ; and the opportunistic relaying protocol can achieve the same distributed spatial diversity gain as the relay-by-relay transmission. The aim of improving spectral efficiency of the opportunistic relaying protocol has motivated researchers to combine link adaptation techniques such as distributed power allocation, adaptive modulation and coding with the best relay selection. For example when relays employ the amplify-and-forward (AF) protocol, an optimal power allocation scheme has been investigated in [13], and its performance has been compared with relay selection schemes. Adaptive modulation schemes have been proposed for parallel AF relaying systems in [14], [15] and opportunistic AF relaying in [16]. Considering the DF protocol, the performance of combining link adaptation with best relay selection has been investigated in [17]. Recently, there are several independent works on the employment of different modulation formats at the source and relays. For instance, the bit-error-rate (BER) analysis of selection combining of signals with different modulation formats was presented in [18], and later on the theoretical analysis was extended to the Nakagami-m fading channels in [19]. The relay selection aims to minimize the approximate BER. Our recent work in [20] presented a new link adaptation technique allowing for the source and best relay to employ different modulation formats. It has been shown that the proposed scheme can significantly improve the spectral efficiency with the target BER to be satisfied for each channel realization. On the other hand, our previous work is optimized only for uncoded sources, and the relay selection scheme requires full channel quality information (CQI) of all links, which is not a practical assumption. This paper presents a novel joint rate adaptation and relay selection scheme for the half-duplex best-relay decode-andforward protocol. Unlike our previous work [20] suitable only for uncoded sources, the proposed scheme aims to maximize the overall transmission rate when relays are allowed to use different rates from the source. It is shown that the proposed scheme outperforms the conventional adaptive scheme in terms of the spectral efficiency at the price of signaling overhead (for instance 10.1% spectral efficiency improvement is observed for SNR= 10 dB with the signaling overhead being increased by 9.87%). In order to reduce signaling overhead of the proposed scheme, a number of joint discrete-rate 1 The original idea of opportunistic relaying is to select the best relay amongst all well-informed relays. The essence of “opportunistic” is mainly referred to the chance of having well-informed relays. In this paper, the best relay is pre-selected amongst all relays by exploiting channel quality information of all communication links. Therefore, the terminology of “opportunistic relaying” is not accurate, and instead we recommend more accurately the terminology “best-relay forward”.

c 2013 IEEE 1536-1276/13$31.00 

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adaptation and relay selection schemes are proposed for both non-reciprocal and reciprocal channels. The relay selection is basically a two-stage scheme. At the first stage, either the destination or relays select a set of candidates based on so-called mixed CQI. For example, the destination when performing relay selection has the instantaneous CQI about the source-todestination (S-D) link, but only has the statistical CQI about the source-to-relay (S-R) links and relay-to-destination (R-D) links. At the second stage, the best relay within the selected candidates is selected based on instantaneous CQI, which can be obtained through carefully designed signaling protocols. The proposed discrete-rate adaptation schemes are evaluated in terms of signaling overhead, rate loss relative to continuousrate adaptation, as well as probability of missing the best relay (PMBR) due to the CQI uncertainty. It is shown that the proposed schemes can offer comparable spectral efficiency with the conventional continuous-rate adaptive scheme with significantly reduced signaling overhead (e.g. 90.7% overhead reduction is observed in non-reciprocal channels and 97.2% overhead reduction in reciprocal channels both for SNR= 10 dB). The rest of this paper is organized as follows. Section II presents the system model, joint continuous-rate adaptation and relay selection as well as the signaling overhead problem. Section III presents joint discrete-rate adaptation and relay selection using limited feedback. Section IV presents the performance of proposed schemes in terms of rate loss and PMBR. Numerical results and discussions are provided in Section V. Finally, Section VI concludes the paper.

Fig. 1. An example of single-source single-destination multiple-relay networks with the best-relay forward protocol.

Basically, the destination operates in two reception modes. When no relay participates in the communication, the destination recovers original message from the received signal y (s→d) . All optimal or sub-optimal receivers can be employed for the single-link message recovery. When the lth relay participates in the communication, the destination recovers original message through an appropriate combination of y (s→d) and (r→d) (r) yl . Since x(s) and xl can have different rates, linear combining techniques such as the maximum-ratio combining are not always valid. Alternatively, we can employ the following maximum a-posteriori probability (MAP) receiver to recover the original message (r→d)

ω ˆ = argmax Pr(ω|y (s→d) , yl ω ˆ

II. S YSTEM M ODEL , O PTIMIZATION , AND P ROBLEM F ORMULATION

(r→d)

, h(s→d) , hl

),

(4)

where ω stands for the original message, ω ˆ for the estimated version of ω, and Pr(·) for the probability.

A. Transmission and Reception Fig. 1 illustrates an example of multi-relay network accommodating one source (S), one destination (D), and L halfduplex parallel relays (R ,  ∈ {1, 2, . . . , L}). The relaying protocol is orthogonal DF, and only the relay offering the maximum transmission rate would forward its re-generated signal to the destination. The discrete-time equivalent form of received signals at different relays as well as at the destination are described by S−D link : y (s→d) = h(s→d) x(s) + z (s→d) (s→r)

S−R link : y R−D link :

(r→d) yl

(s→r) (s)

= h =

x

(r→d) (r) hl xl

(s→r)

(r→d)

(s→r)

+ z +

(1)

, for  = 1, 2, ..., L

(r→d) zl ,

B. Best-relay Selection Criterion and Algorithm The best-relay selection criterion is to assure the maximal transmission rate in bits/s/Hz with communication reliability being guaranteed. Suppose the th relay decoding successfully (s) (s) the message consisting of (R T1 ) bits, where R stands for the transmission rate between the source and the th relay, and T1 for the block length of x(s) . If the th relay transmits (r) the re-generated signal x using the block length of T2 , its (r) (s) transmission rate is given by R = (T1 R )/(T2 ). Then, th the overall transmission rate for the  relay participating in the communication is (s)

(2) for l ∈ {1, 2, ..., L}, (3)

where y (s→d) , y , yl denote the signals received (s→r) through the S-D channel, h(s→d) , S-R channel, h , and (r→d) (s) Rl -D channel, hl , respectively; x denotes the signal (r) sent by the source, and xl the signal sent by the lth relay (r) (xl can use different rates from x(s) by employing different modulation schemes, channel codes, or precoders); z denotes the additive white Gaussian noise of corresponding links with the variance No ; and the subscript l denotes the index of the best relay.

R =

(s)

(r)

R T1 R R = (s) . (r) T1 + T2 R + R

(5)

Based on (5), the best-relay selection criterion is described by the following objective function l = argmax(R ),  = 1, 2, ..., L.

(6)



If the maximum rate Rl is smaller than the rate of S-D link (denoted by R (s→d) ), the system would switch off all the relays. Considering the transmission power of the source and relays to be fixed, the optimization problem (6) is equivalent to finding the best DF relay channel whose achievable rate is

YI et al.: JOINT RATE ADAPTATION AND BEST-RELAY SELECTION USING LIMITED FEEDBACK

the maximum amongst all relay channels. According to the max-flow min-cut (MFMC) principle, the achievable rate of the th relay channel is given by the following statement. Theorem. 1: The th DF relay channel has the following achievable rate (MFMC)

R < C (s)

(s)

=

(s,r→d)

C C (s) C

(s→r)

(MFMC)

(7)

+ C

(s,r→d)

),  = 1, 2, ..., L.

(8)



(s)

The rates Rl (s)

Rl

(r)

Rl

(r)

and Rl

are upper bounded by

(MFMC)


0 and comparison with the signaling overhead of full channel quality (MFMC) (s,r→d) (∂C )/(∂C ) > 0, and thus the achievable rate information (e.g. M = 3 was used for discrete-rate adaptation (MFMC) in [20]). The proposed relay-selection strategy is described as C is a monotonically increasing function of the SNRs below. (r→d) (s→r) (s→d) (i.e. snr , snr , snr ). If there exists a relay (with (s→r) and compute the S-R S1.1 The th relay estimates snr the index l) whose SNRs fulfill the following condition (s) link achievable rate C . Then, it chooses from a finite (s→r) (s→r) (r→d) (r→d) (s) set the maximal discrete-rate corresponding to C , and = max(snr ) and snrl = max(snr ), snrl (11) sends an M -bit rate indicator to the destination. (MFMC) C

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(s→r)

S1.2 The destination recovers a quantized version of snr sending  L a relay selection indicator which consists of (s→r)  bits. log2 K (denoted by snr  ) from the M -bit rate indicator (r→d) S2.3 Those selected relays send their M -bit rate indicator th received from the  relay. It also estimates snr (s) (MFMC) about C to the destination. Then, we can employ S1.2 and snr(s→d) , and then computes C according presented in Section III-A to select the best relay. to (7) and chooses the best relay according to (8). The (s) (r) The signaling overhead for the proposed scheme is transmission rates Rl and Rl are computed according    L to (9) and (10), respectively. Finally, both the index of O = KM + log K + 2M + log . (15) (s) (r) 2 2 K best relay and the discrete version of Rl and Rl are fed back to the source and relays. If K is much smaller than L, the overhead reduction when This scheme can effectively reduce the signaling overhead to comparing with (14) approximates to the ratio of (L − K)/L. The first-stage relay selection can also be performed at reO = LM + log2 L + 2M (14) lays. Specifically, the destination sends an M -bit rate indicator at the price of rate loss due to the rate quantization. On the about C (s→d) so that each relay knows a quantized version of (s→r) other hand, the overhead in (14) is linearly increasing with snr(s→d) (denoted by snr  (s→d) ). Since the p.d.f. p(snr ), respect to the number of relays (i.e. L), and thus it would be p(snr(r→d) ) is common knowledge, each relay can locally  still too large for a large L. Next, we present several two- compute the complementary c.d.f. Pr(C (MFMC) > C ), T  stage relay selection schemes in order to further reduce the ∀. Given the number of candidates K, all terminals know signaling overhead mainly by reducing L. who should forward their rate indicator to the destination. Usingthis  scheme, the destination does not need to send a L B. Two-stage Relay Selection Schemes -bit relay-selection indicator, but instead an M -bit log2 K The key idea here underlies a two-stage relay selection rate indicator. Hence, the signaling overhead is further reduced process. At the first stage, a set of relays are selected according to O = KM + log2 K + 3M. (16) to a carefully defined policy; at the second stage, the best relay within the set is selected based upon instantaneous channel Remark 3: In fact, it is extremely complex to compute the quality information. We investigate the discrete-rate adaptation complementary c.d.f. Pr(C (MFMC) > C ). Instead, we can T  and relay selection scheme for both non-reciprocal channels (s→r) (r→d) replace the terms snr and snr in (7) with their corand reciprocal channels with the following conditions to be (s→r) (r→d) responding average SNR denoted by snr and snr , assumed. and then select K relays offering the largest CMFMC . This C1. Terminals have statistical knowledge of the channel qualscheme would certainly affect the optimality of first-stage ity of all communication links. In this paper, the statistical relay selection, but is more practical. knowledge is specifically referred to as the probability Remark 4: The schemes proposed for non-reciprocal chandensity function (p.d.f.) of SNR. Note that the case (s→r) (r→d) nels are based upon the p.d.f. p(snr ), p(snr ), and without statistical channel knowledge can be recognized thus remain some uncertainty about the best relay. For the as a case with SNR to be uniformly distributed within a approach where relays conduct the first stage relay-selection, certain range. This condition will be used for the case of (s→r) the deterministic knowledge of snr cannot be utilized to non-reciprocal channels. (s→r) reduce the uncertainty. This is mainly because snr is a C2. Each relay has the instantaneous channel knowledge of (s→r) th kind of private knowledge, which is still uncertain to other and their own S-R link, i.e., the  relay knows snr (s) terminals. correspondingly the achievable rate C . The destination 2) Schemes for reciprocal channels: When the system has the instantaneous channel knowledge of S-D link, operates in the reciprocal channels such as on the time-division i.e., snr(s→d) and correspondingly the achievable rate duplexing (TDD) mode, transmitters are able to estimate the C (s→d) . This condition is practical since the source can channel quality of forward links based on the feedback from broadcast training sequences to enable channel estimation receivers. If the destination sends the M -bit rate indicator at receivers. about C (s→d) , relays can estimate the channel quality of 1) Schemes for non-reciprocal channels: When the system their own R -D link. It means that each relay can compute  (MFMC) (s→r) (r→d) (s→d) operates in non-reciprocal channels such as on the frequencyC by employing snr , snr and snr  . division duplexing (FDD) mode, transmitters are not able to Then, we propose two schemes to perform the best-relay estimate the channel quality of forward links. If the destination selection and discrete-rate adaptation. forms the decision of relay selection, the following discrete• The first scheme allows for those relays fulfilling the conrate adaptation and relay selection scheme is proposed. (MFMC) dition C > CT to broadcast their rate indicator S2.1 The destination computes the complementary cumulative (MFMC) about C , so that all terminals know the index of (MFMC) distribution function (c.d.f.) of the capacity C (MFMC) best relay (i.e. l) in terms of the maximum of C . (MFMC) (denoted by Pr(C > CT )) by employing Then, the best relay sends an M -bit rate indicator about (s→r) (r→d) (s) p(snr ), p(snr ), and snr(s→d) , where Pr(·) Rl to the source. Since the best relay already knows stands for the probability, p(·) for the p.d.f., and CT for (r) Rl , the rate-adaptation process is completed. The total a threshold. amount of signaling overhead paid for this approach is S2.2 The destination selects K out of L relays offering O = KM + 2M, (17) the largest complementary c.d.f., and informs relays by

YI et al.: JOINT RATE ADAPTATION AND BEST-RELAY SELECTION USING LIMITED FEEDBACK

•

where the term KM reflects the number of signaling bits sent by K candidates selected at the first stage, and the term 2M reflects the rate indicators sent by both the destination and the best relay. Note that the factor K here is quite random and related to the threshold CT . The second scheme introduces a concept of incremental threshold. Specifically, a relay (say the th 1 relay) fulfilling (MFMC) > CT sends its rate indicator. the condition C1 (MFMC) Then, the threshold CT is updated with CT = C1 . This process repeats until CT becomes stable. The relay offering the transmission rate of CT is the best relay. This approach can further reduce the signaling overhead with (17) to be its worst case and 3M (i.e. K = 1 in (17)) to be the best case. On the other hand, the thresholdincremental approach can complicate the medium access control (MAC)-layer structure. IV. P ERFORMANCE A NALYSIS FOR S CHEMES WITH L IMITED F EEDBACK

The schemes proposed in Section III reduce the signaling overhead mainly by means of reducing the number of relay signaling from L to K as well as employing an M -bit rate indicator. It is well recognized that using M -bit rate indicator results in rate loss in comparison with the achievable rate. Moreover, reducing the number of relay signaling could result in an event of missing the best relay (MBR), and consequently lead to a rate loss. These are two main issues to be discussed in this section. A. Rate Loss Due to M -bit Rate Indicator In the case of single-link rate adaptation, the computation of rate loss is straightforward, i.e., RL = log2 ( 1+snr 1+snr  ). The issue of optimizing the rate loss for single-link adaptation is out of the scope of interest. Instead, we are more interested in whether the proposed schemes would increase the rate loss in comparison with the single-link scenario. This issue is investigated for two modes, i.e., decision at the destination and decision at the relays. Here, we assume that the best relay has been correctly identified, and then the multi-relay problem reduces to the single-relay problem; and the relay index  is dropped for the sake of simplifying the notation. The general problem is easy to state. Given the quantized rate R (s) = R (s) − RL(s) and R (r) = R (r) − RL(r) , what  when compared to is the overall rate loss (denoted by RL) the single-link scenario? We address this problem by applying R (s) and R (r) in (5) in order to obtain the overall transmission when discrete rate is employed at the source and relay. rate R R = =

(R (s) − RL(s) )(R (r) − RL(r) )

(R (s) − RL(s) ) + (R (r) − RL(r) )

(18)

R (s) R (r) − RL(s) R (r) − RL(r) R (s) + RL(s) RL(r) R (s) + R (r) − RL(s) − RL(r)

(s)

(r)

(r)

RL R + RL R R (s) + R (r) > R − max(RL(s) , RL(r) ). >R−

(19)

(s)

(20) (21)

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TABLE I SNR CONFIGURATION FOR THE S–R AND R–D LINKS WHEN COMPARED TO THE S–D LINK SNR. Cases I II III

S–R link +6 dB +20 dB +0 dB

R–D link +6 dB +0 dB +20 dB

Scenario Relay in the middle Relay close to source Relay close to destination

 we can use (21) to obtain RL  < Due to R = R − RL, max(RL(s) , RL(r) ). It means that the overall rate loss is smaller than the larger single-link rate loss.

B. Probability of MBR The probability of MBR is suitable for evaluating the performance of two-stage schemes proposed for non-reciprocal channels, where the instantaneous SNR of S-R link and R-D link is uncertain at the first-stage relay selection. The event of MBR occurs when the best relay is not in the set of K candidates at the first-stage relay section due to its small complementary c.d.f. or small snr(s→r) and snr(r→d) . Denote (MFMC) P = Pr(C > CT ). Without loss of generality, the relationship P1 > P2 > · · · > PL is assumed. Then, the probability of MBR can be mathematically expressed by PMBR = Pr(l ∈ {K + 1, K + 2, ..., L}).

(22)

Analog expression also applies to the case when using the average SNR snr(s→r) and snr(r→d) for the first-stage relay selection. The computation of PMBR is a very complex orderstatistics problem, and it would not lead to a simple closedform solution. Instead, we will numerically study this metric as well as its impact on the overall system performance.

V. N UMERICAL R ESULTS AND D ISCUSSION Computer based Monte Carlo simulations were used to demonstrate pros/cons of the proposed joint rate-adaptation and relay selection schemes. All the communication channels were generated independently according to Rayleigh distribution with unity variance. All transmitters use the equal transmission power. The main metric of interest was the overall transmission rate in bits/s/Hz. The SNR was defined by average received signal power to noise ratio. The numerical results were produced by employing four carefully designed experiments with each having 10, 000 Monte Carlo trials. Experiment 1: The objective of this experiment is to examine the performance of continuous-rate adaptation scheme presented in Section II-B in the single-relay network. In this experiment, the system does not need to perform relay selection, but only decide whether the relay should be used or not. The baseline for comparison is the achievable rate when the source and relay use the same transmission rate, i.e., the equal-time transmission T1 = T2 . Fig. 2 displays the transmission rate versus S-D link SNR for the system configuration given in Table I. It can be observed that the proposed scheme outperforms the equal-time transmission scheme for all cases. The difference is around 0.2 bits/s/Hz at SNR= 0 dB and 0.5 bits/s/Hz at SNR= 20 dB. This difference is considerable for wideband communications.

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5.8

6.4

Case I Case I Case II Case II Case III Case III

5

Transmission Rate (bits/s/Hz)

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L=3 relays L=3 relays L=6 relays L=6 relays L=9 relays L=9 relays

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Experiment 2: The objective of this experiment is to examine the performance of proposed continuous-rate adaptation scheme in the multi-relay scenario. The number of relays is configured by: L = 3, 6, 9, respectively. Moreover, relays are equally allocated into three cases of SNR configuration shown in Table I. For example when L = 3, one relay is configured for Case I, one for Case II, and another for Case III. The baseline for comparison is again the equal-time transmission but in the multi-relay scenario. The simulation results are plotted in Fig. 3. It is observed that the proposed scheme outperforms the equal-time transmission by around 0.4 bits/s/Hz when the S-D link SNR varies within 0−20 dB. Moreover, for both schemes, the transmission rate generally increases by increasing the number of relays. This is because the probability of having good relay channel is direct proportional to the number of relays. This probability increases fast for small number of relays (e.g. L = 1, 2) and slowly for large number of relays (e.g. L = 6, 9). This is why the transmission rate increases around 1 bits/s/Hz for L varying from 1 to 2 (see Fig. 2), and around 0.1 bits/s/Hz for L varying from 6 to 9. Fig. 4 illustrates the simulation results using discrete-rate adaptation and limited feedback (i.e. the scheme presented in Section III-A). The M -bit rate indicator is set by M = 3. Here, the baseline is the continuous-rate adaptation scheme with full channel knowledge as well as the equal-time transmission using discrete-rate and limited feedback. It is observed that the difference between the proposed scheme and the equal-time transmission scheme is still around 0.4 bits/s/Hz when both are using limited feedback. The difference between the proposed scheme with limited feedback and that with full channel knowledge varies within 0.4 − 0.6 bits/s/Hz. This difference is mainly due to the rate loss of discreterate adaptation. Interestingly, it is observed that increasing the number of relays cannot improve the performance of both the equal-time transmission and proposed scheme when the limited feedback is used. This is because the rate loss induced by the limited feedback is much larger than the gain obtained by increasing L. In addition, we compare the proposed scheme with the uncoded adaptive modulation scheme [18] in terms of the

10

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Fig. 3. Transmission rate vs. S-D link SNR for the multi-relay scenario with the number of relays L = 3, 6, 9. 6.4

L=3 relays L=3 relays L=3 relays L=6 relays L=6 relays L=6 relays L=9 relays L=9 relays L=9 relays

6

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Transmission Rate (bits/s/Hz)

Fig. 2. Transmission rate vs. S-D link SNR for the single-relay network operating in three difference cases. Case I: both the S–R and R–D links are 6 dB better than the S–D link; Case II: the S–R link is 20 dB better than both the R–D and S–D links; Case III: the R–D link is 20 dB better than both the S–R and S–D links.

8

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Fig. 4. Transmission rate vs. S-D link SNR of the proposed scheme using discrete-rate adaptation with the number of relays L = 3, 6, 9. The solid line denotes the proposed scheme using limited feedback; the dash dot line denotes the proposed scheme with full channel knowledge; the dash line denotes the equal-time transmission using limited feedback.

transmission rate. The target bit-error-rate of the uncoded scheme is 1 × 10−3. The modulation format can be adaptively selected from the finite set (4-QAM, 16-QAM, 64-QAM, 256-QAM). The simulation results are plotted in Fig. 5. It is not surprised to see a big gap between the uncoded adaptive modulation scheme and the proposed scheme, since the uncoded scheme does not have error-correction capability. Experiment 3: The objective of this experiment is to examine the two-stage discrete-rate adaptation and relay selection schemes proposed for non-reciprocal channels (see Section III-B-1) with the average SNRs snr(s→r) and snr(r→d) being used for the first-stage relay selection. The number of relays is fixed to L = 9, and the number of candidates is configured by K = 1, 3, 6, 8. The baseline for comparison is mainly the continuous-rate adaptation and relay selection scheme with L = 9. Fig. 6 illustrates the transmission rate for two schemes with the first-stage relay selection being performed either at the destination or at the relays. It is observed that both schemes offer almost identical performances. The transmission rate generally increases by increasing the number of candidates K. The performance improves rapidly when K varies from 1 to 3, and shows only minor difference (less than 0.05 bits/s/Hz)

YI et al.: JOINT RATE ADAPTATION AND BEST-RELAY SELECTION USING LIMITED FEEDBACK

TABLE II P ROBABILITY OF MISSING THE BEST- RELAY FOR APPROACHES PROPOSED FOR NON - RECIPROCAL CHANNELS .

6.4

Continuous rate Discrete rate Adaptive modulation (uncoded source)

6

Approach Sel. at Destination Sel. at Relays

5

Transmission Rate (bits/s/Hz)

2803

K=1 87% 86%

K=3 71% 69%

K=6 47% 40%

K=8 9.4% 7.8%

4 6.4

Baseline CT=2Csd

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sd

CT=6Csd C =2C

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T

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sd

C =4C T

sd

CT=6sd

4.5

Baseline

4

3.5

3

2.5

Fig. 5. Comparison between the proposed scheme and the uncoded adaptive modulation with the number of relays L = 3.

Two−Stage Relay Selection

2

1.5 1.2

Baseline K=1 K=3 K=6 K=8 K=1 K=3 K=6 K=8

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Fig. 7. Transmission rate vs. S-D link SNR of the two-stage schemes proposed for reciprocal channels. The number of relays is fixed to L = 9. The marker in white denotes the approach using fixed threshold; the marker in black denotes the approach using incremental threshold.

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Fig. 6. Transmission rate vs. S-D link SNR of the two-stage schemes proposed for non-reciprocal channels. The number of relays is fixed to L = 9. The marker in white denotes the approach with the first-stage relay selection performed at the destination; the marker in black denotes the first-stage relay selection performed at relays.

when K varies from 6 to 9. The difference between K = 3 and K = 9 is around 0.1 bits/s/Hz. Comparing with the baseline, the discrete-rate adaptation scheme has around 0.3 bits/s/Hz rate loss for the case of K = 6, 9. Moreover, in order to study the relationship between the probability of MBR and the transmission rate, Table. II displays the PMBR with respect to different configurations of K. The S-D link SNR2 is fixed to 10 dB. It is shown that the PMBR is very large for small K (= 1, 3 ), and becomes reasonably small for K = 8. We can conclude that the rate difference between the cases of K = 1, 3, 6 is mainly caused by the large PMBR. When the PMBR is smaller than 50%, its impact on the rate loss is negligible. Experiment 4: The objective of this experiment is to examine the two-stage discrete-rate adaptation and relay selection schemes proposed for reciprocal channels (see Section III-B2). The number of relays is fixed to L = 9. The baseline for comparison is the continuous-rate adaptation and relay selec2 Our

0

SD Link SNR (dB)

6.4

simulation results show that the PMBR is not sensitive to the SNR.

tion scheme with L = 9. Fig. 7 illustrates the transmission rate for the schemes using either fixed threshold or incremental threshold. The initial configuration of the threshold CT is: CT = αC (s→d) , α = 2, 4, 6. It is observed that both the fixed threshold approach and incremental threshold approach offer identical performances, which is not sensitive to the configuration of CT . Moreover, the rate loss of proposed schemes when compared to the baseline is around 0.2 − 0.3 bits/s/Hz. This small rate loss is mainly because of the relays using the quantized channel quality information of the S-D link. Fig. 8 illustrates the number of candidates (i.e. K) vs S-D link SNR for both fixed threshold and incremental threshold schemes. It is shown that the number of candidates generally decreases with increasing of SNR. In small SNRs, the fixedthreshold scheme selects a large number of candidates, e.g., K/L = 5.8/9 at SNR= 0 dB or K = 4/9 at SNR= 2 dB, when the threshold-incremental scheme only selects a small number of candidates, e.g., K/L = 1.5/9 at SNR= 0 dB. It means that the threshold-incremental scheme can significantly reduce the signaling overhead at small SNRs in comparison with the fixed threshold scheme. It is also observed that the fixed threshold scheme converges to the threshold-incremental scheme at moderate and high SNRs (e.g. SNR> 12 dB). Hence, we would recommend the fixed-threshold approach for mobile networks operating at moderate and large SNRs because of its relative simpler MAC structure. Finally, since we have presented quite a few joint rateadaptation and relay selection schemes, it might be interesting to have a summary of the performance in terms of the transmission rate (an indicator of forward-link spectral efficiency) and the signaling overhead (an indicator of feedbacklink spectral efficiency). We use the equal-time continuousrate transmission scheme as the baseline to measure the

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TABLE III A SUMMARY OF PROS / CONS OF THE PRESENTED SCHEMES IN TERMS OF TRANSMISSION RATE AND SIGNALING OVERHEAD AT THE TYPICAL SNR = 10 dB WITH L = 9 RELAYS IN R AYLEIGH FADING CHANNELS . F OR THE NON - RECIPROCAL CASE , D: DECISION AT THE DESTINATION ; R: DECISION AT THE RELAYS . Schemes Continuous-rate equal-time Tx The proposed continuous-rate The proposed discrete-rate (Sec. III-A) The proposed discrete-rate (non-reciprocal, K=6) The proposed discrete-rate (non-reciprocal, K=3) The proposed discrete-rate (reciprocal, fixed thres.) The proposed discrete-rate (reciprocal, incremental thres.)

α=2 α=4 α=6 α=2 α=4 α=6

No. Selected Relays at the 1st Stage

Fixed Threshold

4

T2 (r→d) log2 (1 + snr ). (23) T1 + T2 Combining the S-D link with the R -D link can effectively increase the SNR at the destination since x(s) carries exactly (r) the same information as in x . Next, we will discuss the achievable rate by employing different linear precoding at the source and relay. Consider the source and the th relay employing identical channel encoders to encode the message ω. The output of the channel encoder is a coded block, say sM , with the block length of M ≤ min(T1 , T2 ). Without loss of generality, we assume T1 < T2 . Prior to transmission, the source applies linear precoding on s and yields an T1 × 1 block: x(s)  Gs, where G is an T1 × M dimensional matrix with G H G to be an M ×M identity matrix (the superscript (·)H denotes the matrix Hermitian). Analogously, the relay performs linear precoding on sM and yields an T2 × 1 block: x(r)  QGs, where Q is an T2 × T1 dimensional matrix with QH Q to be an T1 × T1 identity matrix. It is easy to see that the source and relay send signal block with different length (i.e., different transmission rates). At the destination, the signal block received through the S-D link and the R -D link can be expressed by (r→d)

3

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Sig. Overhead in bits 324 (0%) 356 (+9.87%) 37 (-88.6%) D: 34 (-89.5%); R: 30 (-90.7%) D: 24 (-92.6%); R: 20 (-93.8%) 9 (-97.2%) 6.8 (-97.9%)

th DF relay channel is limited by both the achievable rate of S-R link and the achievable rate of combining R -D and S-D link. The former is limited by the S-R link capacity, i.e., (s) C in Theorem. 1. Due to the half duplex nature, the overall (s) (s) transmission rate of S-R link is: R < (T1 C )/(T1 + T2 ). Analogously, the achievable rate of R -D link is rather trivial

6

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Trans. Rate in bits/s/Hz 3.25 (0%) 3.58 (+10.1%) 2.77 (-14.7%) 3.17 (-2.46%) 3.03 (-6.76%) 3.30 (+1.5%) 3.30 (+1.5%)

20

SD Link SNR (dB)

Fig. 8. No. of candidates (K) vs. S-D link SNR of the two-stage schemes proposed for reciprocal channels. The number of relays is fixed to L = 9. The marker in white denotes the scheme using fixed threshold; the marker in black denotes the scheme using incremental threshold.

performance at the typical SNR of 10 dB with L = 9 relays. In the computation of signaling overhead, we assumed that the feedback of a real value costs 32 bits, and the M -bit rate indicator costs M = 3 bits as used in simulations. VI. C ONCLUSION In this paper, we have presented a novel joint rate adaptation and relay selection scheme for multi-relay network adopting half-duplex best-relay decode-and-forward protocol. The proposed scheme allows for the source and the best relay to employ different transmission rates so that it can outperform the conventional equal-time transmission scheme. Moreover, a number of discrete-rate adaptation and relay selection schemes have been proposed for both reciprocal and non-reciprocal channels for the sake of reducing signaling overhead. The performance of proposed schemes has been carefully investigated in terms of the reduction of signaling overhead, overall rate loss as well as the probability of missing best relay. It has been shown that the proposed schemes can significantly reduce the signaling overhead. For example at the typical SNR of 10 dB, the schemes proposed for nonreciprocal can reduce the signaling overhead by around 90.7% with the pay of 2.46% in spectral efficiency; the schemes proposed for reciprocal channels can reduce around 97.2% in signaling overhead with 1.5% gain in the spectral efficiency. A PPENDIX : P ROOF OF T HEOREM . 1 The maximum-flow min-cut (MFMC) principle indicates that the lower bound on capacity (i.e. achievable rate) of the


PRN ), respectively. We assumed that the two different frequency bands are employed for BS-RN and for RN-MT transmission. As a result, the RN is possible to simultaneously communicate with the BS and its associated MTs. The considered path-loss model between the target BS and RNs is the ITU-M2135 urban-area LoS [10], and the models between target BS and MTs, between RNs and MTs, and between interference BS and RNs/MTs are all ITU-M2135 urban-area Non Light-of-Sight (NLoS). Shadowing and fast-fading are both not considered. The Signal to Noise plus Interference

313

, and the inter-cell interference from other BSs is N0 zero becaused employing different frequency bands. According to the SINR, one out of the 16 Modulation and Coding Schemes (MCS) defined in LTE-A is adopted. When using the RB-based user scheduling, the SINR threshold (in dB) and its corresponding transmission efficiency η (bits/s/MHz) are listed in the Appendix A. Non-cooperative relaying with at most two hops from BS to MT is assumed. Each MT in the same area Ai compares the achievable transmission efficiency ηBS0 −MT Ai connecting m directly with the BS, to the one ηBS0 −RNn −MT Ai via the m n-th RN. The transmit efficiency of ηBS0 −RNn −MT Ai is m formulated as 1 . (2) ηBS0 −RNn −MT Ai = 1 1 m ηBS −RN + η A 0

n

RNn −M Tmi

If the directly connected tranmisssion has a higher efficiency (ηBS0 −MT Ai ≤ ηBS0 −RNn −MT Ai ), the m-th MT m m communicates directly to the 0-th BS; otherwise, it communicates via the n-th RN. We define a decision vector x = [x1 , . . . , xn , . . . , xN ], where xn equals one if and only if a RN is deployed at the n-th candidate site, otherwise xn equals zero. Hence, if the location of RNs are determined and represented by the vector x, the transmit efficiency of all MTs in the same area Ai is formulated as    η(MT Ai |x) = max ηBS0 −MT Ai , max ηBS0 −RNn −MT Ai . m m m n (3) Naturally, MTs located away from the BS at the cell-edge are more likely to communicate via a RN. We further define a (|A| × N )-size matrix Yx ,     η Ai 1 n = arg max  n  BS0 −RNn −MTm x and ηBS0 −MT Ai < ηBS0 −RNn −MT Ai (4) yin = m m    0 otherwise x =1P represents the MTs in area Ai communicating where yin via n-th RN, n yin = 0 indicates the MTs in area Ai communicating directly with the BS0 .

B. Problem Formulation The teletraffic demanded by the MTs at time t is denoted as rt Ai (bits/s), which varies over time and locations. The MTm

peak value of demanded teletraffic RAi for a certain area Ai is formulated as ! X t RAi = max . (5) rMT Ai t

m

m

The area Ai is covered if the RN/BS is able to allocate WAi MHz frequency-band so that RAi ≤ η(MT Ai |x) WAi . m Naturally, if the RNs are deployed in an optimized manner, and provide high transmission efficiency to the high teletraffic demand area, the precious bandwidth can be minimized. Our target is to optimize the RNs location so as to minimize the required bandwidth and provide full cover to the target cell area at the same time. This could be formulated as follows min Wtotal (RAi , η(MT Ai |x) , Yx , ηBS0 −RNn ), x

m

(6)

subject to: xn ∈ 0, 1, ∀n ∈ {1, N },

(7)

x yin

∈ 0, 1, ∀n ∈ {1, N }, i ∈ {1, |A|}, dRNk −RNj ≥ dRN −min , ∀xk , xj = 1.

(8) (9)

The constraint (9) guarantees that the minimum distance between any two selected locations is larger than dRN −min so as to avoid intra-cell interference. Moreover, the total required bandwidth Wtotal is calculated as   |A| P x RAi yin  |A| N X X RAi   i=1 (10) Wtotal =  + ,  i=1 η(MT Ai |x) n=1 ηBS0 −RNn  m

which consists of two parts representing the bandwidth required for the BS/RN-MT communication and the bandwidth allocated for BS-RN link. III. T HE L OCATION -A IDED S CHEME M EASUREMENT

FOR

T ELETRAFFIC

In order to get the demanded teletraffic RAi of every area Ai , we propose a new measurement scheme, which use MTs to periodically (e.g. hourly) record their own location and demanded traffic. These records are stored in a centralized or distributed database. Giving access to this database, the demanded teletraffic RAi can be obtained, using Equation (5). The feasibility of the proposed scheme is based on the following facts: 1) The computational and storage capability of today’s MTs is much better than those used in the first/second generation of wireless systems. Teletraffic measurement can be carried out not only at the BS, but also at the more and more intelligent MTs; 2) The MTs are capable of tracking their own locations by using location navigation technology such as the Global Positioning System (GPS), and emerging location-based services, such as the “Foursquare check-in service”; 3) The authors of [11] have studied the trajectory of 100,000 anonymous mobile phone users whose position

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Index M T1

mobility patter Time period location 0am-9am home A3 9am-6pm office A5 6pm-12pm home A3

prob. 1 1 1

comms pattern service (K bps) prob. off(0) 1 idle(0) 1 calls(64) 1

TABLE I A N EXAMPLE OF THE DATABASE .

is tracked for six-months. The results demonstrated that human trajectories show a high degree of temporal and spatial regularity. Their further research results in [12] show a 93% potential predictability in user mobility. Hence, because of this regularity, it is promising to record a MT’s mobility pattern without requiring a hugh amount of storage resources. In fact, the technologies for MT users to record their locations and request communication service are already available. Assisted by the Foursqure check-in service and an easy-use map generation program, a journalist named Zachary M. Seward has published an article “Everything the Internet Knows About Me” on The Wall Street Journal1 . In the article, he shows a heatmap of the places he visited in 2010, and several statistical analysis of his daily habit of visiting Twitter, Google, etc.. Considering the information required for RN planning, we construct the database including the following information: 1) the MT’s index m; 2) mobility pattern; and 3) communication pattern. A simplified example is demonstrated in Table I. In this example, M T1 is switched off during the night at home area A3 . It’s in idle state from 9am to 6pm in the office area A5 , and it’s used for phone calls from 6pm to 12pm at home A3 . Although the situation in real life is much more complicated, this methodology is applicable. Compared to the conventional scheme, the advantage of the proposed scheme is in three folds. 1) The proposed scheme is theroretically capable of providing the demanded traffic of an arbitrary small area, by employing high-resolution location navigation technology. 2) The proposed scheme is capable of providing real-time variation of the demanded teletraffic. Assisted with the MTs’ mobility pattern, it could be possible to predict the future demanded teletraffic. 3) The MTs location information could be obtained from location-based service applications provider, which is part of the useful application-layer data, and does not require any additional network resources. The main problem of the proposed scheme is privacy concern. However, this kind of valuable data is not only useful for their own users to achieve self-awareness and reflection as stated by Zachary, but also useful for promoting business, so its amount is expected to expand signifantly influnce people’s life, as well as the communication system itself. IV. O PTIMIZATION A LGORITHM Similar to the problem of optimizing the BSs’ location in a single-hop cellular network, the optimization problem of 1 This article is available at http://blogs.wsj.com/digits/2010/12/22/ everything-the-internet-knows-about-me-because-i-asked-it-to/

Equation (6) is a NP-hard problem, which can not be solved within polynomial time. We adopt an heuristic solution similar to the algorithm proposed in [9]. The detail of the algorithm is illustrated in Algorithm 1 Algorithm 1: The RN deployment algorithm

3 4 5 6 7 8 9 10 11

counter ← 0, x ← 0, f ← 0; while counter < N and ∃n, fn = 0 do Calculate G(RNn , x, f ), ∀n, fn = 0; Find k = arg max{G(RNn , x, f ) > 0}; if k is nil then return x; else xk = 1, counter ← counter + 1;; Mark fj = 1 if dRNk −RNj < dRN −min ; end end

TABLE II S IMULATION PARAMETERS

The algorithm starts with three inputs: an integer number counter = 0, two all zeros vector x and f . counter represents the number of selected RNs’ location, which should be less than the total number of location candidates N . The vector x has been defined in Equation (7), and the initialized all-zeros vector means all areas Ai are covered by the central BS. The vector f also has a length of N , and fn = 0 means the n-th location is still a candidate location, while fn = 1 means the opposite. The function G(RNn , x, f ) is formulated as G(RNn , x, f ) = Wtotal (x) − Wtotal (x, xn = 1)

Value 500 × 500 (m2 ) 44 500 50 × 50 (m2 ) 100 40 (W atts) 20 (W atts) 125(m) [0, 64, 128, 512, 103 , 2 · 103 ] (Kbps)

M Tm

(11)

In every loop, the algorithm find out one RN location from the candidate set, which provides the maximum reduction in the total amount of required bandwidth. Then, the vector x, the variable counter and the flag vector f are updated as shown in Line 8 and 9, so that the distance between the selected k-th RN location and all locations remaining in the candidate set is larger than the required minimum distance dRN −min . The loop stops when no bandwidth reduction can be obtained, or the RNs’ location candidate set becomes empty.

3/4 of the achievable bandwidth reduction is attained after employing the first and the second RNs. The contribution from the forth RN becomes limited. We further consider a more practical scenario, when a fraction of MTs’ data is not able to be obtained in the database. We have repeat the simulation 1000 times, where those missing MTs’ index are randomly chosen. We calculate the distance between the chosen RNs location under incomplete information and those selected with complete information, which is named as misplaced distance. Fig. 4 demonstrates the averaged misplace distance versus the percentage of missing MTs. It is demonstrated that if 10% of the MTs’ data is missing, the same set of RN locations are selected. When the fraction increase from 0.2 to 0.5, the averaged misplaced distance increases accordingly. However, there are still three selected RN locations are the same as those selected under complete information. Fig. 4 shows that the RNs location selection does not require full knowledge of all MTs information. 6

x 10 0

1 6

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150 200 2

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BS

300

V. S IMULATION R ESULTS

350

Following the system model described in Section II, the simulation parameters are summarized in Table II. The MTs are assumed to have two different locations - home and office, and request one throughput from the six possible values shown in Table II. Fig. 2 demonstrates the distribution of demanded teletraffic as well as the selected RN locations using the optimization algorithm detailed in section IV. The square block having color from black to white represents the demanded teletraffic in bits/s. The BS is located in the center, and 7 RNs are deployed denoted by the white dots and the corresponding indices. The slash white lines represents the edges of the coverage area of RNs and the central BS. Fig. 3 shows the total bandwidth reduction when employing more and more RNs. It is clear that with the optimization algorithm, almost

400

315

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50

y−axis (meter)

1 2

Parameter Cell size d × d Number of RN candidate location N Number of MTs M Ai size Number of Areas |A| BS transmit power PBS RN transmit power PRN RN minimum distance dRN−min Throughput demanded set r t Ai

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Fig. 2. Geographic distribution of the demanded teletraffic, the locations of the central BS, the selected relay nodes and the corresponding coverage area.

VI. C ONCLUSIONS Taking advantage of the emerging technologies including smart phones, location navigation technology and locationbased services, we propose a new scheme for teletraffic measurement, which is to employ MTs for collecting their own location information and requested services, and constructing a

SINR (dB) efficiency (bits/symbol) η (bits/s/MHz) SINR (dB) efficiency (bits/symbol) η (bits/s/MHz) SINR (dB) efficiency (bits/symbol) η (bits/s/MHz) SINR (dB) efficiency (bits/symbol) η (bits/s/MHz)

320 300 280

Bandwidth (MHz)

260 240 220 200

-∞ 0 0 -1.2 0.60 345.9K 6.9 1.91 1110K 14.5 3.90 2423K

-7.1 0.15 87.6K 0.9 0.87 504.2K 8.7 2.40 1383K 16.2 4.52 2601K

-5.2 0.21 134.8K 2.7 1.17 676.1K 11.1 2.73 1570K 18.2 5.11 2941K

-3.1 0.34 216.7K 4.9 1.47 849K 12.6 3.32 1910K 22.1 5.55 3193K

TABLE III SINR THRESHOLDS ( D B) AND THE CORRESPONDING TRANSMISSION EFFICIENCY η ( BITS / SYMBOL )

180 160 140 120

0

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2

3 4 Number of RNs

5

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7

Fig. 3. The achievable bandwidth reduction versus the number of RNs employed from 0 to 7. 40 RN1 RN2 RN3 RN4 RN5 RN6 RN7

Averaged misplaced distance (meter)

35

30

25

R EFERENCES

20

15

10

5

0 0

0.1

the symbols are used for reference signal or synchorinzation, which leaves 12 × 14 × 0.7 = 115 symbol/ms. When using 10MHz, the number of RB equals 50, which results 5750K symbol/s. On average, it results 575K symbol/s/MHz. The relationship between SINR, the modulation and coding efficiency in bits/symbol and the corresponding η (bits/s/MHz) are demonstrated in Table III.

0.2 0.3 0.4 Percentage of unknown MTs (%)

0.5

0.6

Fig. 4. The averaged misplace distance versus the fraction of missing MTs.

data-base recording all MTs mobility and communication patterns. Compared to the conventional teletraffic measurement conducted at the access points, the proposed scheme is able to provide the demanded teletraffic of a area smaller than a cell/sector. We use such database in RN location optimization, which is here demonstrated by simulation results. ACKNOWLEDGMENT This work has been performed in the framework of the FP7 project ICT-248894 WHERE2 (Wireless Hybrid Enhanced Mobile Radio Estimators - Phase 2) which is partly funded by the European Union. A PPENDIX A LTE TRANSMISSION EFFICIENCY The basic unit of resource assigned to a user in LTE-A standard is a resource block (RB), which consists of 180KHz and lasts 1 ms. With 15KHz separation, and normal cycle prefix length, a RB has 12 × 15 symbols. Moreover, 30% of

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[1] Y.-d. Lin and Y.-c. Hsu, “Multihop cellular: a new architecture for wireless communications,” in IEEE Annual International Conference of Computer and Communications (INFOCOM). IEEE, 2000, pp. 1273– 1282. [2] TR 36.912 V10.0.0, “Further advancements for E-UTRA (LTEAdvanced),” 3GPP, Tech. Rep., 2011. [3] K. Tutschku, “Demand-based radio network planning of cellular mobile communication systems,” in 7th IEEE Annual International Conference of Computer and Communications (INFOCOM), vol. 3, 1998, pp. 1054– 1061. [4] F. Gordejuela-sanchez, S. Member, and J. Zhang, “LTE access network planning and optimization: a service-oriented and technology-specific perspective,” in IEEE Global Telecommunications Conference, 2009, pp. 1–5. [5] D. Niyato, E. Hossain, and D. I. Kim, “Relay-Centric Radio Resource Management and Network Planning in IEEE 802 .16j Mobile Multihop Relay Networks,” IEEE Transactions on Wireless Communications, vol. 8, no. 12, pp. 6115–6125, 2009. [6] B. Lin, P. Ho, L. Xie, and X. Shen, “Optimal relay station placement in broadband wireless access networks,” IEEE Transactions on Mobile Computing, vol. 9, no. 2, pp. 259–269, 2009. [7] Y. Yu, S. Murphy, and L. Murphy, “A clustering approach to planning base station and relay station locations in IEEE 802.16j multi-hop relay networks,” in IEEE International Conference on Communications, 2008, pp. 2586–2591. [8] A. Engels, M. Reyer, and R. Mathar, “Profit-oriented combination of multiple objectives for planning and configuration of 4G multi-hop relay networks,” in 7th International Symposium on Wireless Communication Systems (ISWCS), 2010, pp. 330–334. [9] H.-C. Lu and W. Liao, “Joint Base Station and Relay Station Placement for IEEE 802.16j Networks,” in IEEEGlobal Telecommunications Conference, 2009, pp. 1–5. [10] M. Series, “Guidelines for evaluation of radio interface technologies for IMT-Advanced,” ITU, Tech. Rep., 2009. [11] M. C. Gonz´alez, C. A. Hidalgo, and A.-L. Barab´asi, “Understanding individual human mobility patterns.” Nature, vol. 453, no. 7196, pp. 779–82, June 2008. [12] C. Song, Z. Qu, N. Blumm, and A.-L. Barab´asi, “Limits of predictability in human mobility.” Science (New York, N.Y.), vol. 327, no. 5968, pp. 1018–1021, Feb. 2010.

A.4

Location-aided MAC layer flexible Round-Robin scheduling

This appendix includes the following published paper: • D. Yang, J. Bastos, C. Verikoukis, J. Rodriguez, “Location-aided Round Robin Scheduling for Fractional Frequency Reused LTE-A Relay Network”, in IEEE IEEE CAMAD 2012, pp. 11-15, 2012.

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2012 IEEE 17th International Workshop on Computer Aided Modeling and Design of Communication Links and Networks (CAMAD)

Location-aided Round Robin Scheduling for Fractional Frequency Reused LTE-A Relay Network Du Yang1 , Joaquim Bastos1,2 , C. Verikoukis3 , Jonathan Rodriguez1 1 Instituto de Telecommunicac ¸ oˆ es. Aveiro,3810-196,Portugal 2 Universitat de Barcelona, Gran Via de les Corts Catalanes, 08007 Barcelona, Spain 3 Centre Tecnol` ogic de Telecommunications de Catalunya (CTTC),00860 Castelldegels, Barcelona,Spain Tel:+351 234 377900. Fax:+351 234 3779 Email:duyang,jbastos,[email protected],[email protected]

band are no longer in any adjacent cells, so that the resultant co-channel interference is reduced. One consequence of employing FFR is that the allocated bandwidth at the BSs and the RNs are only a fractional of the entire available bandwidth, which may not satisfy the heavy traffic demand occasionally occur in busy hours. In this scenario, one solution is to allow the BSs and RNs to temporarily use the same frequency band. In this paper, we propose a location-aided round robin [4] scheduling algorithm to achieve this goal. By exploiting the location information of the MTs, the proposed algorithm is capable of minimizing the resultant co-channel interference. The paper is organized as follows. The system model is first introduced in Section II, then our target problem is formulated in Section III. The proposed algorithm is detailed in Section IV followed by the simulation results in Section V. The conclusion is provided in Section VI.

Abstract—Relay aided cellular network promises numbers of attractive performances such as cell-edge throughput improvement, fairness enhancement, higher throughput and etc, which is considered in Long-Term-Evolution-Advanced (LTE-A) standard. However, the promised advantages can only be achieved under proper co-channel interference control such as employing Fractional Frequency Reuse (FFR). To overcome the drawback of FFR, we propose a location-aided round robin scheduling algorithm in this paper, which allows the several carefully chosen frequencies to be reused among donor eNodeBs and relay nodes, so as to satisfy the fluctuation of traffic demand. Index Terms—LTE-A, relay, FFR, location, scheduling

I. I NTRODUCTION Multi-hop cellular network integrates numbers of relay nodes into the conventional single-hop cellular network, which was first proposed by Lin and Hsu [1] in 2000. These relay nodes are capable of improving its own cells performances in terms of cell-edge throughput, fairness, energy saving and etc. Because of these benefits, multi-hop cellular network has been considered by the standardization community such as 3GPP and IEEE802. The research in decode-and-forward type of relaying technology was started in the Rel-9 3GPP Long Term Evolution (LTE) standard, and it is continuing studied in current Rel-11. Two types of Relay Nodes (RNs) have been defined in 3GPP LTE-Advanced [2]. Specifically, a Type-I RN locates outside the coverage area of its serving Base Station (BS), which is called its donor eNodeB. A Type-I RN has its own cell id, and is non-transparent to Mobile Terminals (MTs). On the other hand, a Type-II RN locates within the coverage of its donor eNodeB, shares the same cell id with its donor eNodeB, and is transparent to MTs. In this paper, we are interested in the Type-II relay network. MTs in the Type-II relay network suffers intercell interference not only from the surrounding BSs, but also from the RNs in other cells, which may locate closer to the MT than the interfering BSs do. The cell-edge throughput will not be improved if the interference issue are not properly controlled. One solution is to employ Fractional Frequency Reuse (FFR), where the three defferent frequency bands assigned to a certain RN, to its donor eNodeB, and to its adjacent interfered RNs, separately [3]. As a result, the RNs using the same frequency

978-1-4673-3125-8/12/$31.00 ©2012 IEEE

II. S YSTEM M ODEL The network layout considered in this paper is illustrated in Fig. 1. Without RNs, directional antennas are employed at each eNodeB, which separates the entire site into three cells. For example, the center site with an eNodeB id of 5 consists of three cells having id 13, 14, and 15 separately. On top of such a single-hop network, one low-power RN is employed in each cell covering the cell-edge area using omnidirectional antenna. We considered a FDD LTE-A downlink transmission scenario in this paper. The RNs operate in half-duplex mode. More explicitly, in the even number Transmission Time Interval (TTI), the eNodeBs communicate to the MTs and the RNs. In the odd number of TTIs, the eNodeBs communicates to the MTs only, and the RNs transmit information to their associated MTs. The scheduling of all MTs is centrally controlled by the eNodeBs. For the original single-hop network, the entire available frequency band is reused in every cell. Hence, a cell-edge MT M T1 located in cell15 shown in Fig. 1 suffers intrasite interference from cell13 and cell14 , as well as inter-site interference from other eNodeBs. If the frequency reuse factor remains 1 per cell, the same MT will inadditionally suffer cochannels interference from RNs in all other cells. To reduce

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Fig. 3.

Fig. 1.

Target Scenario.

handled by the eNodeBs. Supposed that there is a call request for M T1 , the diagram shown in Fig. 2 represents the process of a call set-up. Moreover, eNodeBs and RNs only transmit reference signal within their allocated frequency band. As a result, M T1 located in cell15 can measure the channel quality of frequencies in B0 only for those channels connected to eNodeBs, and the channel quality of frequencies in B3 only for those channels connected to RNs. Depending on the feedback Channel Quality Information (CQI) CQI(B0 , eN odeB) and CQI(B3 , RN ), the eNodeB schedules this user in some Resource Blocks (RB) in B3 , and informs this user via control channels. Based on this RB mapping, the MT will received data information at T5 via a RN. Since this MT only received data and reference signal in frequency band B3 at odd number of TTIs, it will be aware that it is connected via a RN. If the CQIs of frequency band B3 is much higher than those CQIs of B0 , it indicates that the connection via RNs is stable, and this user can only feedback CQIs of B3 to reduce feedback overhead and save energy. Otherwise, it can feedback all detected CQIs.

The layout of a relay-aided LTE-A cellar network.

III. TARGET S CENARIO AND P ROBLEM F ORMULATION The FFR relay network illustrated in Section II can reduce the co-channel interference. However, the resultant frequency reuse factor reduces below 1 per cell, which may cause some problem such in the scenario shown in Fig. 3. Supposed that round robin scheduler is employed at the donor eNodeB in cell15 , there are P MTs connected directly to the eNodeB in frequency band B0 having their QoS requirements just satisfied. Moreover, there are K edge MTs connected to the network via RN22 using frequency band B3 . The service quality of these K users are highger than their required QoS. A request comes into eNodeB asking to communicate with M T(P +1) which is located near the eNodeBs. If FFR is not applied, the scheduler could reduce the allocated bandwidth to the K edge MTs, and allocate the redundent resource in frequency band B3 to M T(P +1) . However, with fixed FFR, this request will be denied or delayed since the frequency band B0 has used up. To overcome the drawbacks of FFR, one possible solution is to allow the direct communication temporarily use some frequency resources in B3 . In fact, the reused frequency resource could be chosen from B2 and B1

Fig. 2. A brief illustration of the signalling process of setting up a call between the eNodeB and a cell-edge MT.

the co-channel interference, especially the strong interference from RNs in adjacent cells, the entire available bandwidth B is divided into four proportions. More explicitly, donor eNodeBs use frequency band B0 to communicate with its associated MTs located in the center of the entire site.The frequency band B1 , B2 and B3 are used by RN20 , RN21 and RN22 separately to communicate with the donor eNodeB at even TTIs, and with MTs located at the cell-edge at odd TTIs. RNs are transparent to MTs since all control information are

12

as well, which may introduce less interference because of the directional antenna. Nevertheless, the principle is the same regardless the specific frequency band. So we will continue using B3 in the following paper. Although satisfying the QoS requirement is our ultimately objective, we decided to use overall achievable throughput as performance metric instead in this paper for simplicity. From now on, we use RBs to represent different frequency band, since RB is one of the basic unit for scheduling in LTE-A system. One RB occupies 180kHz bandwidth and one TTI (1ms) time duration, which consist of 12 × 14 = 168 modulated symbol assuming normal cycle prefix. If a user M T1 can achieve spectral efficiency of η1 (bits/symbol), the achievable throughput of M T1 using one RB is 168η1 Kbit/s. We further simplify the problem by assuming that each user are located with only one RB. More explicitly, our target problem is rephrase as follows. • Assumption 1: The frequency band B0 consist of P RBs, which are equally shared by P MTs denoted as M Tpc (1 RB/MT). The frequency band B3 consist of K RBs, which are also equal shared by K cell-edge MTs denoted as M Tke (1 RB/MT). The superscription (·)c and (·)e represent “center” and “edge” separately. • Assumption 2: All MTs employ the opt2 feedback scheme shown in Fig. 2 for energy saving purpose. • Assumption 3: The location information of all MTs are available. A database recording the long-term averaged pathloss and shadowing for every location in cell15 is also available. • Target 1: Choose one MT p out of {1, 2, . . . , P + 1} cell-center MTs, choose another cell-edge MT k out of {1, 2, . . . , K} cell-edge MTs. The chosen M Tp and M Tk will employed the same RB k originally scheduled to M Tk . As a result, cell-center M T(P +1) can be served. • Target 2: Minimize the throughput loss at cell-edge, at he same time maximize the achievable throughput increasement for center MTs. Before proceeding to the next section, we want to justify the vadility of Assumption 3. The location information of a MT is become more available with the popularity of GPS-aided smart phones. Moreover, both 3GPP and IEEE802 standalization bodies are including positioning information into the future communication system[5]. Furthermore, user-behavior studies show that people location follows a certain pattern everyday, and it is highly predictable[6]. As a result, it is highly likely that in future communication systems, the location knowledge of a large proportional users and the corresponding long-term channel quality at these locations will be available at the eNodeBs.

to the eNodeB, it will receive high interference. An intuitive solution is that the chosen MT M Tk and M T(P +1) should be separated as far as possible, so that the resultant co-channel interference is minimized. Since the center MTs only feedback the CQI(B0 , eN odeB), the instantaneous interference signal strength caused by the RN in frequency band B3 for the center MTs are not available. Similarly, the intaneous interference signal strength caused by eNodeB in frequency band B3 for the cell-edge users are not available either. However, the location information of every MTs and their corresponding long-term channel quality including pathloss and shadowing at these locations are available. As a result, we can compare the long-term channel degradation between all K edge users and the donor eNodeBs, and choose the one having the highest degradation, so that to minimize the potential co-channel interference from eNodeBs. Similarly, we compare the long-term channel degradation between all P center MTs and the RN, then also choose the one having the highest channel degradation, so as to minimize the potential co-channel interference from RNs. These two chosen users will share the same RB. Other users are scheduled normally using the round robin algorithm. More precisely, the proposed algorithm is summarized in the following steps: •

• •

• • •

For each M Tke with coordinates (xek , yke ), searching out the database so as to determine the channel degradation value between this MT and the donor eNodeB PeN odebB−M Tke . Choose the cell-edge user le = e arg maxk {PeN odeB−M T1 , . . . , PeN odeB−M TKe }; For each M Tpc with coordinates (xcp , ypc ), searching out the database so as to determine the channel degradation value between this MT and the RN PRN −M Tpc . Choose the cell-center user mc = arg maxp {PRN −M T1c , . . . , PRN −M TPc }; Assign RB l in frequency band B3 to center user m. Schedule other users using the normal round robin algorithm. V. S IMULATION R ESULTS

In this section, we first demonstrate the essential of using FFR, by comparing the achievable spectral efficiency between relay aided network and single-hop cellular network, with and without FFRs. Secondly, we demonstrate the proposed scheduling algorithm statistically improve the achievable throughput of the entire cell. It has better performance than the random scheduling one. A. FFR-relay vs non-FFR-relay vs single-hop-network We consider a 1200×1000 m2 area with a spatial resolution of 10×10 m2 , where 7 eNodeBs are located with a separation distance of 500 meters. The network layout is as illustrated in Fig. 1. More simulation parameters are summarized in Table I. Single antenna is employed at BSs, RNs and MTs. Only considering the pathloss and shadowing, we calculate the achievable spectral efficiency η at different locations. Then we

IV. L OCATION - AIDED ROUND ROBIN S CHEDULING The first target can be easily satisfied even by radomly choosing one RBs m currently using by M Tk from frequency band B3 , and allocating this RB to the new number M T(P +1) . However, this cannot satisfied the second target, since the location of M Tk and M T(P +1) is random. If M Tk is close

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Transmit power at eNodeB Transmit power at RNs Distance between RN and eNodeB Pathloss between eNodeB and MTs Pathloss between RNs and MTs Pathloss between eNodeB and RNs Shadowing fading

40 Watts 1 Watts dBS−RN 150 meter M2135[7] NLoS M2135 NLoS M2135 LoS zero mean, 8dB deviation BS Pmax RN Pmax

TABLE I S IMULATION PARAMETERS

Fig. 5. The spectral efficiency comparison between relay aided network with FFR and single-hop network, which demonstrate that FFR is essential for achieving cell-edge throughput for a network having close located eNodeBs.

Fig. 4. The spectral efficiency comparison between relay aided network without FFR and single-hop network, which demonstrate that the benefits of relaying are diminished because of the co-channel interference.

compare the situation of using one relay per cell aided network, and the single-hop network. Their spectral efficiencies are denoted as ηr and ηs respectively. Fig. 4 represents the difference ηr − ηs in the interested area. It shows that only a small area has efficiency improvement, some area has even poorer performance than single-hop network. The benefits of relaying are diminished because of the co-channel interference. While Fig.5 compares the spectral efficiency between relay aided network with FFR ηF F Rr and single-hop network ηs , which demonstrate that FFR is essential for achieving celledge throughput for a network having close located eNodeBs.

Fig. 6. Experimental Cumulative Density Function of the total throughput of four edge MTs, in the scenario of 1) no RB reuse; 2) 1 RB reuse with random selection; and 3) 1 RB reuse using the proposed scheduling algorithm.

cell-edge frequency band is randomly chosen and allocated to the 10-th cell-central MT. 3) One cell-edge MT is chosen to share its RB with a chosen cell-central MT using the proposed location-aided round robin scheduling algorithm. Basically, if the CDF curve shift to the right direction, it indicates higher throughput is achieved. As a result, the two experimental CDF demonstrated that firstly, the achievable total throughput for the central MTs are increased by reuse a RB. The proposed algorithm achieves higher total throughput than the random selection method. Moreover, the achievable total throughput at the cell-edge is reduced because of the co-channel interference of reusing one RB at the cell center. Using the proposed algorithm is capable of compensate the degradation compared to random selection algorithm.

B. Performance of the proposed algorithm The relay aided network with FFR employed in the previous section is employed. We considere a transmission scenario in one of the central cell cell15 . Using the problem formulated in Section III, we set up our simulation with the following parameters P = 9, K = 4. The MTs locations are randomly generated, and the simulation results are averaged over 5000 different locations. Fig. 6 and Fig. 7 demonstrates the experimental cumulative density function of the total throughput of cell-edge users, and cell-control users, respectively. Three scenarios are compared: 1) There are 9 cell-central user, and 4 cell-edge user. One Orthogonal RB is assigned to each of them. 2) One RB in the

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[7] M. Series, “Guidelines for evaluation of radio interface technologies for IMT-Advanced,” ITU, Tech. Rep., 2009.

Fig. 7. Experimental Cummulative Density Function of the total throughput of central MTs, in the scenario of 1) no RB reuse; 2) 1 RB reuse with random selection; and 3) 1 RB reuse using the proposed scheduling algorithm.

VI. C ONCLUSION In this paper, we demonstrate that the 3GPP Type-II relay aided cellular network is capable of enhancing the throughput at the cell-edge. However, to achieve the promising gain, the co-channel interference has to be carefully controlled. Frequency fractional reuse is an efficient way of reducing the co-channel interference. To overcome the drawback of FFR, we propose a location-aided round robin scheduling algorithm, which exploit the MTs’ location information to allow some frequency band to be temporarily reused within a cell area, so as to improve center area’s throughput. ACKNOWLEDGMENT This work has been performed in the framework of the FP7 project ICT-248894 WHERE2 (Wireless Hybrid Enhanced Mobile Radio Estimators - Phase 2) which is partly funded by the European Union. R EFERENCES [1] Y.-d. Lin and Y.-c. Hsu, “Multihop cellular: a new architecture for wireless communications,” in IEEE Annual International Conference of Computer and Communications (INFOCOM), vol. 00, no. c. Ieee, 2000, pp. 1273–1282. [2] G. TR 36.814 V9.0.0, “Further advancements for E-UTRA physical layer aspects,” Tech. Rep., 2010. [3] N. Krishnan, R. Yates, and N. Mandayam, “Bandwidth Sharing for Relaying in Cellular Systems,” IEEE Transactions on Wireless Communications, vol. 11, no. 1, pp. 117–129, 2012. [Online]. Available: http://ieeexplore.ieee.org/xpls/abs all.jsp?arnumber=6087250 [4] E. Hahne, “Round-robin scheduling for max-min fairness in data networks,” Selected Areas in Communications, IEEE Journal, vol. 9, no. 7, pp. 1024–1039, 1991. [Online]. Available: http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber= 103550http://ieeexplore.ieee.org/xpls/abs all.jsp?arnumber=103550 [5] G. TS36.355 V10.1.0, “LTE positioning protocols (LPP),” pp. 1–114, 2011. [6] C. Song, Z. Qu, N. Blumm, and A.-L. Barab´asi, “Limits of predictability in human mobility.” Science (New York, N.Y.), vol. 327, no. 5968, pp. 1018–21, Feb. 2010.

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A.5

Novel Contributions to MISO and MIMO multi-User Single- and MultiCell

This appendix includes the following published papers: • F. Negro, M. Cardone, I. Ghauri, D.T.M. Slock, ”SINR Balancing and Beamforming for the MISO Interference Channel”, In Proc. 22nd Annual IEEE Int’l Symp. on Personal, Indoor and Mobile Radio Communications (PIMRC), Sept. 11-14, 2011, Toronto, Canada. • F. Negro, I. Ghauri, D.T.M. Slock, ”Deterministic Annealing Design and Analysis of the Noisy MIMO Interference Channel”, In Proc. IEEE Information Theory and Applications Workshop (ITA), Feb. 6-11, 2011, La Jolla, USA. • F. Negro, D.T.M. Slock, I. Ghauri, ”On the Noisy MIMO Interference Channel with CSI through Analog Feedback”, In Proc. IEEE Int’l Symp. Communications, Control and Signal Processing (ISCCSP), May 2012, Rome, Italy. • D.T.M. Slock, ”Location Aided Wireless Communications”, in Proc. 5th IEEE Int’l Symp. on Communications Control and Signal Processing (ISCCSP), May 2-4, 2012, Rome, Italy. • D.T.M. Slock, ”MIMO Broadcast and Interference Channels with Location Based Partial CSIT”, in Proc. 19th European Wireless Conference (EW), Apr. 2013, Guildford, UK. • W. Guibene, D.T.M. Slock, ”Degrees of Freedom of Downlink Single- and Multi-Cell Multi-User MIMO systems with Location Based CSIT”, in Proc. IEEE 77th Vehicular Technology Conf. (VTCspring), 2-5 June 2013, Dresden, Germany. • H. Chabbi, Y. Lejosne, D.T.M. Slock, Y. Yuan-Wu, ”MIMO Broadcast Channels with Partial CSIT and Application to Location based CSIT”, In Proc. IEEE Conf. Signals, Systems and Computers (Asilomar), 3-6 Nov. 2013, Pacific Grove, CA, USA.

122

SINR Balancing and Beamforming for the MISO Interference Channel † Intel

Francesco Negro∗ , Martina Cardone† , Irfan Ghauri† , Dirk T.M. Slock∗

Mobile Communications, GAIA, 2600 Route des Crˆetes, 06560 Sophia Antipolis Cedex, France Email: [email protected], [email protected] ∗ Mobile Communications Department, EURECOM, 2229 Route des Crˆetes, BP 193, 06904 Sophia Antipolis Cedex, France Email: [email protected], [email protected]

Abstract—In this paper a K user multi-input single-output (MISO) interference channel (IFC) is considered where the interference at each receiver is treated as an additional Gaussian noise contribution (Noisy IFC). We address the MISO downlink (DL) beamformer design and power allocation for maximizing the minimum SINR with per base station power constraints and imposing a minimum quality of service (QoS) requirement for each receiver. We study a distributed iterative algorithm for solving the given beamforming problem based on a combination of duality principles and the property that max min SIN R problem is strictly related to the total power minimization problem. Finally we show that it is possible to characterize the entire Pareto boundary of the SINR (Rate) region for a Kuser MISO IFC solving a sequence of max min SIN R imposing different set of QoS constraints.

I. I NTRODUCTION In modern cellular systems a frequency reuse factor of 1 is considered to optimally exploit all spectral resources across the network. The throughput of such systems however is seriously affected by the inter-cell interference that is commonly identified as the major bottleneck of modern wireless communication systems. This consideration has led to intense research, one outcome of which is to somehow curtail interference in cell edge areas. Network operators and manufacturers have lately pushed for coordination and interference management techniques as policing strategies for cell-edge spectrum use. Other techniques where multiple cell signals are used to serve cell-edge users are also being studied. These methods often relying on collaboration between cell towers through backhaul links and joint processing of signals change the nature of cellular communications and represents a significant paradigm shift. For the purposes of this work we consider cooperation between cell towers up to the point of beamformer design. The underlying problem remains that of inter-cell interference and is mathematically described as a K-user interference channel (IFC) where pairs of users want to communicate between each other without exchanging (data) information with nonintended pairs. Interference at each user is treated as additional Gaussian noise contribution and hence linear beamforming processing is optimal. This, in the information theoretic sense, is the noisy interference channel. This paper addresses the max min SINR problem. This beamforming problem formulation satisfies a fairness require-

ment because at the optimum all the SINRs are equal, for this reason it is also called SINR balancing problem. Balancing the SINR implies that the system performances are limited by the weak users causing a reduction of the overall sum rate. This problem has been extensively studied in [1] for single cell Broadcast (BC) channel under the sum power constraint using the well-established tool of UL-DL duality [2]. In [3] the authors propose a similar algorithm to solve the same problem as in [1]. The multicell problem, that we call the IFC in this paper is more complex to handle due to the per-user (per BS) power constraints. [4] addresses duality in a similar setting which the authors call the multicell setting where previous results on interpretation of UL-DL duality as Lagrangian duality are exploited. [4] then solves the power minimization problem subject to Quality of Service (QoS) constraints and per base station power constraints formulated as weighted total transmit power. The SINR balancing problem in the MISO IFC has been studied, under general power constraints, in a recent paper [5] where only power optimization has been considered. In [6] the authors studied the beamforming design problem for SINR balancing in the MISO IFC under per base station power constraints proposing an iterative algorithm that solves the problem in a centralized fashion. In this paper we are interested in the SINR balancing problem for a MISO IFC with individual power constraints and we propose an iterative algorithm that solves the problem in a decentralized manner. Our solution is based on the relation between the SINR balancing problem and the power minimization problem underlined in [6]. We solve the max min SIN R problem using a sequence of power minimization problems where the QoS constraints in the beamforming problem are increased gradually until an infeasible point is found. Then, using bisection method, the optimal solution is determined. In the MISO IFC with per user power constraints, a subset of users always transmits with full power according to the antenna and user distribution in the system. We propose an iterative algorithm that solves the max min SINR problem for systems where only one user transmits with full power. In systems where the MISO IFC is separable, it can be shown that all users transmitting with full powers maximizes the minimum SINR. Finally we show that is possible to characterize the entire Pareto boundary of the SINR region for a general K-user MISO IFC solving a sequence of Weighted SINR (WSINR)

problems. Thanks to the one to one logarithmic relation between SINR and Rate we can then characterize the Pareto boundary of the Rate region for a general K-user MISO IFC. The basis of this characterization has been studied in [7] for a single-input single-output (SISO) IFC. Here we extend their results to the MISO IFC. II. IFC S YSTEM M ODEL 1 BS1

1

h11

g1

M S1

BS1

M1

M S1 M1

˜ 1K h

hK1 ...

...

...

...

˜ K1 h

h1K 1 BSK

gK MK

˜ 11 h

g˜1

1 M SK

hKK

BSK

g˜K MK

a) MISO DL

˜ KK h

M SK

b) SIMO UL

Fig. 1: System Model Fig. 1 depicts a K-user MISO IFC with K transmitterreceiver (TX-RX) pairs. This setting is relevant in the case of a network of femtocell base stations (BS) where each femtocell BS is serving a single user in the time-frequency unit of interest. The k-th BS is equipped with Mk transmitter antennas and k-th mobile station (MS) is a single antenna node. The k-th transmitter generates interference at all l 6= k receivers. Assuming the communication channel to be frequency-flat, the received signal yk at the k-th receiver can be represented as yk = hkk xk +

K X

hkl xl + nk

(1)

l=1 l6=k

where hkl ∈ C1×Ml represents the channel vector between the l-th transmitter and k-th receiver, xk is the CMk ×1 transmit signal vector of the k-th transmitter and nk represents (temporally white) AWGN with zero mean and variance σk2 . Each entry of the channel matrix is a complex random variable drawn from a continuous distribution. We denote by gk , the CMk ×1 beamforming (BF) vector of the k-th transmitter. Thus xk = gk sk , where sk represents the independent symbol for the k-th user pair. We assume sk to have a temporally white Gaussian distribution with zero mean and unit variance. In the SIMO UL channel the k-th BS applies a receiver ˜gk to suppress interference and retrieves its desired symbol. The output of such a receive filter is then given by

III. M AX -M IN SINR IN THE MISO IFC PER - USER POWER CONSTRAINTS

In this section we consider a MISO IFC in which each signal link has an individual SINR priority γi , ∀i = 1, . . . , K. Fairness then leads to a max min WSINR cost function. max min SIN Rk g1 ,...,gK k=1,...,K γk s.t. gH k gk ≤ Pk , ∀k = 1, . . . , K

where Pk represents the maximum available power at transmitter number k. This problem, under a sum power constraint, was already discussed in [8]. The optimal solution to SINR balancing occurs when all the weighted SINRs are equal, thus the commonly used term SINR balancing. As stated also in [5] and [7] we can claim that for fixed beamforming direction at the balanced point in the MISO IFC, at least one user transmits with full power, i.e., at least one power constraint is satisfied with equality. This is easy to see for the SISO IFC or the MISO case with fixed BF vectors because the user with the worse equivalent channel coefficient, cascade of channel vector and BF, to maximize its SINR tends to use all its available power while the other users will adjust their power in order to equate all the SINRs. Different is the situation when the beamforming design comes into the problem. When the MISO IFC is separable, meaning that each user has a number of antenna greater than or equal to the number of users Mk ≥ K, the following proposition describes the SINR balancing behavior. Proposition 1 At the balanced point in the separable MISO IFC, all users transmit with full power Proof: To prove the above statement consider, without loss of generality, a K = 2 user MISO IFC with Mk ≥ 2. Assume that the optimal solution of the SINR balancing problem is given for g⋆1 and g⋆2 where only transmitter 1 transmits with full power, kg⋆1 k2 = P1 , kg⋆2 k2 < P2 . Because T X2 has an excess of power the BF of user 1 can be modified s.t.: k¯ g1 k2 = kg⋆1 k2 ;

˜kk s˜k + r˜k = ˜gk h

˜kl s˜l + ˜gk n ˜gk h ˜k

l=1 l6=k

where we denoted with (˜.) all the quantities that appear in the UL in order to differentiate with the same quantities in the DL.

|h11 ¯ g1 |2 > |h11 g⋆1 |2 .

This new choice of BF for user 1 increases its SINR but at the same time causes a reduction of the SINR of the other user: SIN R1,2 (g⋆1 , g⋆2 ) < SIN R1 (¯ g1 , g⋆2 ) > SIN R2 (¯g1 , g⋆2 ). T X2 to compensate for the additional interference caused by the new BF ¯ g1 has to increase the transmitted power using a BF of the form: 2

K X

(2)

k¯ g2 k >

¯ g2 = kg⋆2 k2 ;

g⋆2 + δh⊥ 12 |h22 ¯ g2 |2 > |h22 g⋆2 |2

where h⊥ 12 is any vector that belongs to the orthogonal complement of h12 and δ is a complex scaling factor. The choice of δ should be s.t. SIN R1 (¯ g1 , ¯ g2 ) = SIN R2 (¯ g1 , ¯ g2 ). With this choice of ¯ g2 we can rise the useful signal power for user 2 without increasing the interference caused to the non intended receiver.

With the new set of beamformers both the SINRs are increased SIN R1,2 (¯g1 , ¯g2 ) > SIN R1,2 (g⋆1 , g⋆2 ). This means that the original BF vectors were not optimal hence both users should transmit with full power. Different is the situation in low SNR regime. Here we can state that the optimal transmission strategy for each user is to maximize the useful signal component. No matter how strong interference becomes, noise remains the dominant impairment. Hence the optimum transmission strategy is to beamform to match the direct link (maximum ratio BF) at each TX. In this case the user with the worse direct link channel transmits with full power to maximize its SINR, which is also the systemwide worst SINR. This is true also for separable MISO channel, regardless the number of transmitting antennas. A. DL power allocation optimization For cases where a zero forcing solution is not possible (Mk < K, ∀k) only one user has its power constraint active. In this case for fixed BF vectors the corresponding power allocation vector can be found solving an eigenvalue problem [1] imposing only one power constraint to be active. At the optimum all the weighted SINRs are equal. Denoting with τ the optimal value of the ratio SINR over target QoS we can write: 1 p = DΦp + Dσ (3) τ where matrices D and Φ are defined as:  H H gj hij hij gj , j 6= i [Φ]ij = (4) 0, j=i D = diag{

γ1

gH hH h 1

11

11

g1

,...,

γK }. KK hKK gK

gH hH K

(5)

Assuming now that the j−th power constraint is the only one satisfied with equality and multiplying both sides of the previous equation by xTj = P1j ej , where ej is a vector with 1 only in position j, we get: 1 = xTj DΦp + xTj Dσ τ Introducing the compound matrix: ∆=

»

DΦ xTj DΦ

Dσ xTj Dσ

–

(6)

(7)

and the extended vector p = [p 1]T , using the results from the nonnegative matrix framework [9] the solution of the WSINR balancing problem w.r.t. the power optimization is given by: τ = λmax1 (∆) and the power vector is the corresponding positive eigenvector with the (K + 1)−th entry normalized to one. This approach that allows to extend the known result from SIR balancing to SINR balancing is called Bordering Method, it was introduced by [9] and then used in [1]. A different approach to handle noise in the SINR balancing problem is to transform (3) into an homogeneous system of linear equations. This method is based on considering a rank one modification of the matrix DΦ that leads to the same solution obtained using the bordering method. The fact that the j−th power constraint is active: xTl p = 1 allows

us to modify WSINR balancing problem in order to obtain an unconstraint optimization problem in terms of powers. Introducing a reparametrization of the Tx power vector: p=

1 ˜ p ˜ xTj p

(8)

we can rewrite (3) as 1 ˜ = (DΦ + DσxTj )˜ p p. τ

(9)

Also in this case the solution of the problem is given by the 1 positive eigenvalue τ = λ (DΦ+ DσxTj ) and the associated max positive eigenvector is the optimal power vector. At this point a question arises: Which power constraint is the only one satisfied with equality? It is possible to show that the only feasible constraint is given by xj ⋆ = arg maxxj λmax (B) [10], where B can be the rank 1 modified matrix or matrix ∆ in (7). To solve the problem when only one power constraint is active and none of the users can do ZF BF we can determine the following algorithm which solves K different optimization problems, imposing only one power constraint to be active, and finally we choose the optimal solution. The problem can be mathematically expressed as: max τj

{pi },τj

s.t. ej p ≤ Pj

SIN RkDL = γ1k P

(10)

H

pk gH hkk hkk gk k l6=k

pl gH l h

H kl

hkl gl +σk2

≥ τj

∀k

where we assume that the BFs are unit norm and for the moment they are not optimization variables, they are fixed. The Lagrange dual of the optimization problem can be transformed into an equivalent dual UL problem: min max τj µ {λi },τj P 2 s.t. i λ i σ i ≤ Pj , µ ≤ 1 λk gH hH kk hkk gk k SIN RkU L = γ1k P ≥ τj H H l6=k λl gl hkl hkl gl +µej,k

(11) ∀k

where λi represents the Lagrange multiplier associated to the i-th SINR constraint and µ is introduced to handle the power constraint. Those quantities represent the dual UL Tx power and the UL dual noise power respectively. Because we need to minimize the SINRs w.r.t. µ this variable should be large so it will assume its maximum value at the optimum: µ = 1. The UL max min WSINR problem can be solved w.r.t. to the UL power using one of the method described before, for example solving the following: 1 ˜ τl λ

˜ λ= = (DΦT + Dej σ T )λ;

Pj ˜ ˜λ σT λ

(12)

From the SINR constraint in the UL problem (11) we can see that the BF vector plays the role of RX filter. The optimal gk is the one that maximizes the SINR in UL and the solution for this problem is the well known generalized eigenvector

solution that for rank one channels has the following close form solution: X −1 H λl hH hkk (13) gk = ( lk hlk + ηk I) l6=k

where ηk represents the dual noise power, in this case η = ej,k . Finally the DL power allocation can be determined using equation (9). Once the K optimization problems have been solved the optimal solution that satisfies all the power constraints at the same time is obtained looking at the solution that has the minimum l⋆ = arg minj τj . In the corresponding DL power vector the j ⋆ -th user transmits with full power and at the same time all the other power constraints are inactive. For a more general system configuration the max min WSINR problem below: max τ g1 ,...,gK s.t. gH k gk ≤ Pk

SIN RkDL = γ1k P

gH hH kk hkk gk k ≥τ H hH h g +σ 2 g kl kl l l6=k l k

∀k

(14)

∀k

can be solved as in [6] using UL-DL duality. B. SINR Region Characterization The beamforming problem in terms of max min WSINR described in (2) and further refined in (14) can be interpreted as exploring the SINR region along the ray with direction γ = [γ1 , . . . , γK ]. Solving the max min WSINR problem allows us to find the maximum values of SINR on the direction given by γ. Then the optimal point is given by the intersection of the straight line described by γ and the Pareto boundary of the SINR region. This result was claimed for a SISO IFC in [7], here is extended to the MISO case. The Pareto boundary of the SINR region is commonly defined as follows: A SINR tuple (S1 , . . . , SK ) belongs to the Pareto boundary if there is no other tuple (Sˆ1 , . . . , SˆK ) with (Sˆ1 , . . . , SˆK ) ≥ (S1 , . . . , SK ) and (Sˆ1 , . . . , SˆK ) 6= (S1 , . . . , SK ). This result is important from an information theoretic point of view because solving the simple max min WSINR problem allows us to draw the entire Pareto boundary of the rate region, thanks to the logarithmic relation between SINRs and rates. This result is valid for a general K-user MISO IFC regardless of system parameters. In a recent paper [11] the authors provide a characterization of the Pareto boundary of the Rate region where the BF at each base station is a linear combination of the cross channels directly connected to it. This representation requires K(K − 1) complex parameters while the use of max min WSINR only requires (K − 1) real values, the fairness constraints γk . In [12] the authors propose a similar characterization of the Pareto boundary of the rate region using what they call rate profile. That problem can be thought as a rate balancing problem imposing different priority constraints and they state that to solve the problem a centralized solution in necessary. On the other hand for max min WSINR it is possible to develop a distributed algorithm to solve the problem, as shown in the following section, that represents a preferable solution compares to a centralized approach.

IV. D ECENTRALIZED I TERATIVE ALGORITHM In this section we describe an iterative algorithm that solves the weighted SINR balancing problem. It is essentially based on the link between the SINR balancing problem and the power minimization under QoS constraints underlined in [6]. The idea behind the proposed algorithm is to solve a sequence of power minimization problems with per base station power constraints incrementing at each step of the algorithm the QoS requirements imposed on the system. When the QoS constraints become not feasible then using bisection method we determine the optimal value of the max min WSINR problem. The advantage of this algorithm is that there exist a distributed solution [4] for TDD systems where UL and DL channel are reciprocals of each other. The power minimization problem is written as: PK H min g g g1 ,...,gK k=1 k k s.t. gH k gk ≤ Pk ; k = 1, . . . , K gH hH h g DL SIN Rk = P k H kkH kk k 2 ≥ γk ; k = 1, . . . , K l6=k gl hkl hkl gl +σk (15) where Pk represents the maximum TX power for user k. The Lagrange dual of the DL beamforming problem (15) can be rewritten as an equivalent UL optimization problem for the RX filter (13) where the dual noise is ηk = µk + 1. The dual UL problem can be mathematically expressed as: PK PK max min k=1 λk σk2 − k=1 µk Pk SIN RkU L

{µi } {λi } ˜ H hH hkk g ˜ λ g k = ˜ H P k k kk H ˜ g ( λl h hlk +ηk I)g k

l6=k

lk

k

≥ γk ; k = 1, . . . , K

λk ≥ 0; µk ≥ 0; ∀k.

(16) At the optimum the SINR constraints in the UL and DL problems must be satisfied with equality [4]. Using this property it is possible to derive the UL and DL TX powers. The UL TX power is determined using the following: P H ˜ gk a γk gH k ( l6=k λl hlk hlk + ηk I)˜ λk = γk = (17) H H hkk ˜ gk ˜k ˜k hkk hkk g g where a is obtained using (13). Because a scaling factor in the receiver filter at the BS does not affect the SINR, the optimal √ gk and pk is such that the WSINR in DL BF is gk = pk ˜ DL for user k is satisfied with equality. The last quantity that remains to be optimized is the Lagrange multiplier µk . On this purpose we use a subgradient method: (n)

µk

(n−1)

= [µk

+ t(gH k gk − Pk )]+

(18)

where t represents the step size. As stated at the beginning of this section the most important feature of the proposed algorithm is the possibility of distributed implementation that relies on channel reciprocity and few feedback of scalar quantities. V. N UMERICAL E XAMPLES In this section we present some numerical results in which we study the behaviour of max min WSINR. In Fig. 2 we report the Rate region of a 2-user MISO IFC where each

Algorithm 1 Iterative Algorithm for max min WSINR (0) (0) [γ1 , . . . , γK ]

Initialize: i = 0 and a feasible γ 0 = repeat i=i+1 (i) Find gk solving Power min for γ (i) Set γmin = γ (i) Increase γ (i+1) = αγ (i) until γ (i) is feasible repeat Set γmax = γ (i) i=i+1 min Set γ (i) = γmax +γ 2 (i) Find gk solving Power min for γ (i) if γ (i) is feasible then Set γmin = γ (i) else Set γmax = γ (i) end if until |γmax − γmin | > ǫ

VII. ACKNOWLEDGMENT EURECOM’s research is partially supported by its industrial members: BMW Group Research & Technology, Swisscom, Cisco, ORANGE, SFR, ST Ericsson, Thales, Symantec, Monaco Telecom, SAP and by the EU FP7 NoE Newcom++. The research of EURECOM and Intel Mobile Communications France is also supported in part by the EU FP7 FET project CROWN. R EFERENCES

base station has Mk = 2, ∀k transmitting antennas for a single channel realization. We plot on the same figure the rate obtained optimizing the max min W SIN R for different priority constraints γk . The rate region reported is obtained using the BF parametrization proposed in [11] for the 2-user MISO IFC that allows to draw the rate region, and hence the Pareto boundary. As we can see the rates obtained optimizing Rate Region 11 10 9

Rate 1 [bps/Hz]

8 7 6 5 4 γ1 = 100, γ2 = 100

3

γ1 = 80, γ2 = 160

2

γ = 800, γ = 20

1

γ = 400, γ = 80

0

1

2

1

0

1

2

3

4

5

6

VI. C ONCLUSIONS In this paper we show that SINR balancing in the MISO IFC leads to a balanced state where at least one user transmits with full power. When the IFC is separable (number of antennas sufficient to zero force), the SINR balanced state is where all users transmit with full powers. We derive an iterative algorithm to solve the given optimization problem based on the equivalence between SINR balancing problem and the power minimization problem with QoS constraints. Finally we show that WSINR balancing problem can be used to characterize the complete Pareto boundary of the SINR (Rate) region.

2

7

8

9

Rate 2 [bps/Hz]

Fig. 2: Rate region for a 2-user MISO IFC for σk2 = 30 dB the max min WSINR (red points in the figure) lie always on the boundary of the region. In addition we can see that varying the priority constraint γk it is possible to explore different points on the boundary. This figure sustain our statement on the possibility to characterize the entire Pareto boundary of the rate region using max min WSINR. The solid lines drawn on the figure represent the rays with direction given by γk . Those curves are straight lines in the SINR region but due to the log relation between SINR and Rate they have a logarithmic behaviour.

[1] M. Schubert and H. Boche, “Solution of the multiuser downlink beamforming problem with individual SINR constraints,” Vehicular Technology, IEEE Transactions on, vol. 53, no. 1, pp. 18 – 28, jan. 2004. [2] P. Viswanath and D.N.C. Tse, “Sum capacity of the vector gaussian broadcast channel and uplink-downlink duality,” Information Theory, IEEE Transactions on, vol. 49, no. 8, pp. 1912 – 1921, aug. 2003. [3] Xitao Gong, M. Jordan, G. Dartmann, and G. Ascheid, “Max-min beamforming for multicell downlink systems using long-term channel statistics,” in Personal, Indoor and Mobile Radio Communications, 2009 IEEE 20th International Symposium on, sept. 2009, pp. 803 –807. [4] H. Dahrouj and Wei Yu, “Coordinated beamforming for the multicell multi-antenna wireless system,” Wireless Communications, IEEE Transactions on, vol. 9, no. 5, pp. 1748 –1759, may 2010. [5] D. W. H. Cai, T.Q.S. Queck, and C. W. Tan, “Coordinated max-min sir optimization in multicell downlink - duality and algorithm,” in Communications (ICC), 2010 IEEE International Conference on, June 2011. [6] G. Dartmann, W. Afzal, Xitao Gong, and G. Ascheid, “Low complexity cooperative downlink beamforming in multiuser multicell networks,” in Communication Technology (ICCT), 2010 12th IEEE International Conference on, nov. 2010, pp. 717 –721. [7] H. Mahdavi-Doost, M. Ebrahimi, and A.K. Khandani, “Characterization of sinr region for interfering links with constrained power,” Information Theory, IEEE Transactions on, vol. 56, no. 6, pp. 2816 –2828, june 2010. [8] G. Montalbano and D.T.M. Slock, “Matched filter bound optimization for multiuser downlink transmit beamforming,” in Universal Personal Communications, 1998. ICUPC ’98. IEEE 1998 International Conference on, Oct. 1998, vol. 1, pp. 677 –681 vol.1. [9] Weidong Yang and Guanghan Xu, “Optimal downlink power assignment for smart antenna systems,” in Acoustics, Speech and Signal Processing, 1998. Proceedings of the 1998 IEEE International Conference on, May 1998, vol. 6, pp. 3337 –3340 vol.6. [10] V Blondel, L Ninove, and P Vandooren, “An affine eigenvalue problem on the nonnegative orthant,” Linear Algebra and Its Applications, vol. 404, pp. 69–84, 2005. [11] E.A. Jorswieck, E.G. Larsson, and D. Danev, “Complete characterization of the pareto boundary for the miso interference channel,” Signal Processing, IEEE Transactions on, vol. 56, no. 10, pp. 5292 –5296, oct. 2008. [12] Rui Zhang and Shuguang Cui, “Cooperative interference management with miso beamforming,” Signal Processing, IEEE Transactions on, vol. 58, no. 10, pp. 5450 –5458, oct. 2010.

Deterministic Annealing Design and Analysis of the Noisy MIMO Interference Channel † Intel

Francesco Negro∗, Irfan Ghauri† , Dirk T.M. Slock∗

Mobile Communications, GAIA, 2600 Route des Crˆetes, 06560 Sophia Antipolis Cedex, France Email: [email protected] ∗ Mobile Communications Department, EURECOM, 2229 Route des Crˆetes, BP 193, 06904 Sophia Antipolis Cedex, France Email: [email protected], [email protected]

Abstract—We consider the Noisy MIMO Interference Channel (IFC) with linear transmitters and receivers and full CSI. The maximization of the Weighted Sum Rate (WSR) or transceiver design for Interference Alignment (IA) lead to cost functions with many local optima. Deterministic annealing is an approach that allows to track the variation of the known solution of one version of the problem into the unknown solution of the desired version by a controlled variation of a parameter called temperature. When the temperature parameter is chosen as inverse SNR (or noise power), the transceiver design for maximum WSR is known at low SNR and can be tracked to any desired SNR, yielding an elegant technique to find the global optimum. The solution includes filter design for the progressive switching on of streams as the SNR increases. For IA on the other hand, IA feasibility is unchanged when the MIMO crosslink channel matrices have a reduced rank equal to the maximum of the number of streams passing through them in forward and dual IFC (this would correspond to LOS channels in the case of single streams). The rank reduction simplifies IA design and feasibility analysis, and allows in particular a counting of the number of IA solutions. By choosing now the temperature parameter to be a scale factor for the remaining channel singular values, the solution for reduced rank channels can be evolved into that for arbitrary channels. Index Terms—MIMO, MMSE, weighted sum rate, interference channel, linear transmitter, linear receiver, interference alignment, deterministic annealing

I. I NTRODUCTION To achieve higher system capacity in modern cellular communication standards a frequency reuse factor of 1 is used. This increment in system performances determines, on the other hand, a drastical reduction of the capacity of the celledge users due to the fact that this aggressive frequency reuse factor increases the inter-cell interference. To handle this problem current communication systems include different interference management solutions. Even if interference coming from out-of-cell transmission can be reduced using careful planning or introducing little cooperation among neighboring cells, such as smart user scheduling or soft handover, these techniques are sometimes not enough to guarantee high performance to cell-edge user. For that major standardization bodies are now including explicit interference coordination strategies in next generation cellular communication standards. These techniques are based on more interference-aware base station cooperation. A systematic study of the performance of cellular communication systems where each cell communicates multiple streams to its users

while enduring/causing interference from/to neighboring cells due to transmission over a common shared resource comes under the purview of MIMO interference channels (MIMO IFC). A K-user MIMO-IFC models a network of K transmitreceive pairs where each transmitter communicates multiple data streams to its respective receiver. In doing so, it generates interference at all other receivers. While the interference channel has been the focus of intense research over the past few decades, its capacity in general remains an open problem and is not well understood even for simple cases. In [1] they show that even for the 2−users system, the most studied case, to achieve the system capacity within one bit very complicated transmission schemes are required. Recently, it was shown that the concept of interference alignment (IA) [2], allows each receiver to suppress more interfering streams than it could otherwise cancel in interference channels. This can be done using more simple linear transmitter and receiver filter. This makes IA a very attractive solution in practical systems. The focus of this paper is on the K-user frequency-flat MIMO IFC. In a frequency-flat MIMO IFC, the total number of streams contributing to the input signal at each receiver are, in general, greater than the number of antennas available at the transmitter or at the receiver. This would lead one to believe that, at least in the high-SNR regime, the network (comprising of K user pairs) performance can be maximized (i.e, the sum-rate can be maximized) using IA since aligning the streams at the transmitter will now allow the maximization of the capacity pre-log factor in a K-user IFC. The problem of determining whether an IA solution exists or not for a given antennas and stream distribution among the users for a K-user MIMO IFC it has been studied in [3] and [4]. In the former an extensive study of IA feasibility solution for the single stream case has been proposed. In the latter the authors propose a systematic method, and less computational expensive, to check feasibility regardless of the number of transmitted stream per user. A distributed algorithm that exploits the reciprocity of the MIMO IFC to obtain the transmit and receiver filters in a K-user MIMO IFC was proposed in [5] (a similar algorithm has been proposed in [6]). It is was shown there that IA is a suboptimal strategy at finite SNRs. In the same paper, the authors propose a signal-to-interference-plus-noise-ratio (SINR) maximizing algorithm which outperforms the IA in

stream MIMO systems. The objective of this paper is to further study the concept of DA applied to WSR maximization in a general K-User MIMO interference channel where a general number of stream distribution is assumed. In addition the IA feasibility problem has been studied, in particular we propose a new approach to address the problem. It is based on the principle that IA feasibility is unchanged when the MIMO crosslink channel matrices have a reduced rank equal to the maximum of the number of streams passing through them in forward and dual IFC, then increasing constantly the rank of the channels the number of IA solutions will not decrease. II. S IGNAL M ODEL 1

G1

H11 H21 M1

d1 1

1

F1

N1

HK1

d1

1

1

...

1

...

...

1

...

1

H22 M2

N2

d2

...

HK2

...

d2

F2

...

...

...

H12 G2

...

H1K

dK

1

GK

H2K

1

HKK NK

MK

FK

...

1

...

...

1

...

finite SNRs and converges to the IA solution in the high SNR regime. However, this approach can be shown to be suboptimal for multiple stream transmission since it allocates equal power to all streams. In [7] the authors present an iterative algorithm that finds an IA solution that maximize the average sum-rate. At each step an IA solution is found using a technique proposed in [5] and then they move the solution along the direction of the gradient of the sum-rate w.r.t. the beamformers in the Grassmann manifold. Even though this algorithm performs better than traditional IA solutions in the High SNR regime it is highly sub-optimal, in terms of sumrate, in medium SNR ranges. Thus an optimal solution for MIMO IFC at finite SNR remains an open problem. Some early work on the MIMO IFC was reported in [8] by Ye and Blum for the asymptotic cases when the interference to noise ratio (INR) is extremely small or extremely large. It was shown there that a ”greedy approach” where each transmitter attempts to maximize its individual rate regardless of its effect on other un-intended receivers is provably suboptimal.There have been some attempts to port the solution concepts of the MIMO BC and MIMO MAC to the MIMO IFC. For instance, the problem of joint transmitter and receiver design to minimize the sum-MSE of a multiuser MIMO uplink was considered in [9] where iterative algorithms that jointly optimize precoders and receivers were proposed. Subsequently [10] applied this algorithm to the MIMO IFC where each user transmits a single stream. In [11] the authors proposed an algorithm for finding the beamformer in the single stream Kuser MIMO IFC that attempts to maximize the weighted sum rate (WSR). The beamforming vectors can be interpreted as a balance between an egoistic approach, where the transmitter tries to maximize its own rate and an altruistic approach where each beamformer put its effort to minimize the interference that it causes to the non intended receivers. The problem of a more general multi-stream MIMO IFC has been addressed in [12] where the objective of the algorithm proposed by the authors is to design a set of BF matrices in order to maximize the WSR. The algorithm proposed is based on a previous work on broadcast channel [13] but extended to a MIMO IFC and it has been further refined in [14]. The main problem with the maximization of the WSR is the highly non convexity of the cost function. This implies that even if it is possible to prove convergence of the proposed algorithms to a local optimal point convergence to global optima can not been shown. In addition convergence to local optimal solution is not a rare event if the initialization point of the algorithm is not carefully chosen. To avoid this situation several heuristic approach can be used. In [14] in order to avoid to converge to a local optima Deterministic Annealing (DA) has been proposed. DA is an heuristic approach based on Simulated Annealing (SA) where the basic principle is that the optimum of a problem in the next value of temperature (in our case SNR) is in the region of attraction of the solution of the problem in the previous temperature (more details will be provided further in the paper). In another independent work [15] the same principle has been explored but only for single

dK

Fig. 1: MIMO Interference Channel Fig. 1 depicts a K-user MIMO interference channel with K transmitter-receiver pairs. The k-th transmitter and its corresponding receiver are equipped with Mk and Nk antennas respectively. The k-th transmitter generates interference at all l 6= k receivers. Assuming the communication channel to be frequency-flat, the CNk ×1 received signal yk at the k-th receiver, can be represented as K X yk = Hkk xk + Hkl xl + nk (1) l=1 l6=k

where Hkl ∈ CNk ×Ml represents the channel matrix between the l-th transmitter and k-th receiver, xk is the CMk ×1 transmit signal vector of the k-th transmitter and the CNk ×1 vector nk represents (temporally white) AWGN with zero mean and covariance matrix Rnk nk . Each entry of the channel matrix is a complex random variable drawn from a continuous distribution. It is assumed that each transmitter has complete knowledge of all channel matrices corresponding to its direct link and all the other cross-links in addition to the transmitter power constraints and the receiver noise covariances. We denote by Gk , the CMk ×dk precoding matrix of the kth transmitter. Thus xk = Gk sk , where sk is a dk × 1 vector representing the dk independent symbol streams for the k-th user pair. We assume sk to have a spatio-temporally white Gaussian distribution with zero mean and unit variance, sk ∼ N (0, Idk ). The k-th receiver applies Fk ∈ CNk ×dk to suppress

interference and retrieve its dk desired streams. The output of such a receive filter is then given by rk = F H k Hkk Gk sk +

K X

H FH k Hkl Gl sl + Fk nk

l=1 l6=k

Note that Fk does not represent the whole receiver but only the reduction from a Nk -dimensional received signal yk to a dk -dimensional signal rk , to which further (possibly optimal) receive processing is applied. III. W EIGHTED

SUM RATE MAXIMIZATION FOR THE

MIMO IFC The stated objective of our investigation is the maximization of the WSR of MIMO IFC. In this paper we consider the weighted sum rate maximization problem for a K-user frequency-flat MIMO IFC and propose an iterative algorithm for linear precoder/receiver design. With full CSIT, but only knowledge of sk at transmitter k, it is expected that linear processing at the transmitter should be sufficient. On the receive side however, optimal WSR approaches may involve joint detection of the signals from multiple transmitters. In this paper we propose to limit receiver complexity by restricting the modeling of the signals arriving from interfering transmitters as colored noise (which is Gaussian if we consider Gaussian codebooks at the transmitters). As a result, linear receivers are sufficient. For the MIMO IFC, one approach to linear transmit precoder design is the joint design of precoding matrices to be applied at each transmitter based on channel state information (CSI) of all users. Such a centralized approach [8] requires (channel) information exchange among transmitters. Nevertheless, studying such systems can provide valuable insights into the limits of perhaps more practical distributed algorithms [16] [17] that do not require any information transfer among transmitters. A. Per-User WSR maximization The WSR maximization problem can be mathematically expressed as follows. ⋆

⋆

H k

{Gk , Fk } = arg

min R s. t Tr(G Gk ) = Pk ∀k (2) {Gk , Fk } P where R = k −uk Rk with uk ≥ 0 denoting the weight assigned to the k-th user’s rate and Pk it’s transmit power constraint. We use the notation {Gk , Fk } to compactly represent the candidate set of transmitters Gk and receivers Fk ∀k ∈ {1, . . . , K} and the corresponding set of optimum transmitters and receivers is represented by {G⋆k , F⋆k }. Assuming Gaussian signaling, the k-th user’s achievable rate is given by Rk = log |Ek |, Ek = Ik + FH Hkk Gk (FH Hkk Gk )H (FH Rk Fk )−1 k k k where the interference plus noise covariance matrix Rk is: X H Rk = Rn k n k + Hkl Gl GH l Hkl . l6=k

(3)

We use here the standard notation | . | to denote the determinant of a matrix. The MIMO IFC rate region is known to be non-convex. The presence of multiple local optima complicates the computation of optimum precoding matrices to be applied at the transmitter in order to maximize the weighted sum rate. What is known however, is that, for a given set of precoders, linear minimum mean squared error (LMMSE) receivers are optimal in terms of interference suppression. In addition we can extend this concept saying that, for a given set of linear beamforming filters applied at the transmitters, the LMMSE interference-suppressing filter applied at the receiver does not lose any information of the desired signal in the process of reducing the Nk dimensional yk to a dk dimensional vector rk . This is of course under the assumption that all interfering signals can be treated as Gaussian noise. In other words, the linear MMSE interference suppressor filter is information lossless and is thus optimal in terms of maximizing the WSR. Thanks to this property of the LMMSE Rx filter, we consider a (more tractable) optimization problem where MMSE processing at the receiver is implicitly assumed. The WSR maximization problem in (2) that we consider becomes: K X H {G⋆k }=arg min −uk log |E−1 k | s. t Tr(Gk Gk ) ≤ Pk ∀k {Gk } k=1 (4) where Ek is given by H −1 −1 Ek = (I + GH . k Hkk Rk Hkk Gk )

(5)

This problem in non convex and hence finding a solution is a complex task. In order to obtain the stationary points for the optimization problem (4), we solve the Lagrangian: L ({Gk , λk }) =

K X

k=1

−uk log |E−1 | + λk (Tr{GH Gk } − Pk ) k k

Now setting the gradient of the Lagrangian w.r.t. the transmit filter Gk to zero, we have: ∂J ({Gk ,λk }) ∗

∂ Gk

P

=0

ul HH R−1 Hll Gl El GH HH R−1 Hlk Gk lk l ll l l H −1 −uk Hkk Rk Hkk Gk Ek + λk Gk = 0

(6)

l6=k

Our approach to the design of the WSR maximizing transmit filters for the MIMO IFC is based on introducing an augmented cost function in which two additional optimization variables appear [13]. The optimization problem that we consider now is {G⋆k , F⋆k , W⋆k } =X arg max −uk (Tr(Wk E k ) − log |Wk | − dmax ) k {Gk , Fk , Wk } k X s. t Tr(Gk GH k ) ≤ Pk .

(7)

k

where d ≤ min{Nk , Mk } represents the maximum number of independent data streams that can be transmitted to user k. This cost function is concave or even quadratic in one set of max k

variables, keeping the other two fixed. Hence we shall optimize it using alternating maximization. Assuming E{ssH } = Idk , the MSE covariance matrix for general Tx and Rx filters is Ek = =

H H E[(s − FH k yk )(s − Fk yk ) ]} H H H I − Gk Hkk Fk − Fk Hkk Gk H + FP Hkk Gk GH HH F k k kk k H H H + l6=k Fk Hkl Gl GH l Hkl Fk + Fk Rnk nk Fk

The corresponding Lagrangian can be written as: X J({Gk , Fk , Wk , λk }) = − λk (Tr{GH Gk } − Pk ) k −

X k

l6=k

(8)


+ Pukk Tr{Wk FH Rn k n k F k } . k

(9)

This new cost function will be optimized w.r.t. one set of variables, keeping the other two fixed. The first step in our optimization process is the calculation of the optimal Rx filters assuming fixed the matrices Gk and Wk . It can easily be seen that the optimal Rx filter is an MMSE filter: M SE H −1 FLM = (Rk + Hkk Gk GH Hkk Gk k k Hkk )

(10)

The following step in the optimization procedure is the determination of the optimal expression for the matrix Wk while keeping the other two variable sets fixed. What we get is: Wk = E−1 (11) k The final step is the maximization of the given cost function w.r.t. the BF matrix. To accomplish this task we derive the Lagrangian w.r.t. the matrix Gk and equate it to zero: ∂ J({Gk ,λk }) ∗ ∂ Gk P

H kk

(15)

With this value of the Lagrange multiplier the final expression for the BF becomes (16). The algorithm proposed in [13] was developed for a MIMO broadcast channel, where only an overall Tx power constraint is applied on the system and, in addition, maximizing the WSR automatically requires to transmit with full power. On the other hand in the MIMO IFC the WSR maximization may require some links to transmit with a power less than the maximum power available at that links. At low SNR regime the maximization of the WSR leads to activate only one stream per link, allocating full power on the best singular mode of the direct channel Hkk . For SNR values sufficiently high the maximization of the sum rate converges to an IA solution. IA feasibility may imply zero streams for some links. Here we propose to determine the optimal value of λk ≥ 0 using a linear search algorithm. Grouping together all the optimization steps that describe our maximization procedure we have the following two-steps iterative algorithm to compute the precoders that maximize the weighted sum rate for a given MIMO IFC (c.f Table Algorithm 1). Introducing the augmented cost function, for

=

K

ul HH F Wl FH Hlk Gk = 0. lk l l (12) This leads to the following expression for the optimizing BF: !−1 K X H H Gk = ul Hlk Fl Wl Fl Hlk + λk I HH F Wk uk (13) kk k uk H Fk Wk − λk Gk −

+ P1k

  X  uk Tr{Wk FH Hkl Gl (FH Hkl Gl )H } k k l6=k

k

uk (Tr(Wk E k ) − log |Wk | − dmax ) k

Using the definition of the MMSE Rx filter we get the   following expression for the Lagrange multiplier: X λk = − P1k  ul Tr{Wl FH Hlk Gk (FH Hlk Gk )H } l l

Algorithm 1 MWSR Algorithm for MIMO IFC

l=1

l=1

The only variable that still needs to be optimized is the Lagrange multiplier λk . First check if Tr(GH Gk ) ≤ Pk for k λk = 0. If yes, than λk = 0. If not, the Tx power equality constraint is active. In this case to determine the optimal value of the lagrange multiplier λk we consider equation (12) that for the optimality of the BF matrix it is satisfied. In addition pre-multiplying the derivative of the cost function w.r.t. the BF matrix by GH k and taking the trace the product is still equal to zero:   ∂J({Gk , λk }) Tr GH =0 k ∂G∗k H H Tr {uk GH k Hkk Fk Wk } − λk Tr {Gk Gk } K X H H − ul Tr {GH k Hlk Fl Wl Fl Hlk Gk } = 0.

(14)

Fix an arbitrary initial set of precoding matrices Gk , ∀ ∈ k = {1, 2 . . . K} set n = 0 repeat n=n+1 (n−1) (n) (n) Given Gk , compute Fk and Wk from (10) and (11) respectively ∀k (n) (n) (n) Given Fk and Wk , compute Gk ∀k using (13) until convergence the calculation of the optimal BF matrix that maximize the WSR, we are able to determine an iterative algorithm that can be easily proved to converge to a local optima that corresponds also to an extremum of the original cost function (4). Each step of our iterative algorithm increases the cost function, which is bounded above (e.g. by cooperative WSR), and hence convergence is guaranteed. In addition the augmented cost function once we substitute Wk and Fk with their optimal values, becomes exactly the original WSR cost function (4). Finally using matrix inversion lemma1 it is possible to rewrite

l=1

In equation (14) we impose the power constraint to be satisfied with equality hence the contribution λk T r {GH Gk } = λk Pk . k

1 If

P and R are positive definite the following relation is true: PBT (BPBT + R)−1 = (P−1 + BT R−1 B)BT R−1

the expression of the MMSE (10) as Fk = R−1 Hkk Gk Ek . k With this representation of the Rx filters it is possible to interpret some quantities in the gradient of the WSR (6) as Rx filters and hence the expression that comes out of this elaboration is the same as the gradient of the augmented cost function w.r.t. the BF matrix (12). This implies that a stationary point of the original cost function is also a stationary point of the augmented cost function. A final remark can be made about the dimensions imposed on the beamforming matrix. In particular at high SNR we can put dk = Mk if we want the algorithm to figure out the feasible set of {dk }, in this case all IA-feasible solutions represent local optima. Another possible choice is to use dk that corresponds to an IA-feasible solution if we want to focus on that particular stream distribution. At low or medium SNR regime a possible choice is dk = IA max{1, dIA k } where the set {dk } form a IA-feasible set. B. Per-Stream WSR maximization In the algorithm presented so far the stream of each user are correlated to each other. It is possible to show that modifying the BF in order to decorrelate the stream of each user does not reduce the overall sum rate. Using a per-stream approach leads to a solution in which the MMSE matrix is diagonal. This property will be explored further later in the paper. The cost function proposed in this paper for the per-user approach can be written in the per-stream case as: O=−

K X

k=1

uk

dk X

(− ln(wkn ) − 1

n=1

H kn

H kn

H

+wkn (1 − f Hkk gkn )(1 − f Hkk gkn ) X

+wkn fH (Rnk nk + kn

Hki gim gH HH ) fkn ). im ki

(im)6=(kn)

{z Rkn

|

}

(17) The optimization problem when we work per stream becomes: max fkn ,gkn ,wkn s.t.

Pdk n

O gH kn gkn ≤ Pk ∀k

(18)

and the corresponding lagrangian is: J =O+

K X

k=1

λk (Pk −

dk X

gH g ) kn kn

H −1 −1 where ekn = (1 + gH . The third step is kn Hkk Rkn Hkk gkn ) the optimization of the beamforming vectors:  −1 dl K X X H  HH gkn =  ul HH lk flj wlj flj Hlk + λk I kk fkn wkn uk l=1 j=1

(22) To determine the optimal value of the lagrange multiplier λk we can multiply the derivative of the lagrangian w.r.t gkn by the BF vector hence the following holds true:  dk  X ∂J gH =0 kn ∂g∗kn n=1 solving the equation above w.r.t. the lagrange multiplier we get: λk =

1 Pk

"

− P1k

dk X

H kn

H kk kn

g H f wkn uk

n=1 "d k

dl K X XX

#

H H ul gH kn Hlk flj wlj flj Hlk gkn

n=1 l=1 j=1

#

(23)

The final algorithm (PS-MWSR algorithm in Table Algorithm 2) for the per-stream optimization requires the iteration of the three steps for the optimization of Rx filters, weights, Tx beamforming vectors, in the prescribed order, untill convergence. Algorithm 2 PS-MWSR Per-Stream Algorithm for MIMO IFC Fix an arbitrary initial set of precoding matrices Gk , ∀ ∈ k = {1, 2 . . . K} set n = 0 repeat n=n+1 for k = 1 to K do (n) (n) Given gi(n−1) ∀i, compute fkl from (20) and and wkl (21) respectively for l = 1, . . . , dk (n) (n) Given f(n) and wkl for l = 1, . . . , dk , compute gkl kl for l = 1, . . . , dk using (22) end for until convergence

(19)

n=1

To solve the given optimization problem we use alternating optimization. As first step we determine the Rx filter assuming all the other optimization variables to be fixed. Deriving the cost function above w.r.t. the Rx filter we obtain an MMSE receiver per stream: fkn = (Hkk gkn gH HH + Rkn )−1 Hkk gkn kn kk

Given the optimal Rx filter we derive (19) w.r.t. the scalar weight and we find: wkn = e−1 (21) kn

(20)

C. Rate Duality in MIMO IFC In the previous section the expressions of the beamformer (22) and the MMSE Rx filter (20) are given when we assume to work per stream. Looking deeper at the expression of the cost function (17) it is possible to establish a duality relationship between the DL IFC considered and a dual UL IFC: ˜H • The DL channel matrix Hkl becomes H lk in the dual UL

Gk =

K X l=1

1 H Fl Wl F Hlk − Pk H lk

H l

X l6=k

(k) l

(l) k

Tr{Wl J } − Tr{Wk J }

!

H H H H H J(k) = FH J(l) l l Hlk Gk Gk Hlk Fl ; k = Fk Hkl Gl Gl Hkl Fk ;

The Rx (Tx) filter in the DL (UL) fkn (gkn ) becomes the ˜H Tx (Rx) filter in the UL (DL) ˜gH kn (fkn ) • The unit DL Tx signal variance for stream (k, n) becomes uk wkn in the dual UL channel 2 • DL noise covariance matrix Rnk nk = σk I becomes λk I in the UL. With this relationship we can interpret the BF filter in the DL as an MMSE Rx filter in the virtual UL IFC. A similar reasoning can be naturally extended to the per-user approach discussed in section III-A •

! !−1

− Tr{Wk Nk } I

HH F Wk kk k

(16)

Nk = FH k Rn k n k F k

into several trajectories. From a mathematical perspective a phase transition is characterized by the Hessian of the problem becoming singular at a critical temperature (hence being positive semidefinite instead of postive definite). In our problem the cost function is the WSR, a highly non convex function, and the annealing parameter is related to the noise variance, t ∝ σ 2 (or the inverse of the SNR).

IV. D ETERMINISTIC A NNEALING TO AVOID L OCAL O PTIMA In the previous section we have described an alternating optimization algorithm that designs BF and RX filters in order to maximize the WSR in a K-user MIMO IFC. As already remarked, the WSR cost function is a non convex function and this makes the optimization troublesome due to the presence of many local optima. In optimization, a number of heuristic approaches exist to handle non convex optimization problems. Some examples of such methods are: genetic algorithms, ant colony optimization or simulated annealing (SA). We will describe briefly the SA approach. This method takes its name from the physical annealing process in which a system is first “melted” and then slowly cooled down in order to allow the atoms in the system to find a state with lower energy until the system is “frozen” in a globally optimum state. In SA the problem is optimized using a sequence of random moves, the size of which reduces as a parameter called temperature decreases. The random moves would allow the optimization process to get out of local optima. In a certain sense, the randomness tend sto convexify the problem. Cooling protocols have been derived to allow ending up in the global optimum with high probability. Deterministic Annealing (DA) is a related technique but does not involve any randomness, see e.g. [18]. In DA, an increase of the temperature parameter allows to convexify the problem: the temperature parameter transforms (deterministically) the originally nonconvex cost function into a convex cost function (convex should be replaced by concave in the case of maximization). So, at high temperature, there is no problem in finding the global optimum. Then gradually the temperature gets reduced, making the problem increasingly non-convex. However, if the temperature variation is sufficiently small, the gobal optimum at the previous higher temperature will be in the region of attraction of the global optimum at the next lower temperature and the global optimum remains tracked in this way. As in physical systems, also in the optimization problem it can happen that phase transitions occur as the temperature cools down [18]. A phase transition corresponds to a split of the trajectory (as a function of temperature) of the global optimum

Fig. 2: Phase transitions representation Interestingly also in WSR maximization in a K-user MIMO IFC, phase transitions can appear. At low SNR (high noise variance), any interference is negligible compared to the noise. Hence, all links can be considered decoupled, and, like in single-user MIMO, rate maximization becomes SNR maximization for a single stream to which all transmit power is devoted. Hence in link k, the optimal Tx and Rx filters correspond to the left and right singular vectors corresponding to the largest singular value of Hkk . Hence, as the SNR goes to zero, the globally optimum solution is clear. However, zero SNR itself is already a phase transition because as soon as the SNR becomes positive, a multitude of local optima may exist that we shall interpret below. As the SNR increases further, at some point another phase transition may occur, at which point a second stream needs to be introduced in one of the links. We shall see that at such a phase transition, it is possible to determine the filters corresponding to the new stream. However, as soon as the SNR increases further, many further local optima get introduced due to the appearance of the additional stream. Then, as the SNR increases further, another phase transition can occur, with the introduction of one more stream at one of the transmitters. This process goes on until a stream distribution is reached, at some higher SNR, corresponding to a maximal stream distribution for which interference alignment is feasible. Indeed, at very high SNR, the Tx and Rx filters coverge to the (max WSR-)IA solution, and the sum rate prelog is maximized if the number of streams is maximized (see [14]). This whole process is depicted schematically in Fig.2. One interesting observation is that it is fairly straightforward to check that all extrema of the WSR correspond to local maxima. So, whereas the Hessian is in general indefinite, reflecting the non-concavity of the WSR cost function, it turns out that the Hessian is always negative definite when evaluated at an extremum (or semidefinite at the

phase transitions). Whereas DA is about tracking of a global optimum, the tracking of extrema, the zeros of the KKT conditions, is actually called a homotopy method. So in DA, going from one phase transition to the next and tracking the (appropriate) extremum, this could be considered a homotopy method. A. Homotopy Methods Homotopy methods [19] are used to find the roots of a non-linear system of equations F (x) = 0. A homotopy transformation is such that it starts from a trivial system G(x), with known solution, and it evolves towards the target system F (x) via continuous deformations according to the homotopy parameter t = 0 → 1: H(x, t) = (1 − t) G(x) + tF (x) Predicting the solution at the next value of t(i+1) = t(i) + ∆t is called an Euler prediction step; a solution at t(i+1) can be refined using a Newton correction step for fixed t. A property of Homotopy continuation methods for the solution of system of equation is that the number of solutions in the target system is at most equal to the number of solutions in the trivial system. The number of solutions with varying t remains constant as long as the Jacobian (w.r.t. x and t jointly) is full rank. So as t reaches 1, it can happen that the Jacobian becomes singular. B. Homotopy Applied to IA Homotopy method can be applied to the IA problem, in particular here it is not really suggested for computing IA solutions, but for counting number of solutions. The objective in IA is to design Tx and Rx filters that satisfy the ZF conditions FH (24) k Hkl Gl = 0 ∀l 6= k and the rank conditions rank(FH k Hkk Gk ) = dk

∀k ∈ {1, 2, . . . , K}

(25)

which correspond to the traditional single user MIMO constraint dk ≤ min(Mk , Nk ) for dk streams to be able to pass over the k-th link. The main constraints are the n ZF conditions in (24). These conditions are bilinear equations in the Tx and Rx filters, hence they are of second order. As a result, the overall order of the ZF conditions jointly is 2n , which is also the maximum number of solutions. It turns out that due to the particular structure of the ZF conditions (in a given ZF condition only one Tx and Rx filter appear), the actual number of solutions is much more limited. To analyze the number of IA solutions, the following approach has been proposed in [20]. Instead of choosing the homotopy parameter to be related to SNR, we choose it here to attenuate the MIMO channel singular values beyond the main ones: Hji =

d X

k=1

σjik ujik vH jik + t

X

solutions when t = 0. The case of dk ≡ d = 1 is considered here. Then finding the IA solutions at t = 0 becomes trivial. Indeed, IA requires H fH j uji1 vji1 gi = 0 H or hence either fH j uji1 = 0 or vji1 gi = 0. The joint TxRx ZF is achieved by either the Tx or the Rx suppressing the particular interfering stream. This analysis supports a suggestion provided in [4] which states that it should be possible to check IA feasibility and count the number of IA solutions by verifying if the ZF task can be properly distributed over Tx and Rx filters. The idea is that a stream transmitted from TX k and causes interference to the non intended RX j needs to be suppressed at either the Tx or at the Rx. Denoting with tkj the size of the subset of streams dk , that are received at Rx j that the k-th Tx suppresses, and with rkj the size of the subset of streams dk , that are received at Rx j, that the j-th Rx suppresses, the sum of these two quantities should be: tkj + rkj ≥ dk . The total number of streams that Tx k can suppress is at most Mk − dk and the total number of streams that the j-th Rx can suppress is not greater than Nj − dj . Therefore, to check the feasibility of an interference alignment solution, the following conditions should be satisfied: P t ≤ Mk − dk P j6=k kj (26) r ≤ Nj − dj kj k6=j

∀tkj , rkj ∈ {0, 1 . . . , dk }, and tkj + rkj = dk

maxk6=j (dj − [Mk − Nj ]) ≤ (Nj − dj )∀j ∈ {1, . . . , K} As before, due to alignment duality, IA must be checked also when the sets of Mk and Nk are interchanged (the dual channel case). One possible way to verify if all this QKinequalities are satisfied or not is to check all the possible k=1 (dk + 1)K−1 combination of tkj and rkj . So, the homotopy method allows to substantiate this approach, at least in the single stream per link case. More generally, determining IA solutions by continuation methods can be obtained by perturbing the ZF conditions up to first order H (FH j + dFj )(Hji + dHji )(Gi + dGi ) = 0

Assuming that an IA solution for channel Hji , ∀(i, j) has already been determined using filters Fj and Gi then considering only the terms up to first order in the product above we get: H H FH j Hji dGi + dFj Hji Gi = −Fj dHji Gi . To find the IA solution for channel (Hji +dHji ) we determine the matrices dFH j and dGi ∀i, j by solving linear equations. C. Homotopy Applied to WSR

σjik ujik vH jik .

k=d+1

The IA Jacobian is still full rank if we reduce rank(Hji ) to max(dj , di ). Hence we can still count the same number of IA

As remarked previously, maximizing WSR at very high SNR corresponds to determining IA solutions, as can be seen immediately from the augmented WSR cost function. Any IA solution leads to a local maximum of WSR. Now, consider

again the low rank channels considered above, in which we can discribe and count the number of IA solutions. Instead of increasing the channel rank first, we shall lower the SNR (or increase the noise variance). Note that we can even consider linear homotopy here by using t to multiply the transmit powers or the noise variances, since the augmented WSR cost function is linear in transmit powers or noise covariances. By non-singularity of the Jacobian, the various IA solutions will each get transformed into a local WSR maximum as the SNR lowers. Until a phase transition is reached in which some stream gets switched off. This will eliminate a subset of the IA possibilities and hence a subset of the local WSR maxima. This process continues until at low SNR there is one stream per link. For any given SNR, the low rank channel can also be transformed until the original full rank channel, without affecting the number of local maxima. V. D ETERMINISTIC A NNEALING M AXIMIZATION

FOR

WSR

Considering only the contribution up to first order in xkn the minimization of the MSE leads to the maximization of xkn and hence the optimal BF vector direction is gkn = vmax (HH R−1 Hkk ) kk kn

(28)

where vmax (A) represents the eigenvector corresponding to the maximum eigenvalue of matrix A. Once we have the direction of the BF associated to the new stream we need to determine the corresponding power. Consider Gk the BF matrix obtained untill the current SNR 1/2 point for link k and its decomposition as Gk = Gk Pk , where 1/2 Gk has normalized columns and Pk is the power allocation matrix. For the per-stream approach the MMSE is diagonal and hence: H H −1 H H E−1 k = I + Gk Hkk Rk H Gk = I + DPk

What we propose in this paper is to extend the MWSR algorithm presented before in order to include DA and hence reduce the probability to be trapped in local optima. So we consider again DA for the original full rank channels, for SNR increasing from zero. To modify the algorithm proposed in Table Algorithm 1 to include DA we only need to run the algorithm for each SNR point initializing the algorithm with the optimal beamformers found at the previous SNR iteration. However, this does not handle phase transitions, corresponding to the introduction of a new stream. Hence, at every SNR increment, we need to try adding a stream to each of the K links (one at a time). It is possible to find the proper initialization for the Tx and Rx filters of the new stream analytically. A. Initialization at Phase Transitions To find the direction of the BF vector corresponding to the new stream, indexed as (k, n), we need to optimize our perstream cost function (17) w.r.t. the quantities corresponding to the new allocated stream. Note that the new stream, if it should be switched on, will be switched on with very small power. Hence the new stream will barely perturb the existing streams. For the moment we do not include in the optimization function the power constraint, so we need to find the Tx and Rx filter that minimize the MSE for stream (k, n). The derivative of the MSE w.r.t. the Rx filter is: ∂O = −gH HH + fH Hkk gkn gH HH + fH Rkn kn kk kn kn kk kn ∂fkn

in function of the BF, the MSE cost function can be written as: ekn = 1 − pkn xkn + (pkn xkn )2

Introducing the additional stream we obtain the following matrix : −1 H X = [Gk gkn ]H HH kk Rk Hkk [Gk gkn ] =



√

DPk pkn uH

√

pkn u apkn



H −1 H H −1 where u = GH k Hkk Rk Hkk gkn and a = gkn Hkk Rk Hkk gkn . The corresponding rate for user k is

ln |E−1 k | = ln |I + X| = ln |I + DPk | + ln(1 + pkn dkn )

dkn = a − uH (I + DPk )−1 u. Finally to find the power allocation among different streams of user k we propose the following. 1) Jammer Water-Filling (JWF) algorithm: Include in the matrix Pk the power allocated to the new stream pkn and in the diagonal matrix D include the element dkn associated to the new stream. To find the power allocation matrix we take the original per-stream cost function (17) and optimize it with respect to (and then eliminate) the weights wkn for link k. After this, the terms in the WSR affected by Pk are O = ln |I + DPk | − T r{Pk ∆} − λk (T r{Pk } − Pk ) where T r{Pk ∆} takes into account the interference power generated to the non intended receivers (for this reason we called this algorithm Jammer WF): T r{Pk ∆} =

X i

pki

dl X ul X 2 wlm |fH lm Hlk gki | . u k l6=k m=1 | {z } ∆ki

(27)

considering only the terms up to first order in gkn the expression for the receiver is fkn = R−1 Hkk gkn that has an kn expression like matched filter (MF) in colored noise. Consider a parametrization of the BF vector in direction vector and √ power allocation like: gkn = gkn pkn and define xkn = H H gkn Hkk Hkk gkn . Substituting the Rx filter with its expression

Deriving the cost function above w.r.t. pki the expression for the power allocation is:   1 1 pki = − (29) λk + ∆ki dki + where [(.)]+ = max((.), 0). To find the optimal value of λk we first check if the power constraint is inactive. In particular we determine the powers using (29) assuming λk = 0 and

as we can see T (λk ) is a decreasing function of λk . In particualr for λ0k = 0 T (λk ) > 0 while for λ1k , determined as water-level of a tradition WF algorithm on T (λk ) when ∆ki = 0, ∀i, the function T (λk ) < 0. The optimal value λ⋆k can be found using a bisection algorithm to solve T (λk ) = 0. The final extended BF matrix Gk = [Gk gkn ] obtained using the procedure described so far is used as initialization of the DA-WSR for the following SNR point.

Algorithm 3 DA-MWSR Algorithm for MIMO IFC set t = 0 Fix the initial set of precoding matrices Gk , ∀ ∈ k = {1, 2 . . . K} repeat increment SNR: t(i+1) = t(i) + δt Augment G repeat Given Gk compute Fk and Wk , ∀k Given Fk , Wk , compute Gk ∀k until convergence until target SNR is reach

K=3, M=[2 2 2], N=[2 2 2] 20

DA−MWSR IA d=[1 1 1] WSR [Schmidt−allerton10]

18 16

Sum Rate bit/sec/Hz

we verify if the transmitted power is less then the power constraint. If the power constraint is not satisfied we determine λk using a bisection method. Consider the following function of the lagrange multiplier  X 1 1 T (λk ) = − − Pk λk + ∆ki dki + i

14 12 10 8 6 4 2

0

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Fig. 3: WSR for K = 3, Mk = 2, Nk = 2 realizations. In Fig. 3 we compare the SR obtained using three different algorithms. In particular we compare our algorithm DA-MWSR with IA algorithm proposed in [5] and another WSR algorithm recently proposed in [15] where also a numerical continuation method is used to find the BF to maximize the WSR. This algorithm works only for single stream transmissions. As we can see both algorithms that maximize the WSR outperform IA in all SNR regimes. On the other hand there is no difference between the proposed algorithm and the one in [15]. K=3, M=[3 3 3],N=[3 3 3] 45

VI. S IMULATION R ESULTS We provide here some simulation results to compare the performance of the proposed max-WSR algorithm (DA-MWSR) where we deterministic annealing is used to avoid local optimal point. i.i.d Gaussian channels (direct and cross links) are generated for each user. For a fixed channel realization transmit and receiver filters are computed based on IA algorithm and DA-MWSR algorithm over multiple SNR points. The resulting sum rate (SR) is averaged over 50 channel

DA−MWSR IA d=[2 1 1]

40 35

Sum Rate bit/sec/Hz

A remaining open question is now the following: at a phase transition, even if we are able to determine the solution analytically, the global maximum splits up into a whole set of local maxima trajectories. The question is whether the algorithm above will in fact track the global maximum. The answer is yes. Indeed it turns out that an alternating optimization approach as the one considered here (or also the one used in [15]), in spite of the non-concavity of the problem, optimizes (globally) the WSR up to second order in transmit power (or SNR). Indeed, we are able to determine analytically the optimal Tx and Rx filters up to zeroth order in Tx power, the one iteration of an alternating optimization approach will provide the optimal Tx and Rx filters up to first order in Tx power, which maximize WSR up to second order in Tx power. In other words, the alternating optimization approach inherently sets course on the trajectory of the global optimum.

30 25 20 15 10 5 0

0

5

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20

25

30

SNR[dB]

Fig. 4: WSR for K = 3, Mk = 3, Nk = 3 In Fig. 4 we report the SR for a K = 3 users IFC where each Tx and Rx are equipped with Mk = Nk = 3 antennas. According to IA the total maximum number of streams that can be transmitted in the system is d = 4. We determine the IA beamformers and receiver filters using the algorithm in [5] for a stream distribution d1 = 2, d2 = d3 = 1. We compare the performance of IA with our algorithm where the annealing parameter, noise variance, has been increased of δt = 0.5 dB. As we can see the proposed algorithm outperforms IA even at high SNR regime. The slope of the sum rate obtained using our algorithm is the same of the IA curve. This shows that the correct number of streams has been sent.

K=3, M=[5 4 4],N=[5 4 4]

R EFERENCES

70

DA−MWSR IA d=[2 2 2]

Sum Rate bit/sec/Hz

60

50

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Fig. 5: WSR for K = 3, M1 = N1 = 5, Mi = Ni = 4, i = 2, 3, dk = 2 ∀k Finally Fig. 5 depicts the performances of the proposed algorithm, WSR DA, in comparison with IA for a K = 3 user IFC with an asymmetric antennas distribution. We assume that M1 = N1 = 5, Mi = Ni = 4 i = 2, 3, the stream distribution, according to IA is dk = 2 ∀k. As we can see also in this case the proposed algorithm outperform IA keeping the same slope in the high SNR regime. VII. C ONCLUSIONS In this paper we addressed maximization of the weighted sum rate for the MIMO IFC. We introduced an iterative algorithm to solve this optimization problem that is characterized by the presence of several possible local minima. To avoid to be stack in one suboptimal stationary point we propose to introduce Deterministic Annealing. This approach allows to track the variation of the known solution of one version of the problem into the unknown solution of the desired version by a controlled variation of a parameter called temperature. In our problem the temperature is related to the inverse of the SNR. The proposed algorithm include filter design for the progressive switching on of streams as the SNR increases In the second part of the paper we study IA feasibility. Exploring the fact that IA feasibility is unchanged when the MIMO crosslink channel matrices have a reduced rank, equal to the maximum of the number of streams passing through them we propose a new way to study the problem using numerical continuation method. The rank reduction simplifies IA design and feasibility analysis, and allows in particular a counting of the number of IA solutions. In this approach the temperature parameter is a scale factor for the remaining channel singular values, the solution for reduced rank channels can be evolved into that for arbitrary channels. VIII. ACKNOWLEDGMENT EURECOM’s research is partially supported by its industrial members: BMW Group, Swisscom, Cisco, ORANGE, SFR, ST Ericsson, Thales, Symantec, SAP, Monaco Telecom. The research of EURECOM and Intel Mobile Communications France is also supported in part by the EU FP7 projects CROWN, SACRA and WHERE2.

[1] R. H. Etkin, D. N. C. Tse, and Hua Wang, “Gaussian interference channel capacity to within one bit,” IEEE Trans. on Inform. Theory, vol. 54, no. 12, pp. 5534–5562, 2008. [2] V.R. Cadambe and S.A. Jafar, “Interference alignment and degrees of freedom of the K-user interference channel,” IEEE Trans. on Inform. Theory, vol. 54, no. 8, pp. 3425 –3441, Aug. 2008. [3] C.M. Yetis, Tiangao Gou, S.A. Jafar, and A.H. Kayran, “On feasibility of interference alignment in mimo interference networks,” Signal Processing, IEEE Transactions on, vol. 58, no. 9, pp. 4771 –4782, 2010. [4] F. Negro, S. P. Shenoy, I. Ghauri, and D.T.M. Slock, “Interference alignment feasibility in constant coefficients MIMO interference channel,” in Proc. 11th IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC 2010), June 2010. [5] K. Gomadam, V.R. Cadambe, and S.A. Jafar, “Approaching the capacity of wireless networks through distributed interference alignment,” in Proc. IEEE Global Telecommunications Conf. (GLOBECOM), Dec 2008. [6] Steven W. Peters and Robert W. Heath, “Interference alignment via alternating minimization,” in Proc. IEEE Conf. on Acoustics, Speech and Signal Processing (ICASSP), April 2009, pp. 2445–2448. [7] I. Santamaria, O. Gonzalez, R.W. Heath, and S.W. Peters, “Maximum sum-rate interference alignment algorithms for mimo channels,” in GLOBECOM 2010, 2010 IEEE Global Telecommunications Conference, 2010, pp. 1 –6. [8] Sigen Ye and R.S. Blum, “Optimized signaling for MIMO interference systems with feedback,” IEEE Trans. on Signal Processing, vol. 51, no. 11, pp. 2839–2848, Nov 2003. [9] S. Serbetli and A. Yener, “Transceiver optimization for multiuser MIMO systems,” IEEE Trans. on Signal Processing, vol. 52, no. 1, pp. 214 – 226, Jan. 2004. [10] David A. Schmidt, Shi Changxin, Randall A. Berry, Michael L. Honig, and Wolfgang Utschick, “Minimum mean squared error interference alignment,” in Proc. 43rd IEEE Annual Asilomar Conference on Signals, Systems & Computers, Pacific Grove,California, USA, Nov 2009. [11] Z.K.M. Ho and D. Gesbert, “Balancing egoism and altruism on interference channel: The mimo case,” in Communications (ICC), 2010 IEEE International Conference on, May 2010, pp. 1 –5. [12] F. Negro, S.P. Shenoy, I. Ghauri, and D.T.M. Slock, “On the mimo interference channel,” in Information Theory and Applications Workshop (ITA), 2010, 31 2010-feb. 5 2010, pp. 1 –9. [13] S.S. Christensen, R. Agarwal, E. Carvalho, and J. Cioffi, “Weighted sumrate maximization using weighted MMSE for MIMO-BC beamforming design,” IEEE Trans. on Wireless Communications, vol. 7, no. 12, pp. 4792–4799, December 2008. [14] Francesco Negro, Irfan Ghauri, and Dirk T.M. Slock, “Optimizing the noisy mimo interference channel at high snr,” in Communication, Control, and Computing (Allerton), 2010 48th Annual Allerton Conference on, 29 2010-oct. 1 2010, pp. 254 –261. [15] David A. Schmidt, Wolfgang Utschick, and Michael L. Honig, “Beamforming techniques for single-beam mimo interference networks,” in Communication, Control, and Computing (Allerton), 2010 48th Annual Allerton Conference on, 29 2010-oct. 1 2010, pp. 1182 –1187. [16] Scutari Gesualdo, Daniel P Palomar, and Sergio Barbarossa, “The MIMO iterative waterfilling algorithm,” IEEE Trans. on Signal Processing, vol. 57, no. 5, pp. 1917–1935, May 2009. [17] Shi Changxin, David A. Schmidt, Randall A. Berry, Michael L. Honig, and Wolfgang Utschick, “Distributed interference pricing for the MIMO interference channel,” in Proc. IEEE Int’l Communications Conf. (ICC), Dresden, Germany, 2009. [18] K. Rose, “Deterministic annealing for clustering, compression, classification, regression, and related optimization problems,” Proceedings of the IEEE, vol. 86, no. 11, pp. 2210 –2239, nov 1998. [19] E.L. Allgower and K. Georg, “Introduction to numerical continuation methods,” Philadelphia, PA: Society for Industrial and Applied Mathematics, 2003. [20] O.. Gonzalez and I. Santamaria, “Interference Alignment in SingleBeam MIMO Networks via Homotopy Continuation,” in IEEE Int’l Conf. on Acoustics, Speech and Signal Proc. (ICASSP), Prague, 2011.

ON THE NOISY MIMO INTERFERENCE CHANNEL WITH CSI THROUGH ANALOG FEEDBACK Francesco Negro, Dirk T.M. Slock ∗ EURECOM Mobile Communications Department 2229 Route des Crˆetes, BP 193 06560 Sophia Antipolis Cedex, France Email: {francesco.negro, dirk.slock}@eurecom.fr ABSTRACT In this paper we propose a transmission protocol through which base stations (BSs) and user equipments (UEs) acquire the necessary channel state information (CSI) for Interference Alignment (IA) transmit (Tx) and receive (Rx) filters design. We focus our attention on the frequency-flat noisy MIMO interference channel (IFC) without symbol extension and with initial assumption of no CSI neither at the BS nor at the UE. Each device acquires the necessary CSI through channel training and analog feedback. We consider optimizing the sum rate by focusing in particular on the resulting degrees of freedom (DoF). This approach allows us to easily optimize any set of parameters to unveil the trade-off between the cost and the gains associated to CSI acquisition overhead. 1. INTRODUCTION The interference channel, including related interference mitigation techniques, has recently attracted intense research interest. This is because cellular communication systems, which are severely affected by intercell interference, can be modeled using the K-user Interference Channel (IFC). In spite of the efforts of several research groups over the past few decades, the capacity of a general K-user IFC remains an open problem and is not well understood even for simple cases [1]. In the seminal work [2] a new approach to handle interference with linear transmit and receive filters has been introduced. The authors have shown that the conventional approach of orthogonalizing the resource blocks can be overcome by the use of a new signaling technique called Interference Alignment (IA). This approach is based on designing (transmit) interferer signal subspaces such that their received contributions align in reduced dimension subspaces at the unintended receivers. They have proven that for (time or frequency) varying SISO channels a total of K 2 interference-free streams can be received with IA instead of the 1 obtained through orthogonalization. This significant increase in degrees of freedom (DoF) can be achieved by asymptotic signal-space expansion in time or frequency called symbol extension. The sum degrees of freedom for a general MIMO IFC is still an open problem, the only known result is given in [3] for a K = 2 user MIMO ∗ EURECOM’s

research is partially supported by its industrial members: ORANGE, BMW Group, Swisscom, Cisco, SFR, ST Ericsson, Symantec, SAP, Monaco Telecom, and also by the EU FET project CROWN and FP7 projects SACRA and WHERE2. † The research of Intel Mobile Communications France is supported in part by the EU FP7 projects CROWN, SACRA.

Irfan Ghauri† Intel Mobile Communications GAIA, 2600 Route des Crˆetes 06560 Sophia Antipolis Cedex, France Email: [email protected]

IFC. For the case K > 2 some bounds have been provided in [4]. IA requires perfect and global channel state information (CSI) at all Tx/Rx. This assumption does not come for free in practical timevarying channels. For this reason different studies have been conducted for more practical situations. In [5] the authors consider the SISO IFC with frequency selective channels. Using quantized channel feedback they show that the full multiplexing gain can be achieved if the feedback bitrate scales sufficiently fast with the SNR. This result is extended in [6] to the MISO and MIMO IFC. In [7] the author shows for different selected multiuser communication scenarios that it is possible to align the interference when the transmitters do not know the channel coefficients but they only have information about the channel autocorrelation structure of different users. In [7] a staggered block fading channel model is the only assumption required to achieve IA. The resulting multiplexing gain is much lower however than for the case of full CSI. These techniques are now known by the terms delayed CSIT or retrospective IA. The authors of [8] propose to use analog feedback for the acquisition of full CSIT. The channel coefficients are directly fed back to the base station (BS) without any quantization process. This has the advantage, in contrast to digital feedback, that the complexity does not increase with SNR. In [8] CSIT processing and transmitter computation is centralized, and CSIR issues are neglected. They show that using IA with the acquisition of CSIT using analog feedback incurs no loss of multiplexing gain if the feedback power scales with the SNR. In this paper we introduce two transmission protocols for the distributed CSI acquisition at the BS and UE that are based on channel training and analog feedback (FB), for both TDD and FDD communication systems. The main difference between the two approaches is in the FB part: channel FB or output FB. In the channel FB solution, described also in [8] and [9], each UE feeds back to the BS the downlink channel estimates while in the output FB scheme, the UE feeds back directly the received samples of the DL training phase. In FDD communications uplink (UL) and downlink (DL) transmission can take place at the same time. Hence with output FB, it is possible to shrink the time overhead, reducing partially the silent periods. 2. SIGNAL MODEL Fig. 1 depicts a K-link MIMO interference channel with K transmitter receiver pairs. To differentiate the two transmitting and receiving devices we assume that each of the K pairs is composed of a Base station (BS) and a User equipment (UE). This is only for notational purposes. The k-th BS and its corresponding UE are equipped with Mk and Nk antennas respectively. The k-th transmitter generates in-

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In this section we describe briefly the different phases of the transmission protocol for CSI acquisition proposed in [9]. This protocol can be used in both TDD and FDD communication systems but here we focus on FDD, refer to [9] for further details. We assume a block fading model, in which the channel is assumed to be constant over T channel uses. This time period T will need to be shared between the different training Tovrhd and data transmission phases Tdata = T − Tovrhd of the overall transmission scheme.

Fig. 1: MIMO DL/UL Interference Channel terference at all l = k receivers. The received signal in the Downlink (DL) phase yk at the k-th UE, can be represented as K  yk = Hkk xk + Hkl xl + nk (1) l=1 l=k

where Hkl ∈ CNk ×Ml represents the channel matrix between the l-th BS and k-th UE, xk is the CMk ×1 transmit signal vector of the k-th BS and the CNk ×1 vector nk represents (temporally white) AWGN with zero mean and covariance matrix Rnk nk . The channel is assumed to follow a block-fading model having a coherence time of T symbol intervals without channel variation. Each entry of the channel matrix is a complex random variable drawn from a continuous distribution. It is assumed that each transmitter has complete knowledge of all channel matrices corresponding to its direct link and all the other cross-links in addition to the transmitter power constraints and the receiver noise covariances. We denote by Gk , the CMk ×dk precoding matrix of the k-th transmitter. Thus xk = Gk sk , where sk is a dk × 1 vector representing the dk independent symbol streams for the k-th user pair. We assume sk to have a spatio-temporally white Gaussian distribution with zero mean and unit variance, sk ∼ N (0, Idk ). The k-th receiver applies Fk ∈ Cdk ×Nk to suppress interference and retrieve its dk desired streams. The output of such a receive filter is then given by K  Fk Hkl Gl sl + Fk nk rk = Fk Hkk Gk sk + l=1 l=k

In the reverse transmission link, Fig. 1(b) Uplink (UL) phase, the received signal at the k-th BS is given by: K  rk = Fk Hkk Gk sk + Fk Hkl Gl sl + Fk nk l=1 l=k

where Fk and Gl denote respectively the dk × Mk Rx filter at BS number k and the Nl ×dl BF matrix applied at Tx l. The UL channel form the l-th UE and the k-th BS is denoted as Hkl . In this paper we design the transmit and receive filters according to IA. The objective then is to design spatial filters to be applied at the transmitters such that, the interference caused by all transmitters at each non-intended RX lies in a common interference subspace [2]. Since IA is a condition for joint transmit-receive linear ZF, the transmit and receive filters should satisfy the following conditions: Fk Hkl Gl = 0 ∀l = k rank(Fk Hkk Gk ) = dk

∀k ∈ {1, 2, . . . , K}

(2) (3)

Fig. 2: MIMO IFC transmission phases - channel FB. 3.1. Downlink Training Phase During this phase each BSk sends orthogonal pilot sequences that can be received by all the UE for a total duration of TTDL . In this way U Ei can easily estimate the DL channels Hi = [Hi1 , . . . , HiK ] directly connected to it.Because the compound channel matrix Hi has dimensions Ni × k Mk the minimum total duration of this training phase is K  TTDL ≥ Mk . k=1

Each BS independently transmits an orthogonal matrix Ψk of dimension Mk × TTDL with power PTDL hence the total received Ni × TTDL matrix at Rx i is:  Yi = PTDL Hik Ψk + V (4) k=1

where V represents the zero mean additive white Gaussian noise with variance σv2 . The DL Tx power can be related to the time duration of the corresponding Tx phase as

DL

T DL DL PTDL = T P T . Mk

(5)

where P T represents the DL power constraint. From the Rx signal (4) U Ei performs an MMSE estimate of the DL channels. 3.2. Uplink Training Phase This phase can be seen as the dual of the DL training where now all UE send orthogonal pilots to each BS for the estimation of the UL channel matrices. The time duration of this phase is: TTU L ≥

K 

Nk .

k=1

Then BSk can estimate the compound channel matrix Hi = [Hi1 , . . . , HiK ] using an MMSE estimator as described for the DL training phase. We are describing all the transmission phases for the FDD transmission scheme, hence different frequency bands are used for UL and DL communications. This separation implies that transmission and reception can take place at the same time. If we take advantage of this possibility the two training phases, UL and DL, can collapse in only one training slot that have duration TT = max{TTDL , TTU L }. Accounting for this new training phase implies a reduction of the total overhead Tovrhd .

3.3. Uplink Feedback Phase Once the UL and DL training phases are completed each terminal knows the channel directly connected to it in the UL and DL respectively. In order to compute the IA BF matrices full DL CSI is required. In FDD case, the one under investigation, each UE has to  i to all BS, this task can be FB the DL channel estimate (CFB) H done using Analog FB. This particular transmission phase should be designed according to the particular type of processing used for the computation of the BF matrices. We can describe two approaches: centralized and distributed. In the former a central controller acquires the necessary CSI, computes the BFs and then it disseminates this information among the K BSs. In the latter approach each BS should have full CSI to compute the IA BF, using e.g. the approach of [10]. This solution can be also called Duplicated because each BS essentially solves the same problem and finds the complete solution, all the IA BFs, and then it will use only its own transmit filter. Centralized Processing The Rx signal vector at each BS is sent to the centralized controller that retrieves the useful channel information and computes the BF matrices. If we stack all the received vector from the K BSs in Y we get: ⎡

H11 1 2 ⎢ Y=PF B⎣ ... HK1 where N =



i

. . . H1K .. .. . . . . . HKK



M ×N

⎡ ⎤ ⎤H ⎡ ⎤⎡ ⎤ 0 ... 0 1 V1  2 . . . 0 ⎥ Φ1 ⎢0 H ⎥ ⎢ . ⎥⎢ .⎥ ⎥⎢ . ⎥ ⎣ . ⎦+⎣ .. ⎦ ⎦⎢ . .. ⎣ .. . 0 ⎦ Φ V  K K  K  0 ... ... H

  KM ×TF B V N ×KM

Ni and M =



i

Mi and

PF B = P F B

TF B Ni M

(6)

with P F B is the FB power constraint. Using a centralized controller to gather all Rx data the entire system can be interpreted as a unique single user MIMO link with a BS that is equipped with M total antennas and a UE with N antennas. With this interpretation we can calculate the total amount of time necessary to satisfy the identifiability conditions. In particular we get: TF B ≥

N ×M = max{N, M } ∝ K. min{N, M }

(7)

N ×KM

where

PF B = P F B

TF B Ni M

⎤

⎡

⎤

Φ1 .. ⎥ +V k . ⎦ ΦK  

⎥ ⎥⎢ ⎥⎣ ⎦

TF B ≥

N ×M ∝ K2 mini {Mi , Ni }

(9)

Another possible strategy to receive the channel FB is to use linear MMSE estimate instead of the least square approach described in this section. The two solutions will be identical at high SNR but in different SNR regimes LMMSE should give better performances. The analog FB transmission described here is based on the assumption that the number of Tx and Rx antennas satisfy the relation that min{Mi } ≥ Nj , ∀j. If this condition is not satisfied then a different transmission scheme should be applied. In particular each UE should apply a precoding matrix such that the identifiability conditions should be satisfied at all BS, this requires a more careful precoding design. A possible design criterion could be to optimize the performance of the worst FB link. This solution can be also used to introduced more redundancy in the transmission that can increase the performances of the FB reception. A simple approach could be to use a Kronecker model precoder at each UE of the form: TF B ×M

T k = Sk

Nk sk

N ×sk

⊗ Bk k

where Sk and Bk are optimize according to the channel conditions and sk represents the number of transmitted streams such that the identifiability conditions are satisfied at all BS. With this model the compound channel matrix from U Ek to BSi can be written as T

GikF B

Mi ×M Nk

= (ITF B ⊗ Hik )Tk = Sk ⊗ Hik Bk

then the equivalent channel matrix is designed for the transmission M N ×1  k }. of the total number of FB hk k = vec{H

3.4. Downlink Training Phase

Once the beamformers have been computed, using a centralized or distributed approach, they can be used for the DL communications. According to IA each UE should apply a ZF receiver, in order to compute the Rx filters each UE requires some additional information on the DL communication. On this purpose two approaches are possible: DL training or analog transmission of the entire Rx filters. In the former case BSk sends a set of beamformed pilots that allow U Ei to estimate the cascade Hik Gk . This phase lasts  dk . TDL ≥ k

Distributed Processing In this case the CFB transmission is organized in such a way that each BS can gather full channel knowledge from all UE. The Rx matrix at BSk can be written as: ⎡ H1 0 . . . 0   ⎢ √ ⎢ 0 H2 . . . 0 Yk = PF B Hk1 . . . HkK ⎢ . .. .

 ⎣ . . 0 Mk ×N K 0 ... ... H



with P F B is the FB power constraint. In the distributed approach to satisfy the identifiability conditions the CFB length should be:

 KM ×TF B

(8)

Then each UE can estimate the interference subspace and the signal subspace for the Rx filter design. The other possibility consists in the transmission to the i-th UE of the entire Rx filter matrix Fi using analog transmission. This solution requires a duration TDL ≥

 k

Nk dk min{Nk , Mk }

The two solutions proposed here are not equivalent. Training is shorter but the estimation error will have a bigger impact in the calculation of the Rx filter compare to the one in the analog transmission. Which solution should be preferred depends also on the operating SNR point. For example in high SNR, where we are interested more in maximizing the total degrees of freedom the duration of this phase has a bigger impact compare to the estimation error then DL training is the preferable solution.

4. OUTPUT FEEDBACK

while for CFB we have:

In the previous sections we have described the scheme proposed in [9] to acquire the necessary channel state information at each BS using analog FB based on the DL channel estimates obtained at each UE. A different strategy consists to FB directly to BSs the noiseless version of the received signal at each UE during the DL training phase instead of the DL channel estimates. This technique is called output FB (OFB). Then, once each BS accumulates enough FB samples, it estimates directly the required DL channels. The advantage of this strategy, compare to the traditional channel FB, is that the FB phase can start one time instant after the reception of the first DL training samples. In FDD transmission schemes UL and DL communications can take place at the same time. Assuming the DL frame aligned with the end of the UL training phase, the difference between the two schemes can be pictorially represented as in Fig. 3. At time t the received signal at UEk during the DL training phase is

Fig. 3: Output Feedback and Channel Feedback yk [t] =

K 

Hki ψi [t] + nk [t].

(10)

i=1

In the next time instant [t+1] UEk transmits back to all BSs the noiseless version of the RX signal at time instant [t]. So BS number l receives: yl [t + 1]

= =

K  j=1 K  j=1

From the equations above we see that using OFB we save TTDL − 1 time instants. 5. DOF OPTIMIZATION AS FUNCTION OF COHERENCE TIME In [9] we considered optimizing the length of different training and FB phases to maximize the sum rate. Here the goal is different, we want to optimize the number of transmitted streams as a function of coherence time. The rationale behind this optimization problem is the following. If the coherence time is not long enough to host the total overhead due to CSI acquisition then the transmission of dtot = k dk is no longer possible. Then we should use blind IA or noncoherent transmission techniques. Another possibility is to reduce the total amount of transmitted streams. The reduction of d implies a reduction of the required number of transmit and receive antennas so that the amount of CSI exchange is optimized as a function of the coherence time. To solve this problem we should be able to define a relationship between the number of transmitted streams and antennas. Unfortunately this relation only exists for symmetric systems of the form (N, N, d)K where each user is equipped with the same number of antennas N and transmits the same number of streams d. According to feasibility conditions in [11] and [12] we can write: d N ≥ (K + 1). (12) 2 Using (12) we can express the total time overhead as a function of the number of transmitted streams d. According to the previous sections we can write the total DL time overhead for CFB as: ⎧ (Centr.) ⎨ dK(K + 2) (13) Tovrhd = TTDL+TF B+TDL= ⎩ Kd ((K + 1)2 + 2) (Distr.) 2 In the equations above we derived the overhead length for the centralized and distributed FB case as in section 3. The optimization problem that we need to solve is the following:

Hlj xj [t + 1] + nl [t + 1] Hlj αj

K 

max J(d) = max(1 − d

Hji ψi [t] + nl [t + 1]

i=1

where αj denotes a scaling factor that takes into account the TX power constraint at j-th UE. In order to being able to separate the different contributions coming from different UEs we assume to use time multiplexing. Each BS has to estimate all the matrices Hi = [Hi1 , . . . , HiK ]Ni ×M . To estimate this many coefficients the required total length of the output FB phase is: TFo B

DL = TTDL + TF B + TDL . Tovrhd

N ×M ≥ mini {Ni , Mi }

(11)

Comparing equation (11) with (8) we can see that there is no reduction in the length of the FB phase using OFB comparing to traditional channel FB. The reduction of the overhead comes from partial elimination of silent periods, as shown in Fig.3. The DL overhead time due to CSI acquisition for the case of OFB can be quantified as: DL Tovrhd = (TFo B + 1) + TDL

d

Tovrhd )Kd log SN R T

(14)

The cost function that should be maximized is concave in the optimization variable then it admits a unique maximum. To find the optimal solution we calculate the derivative w.r.t. the optimization variable d, imposing: ∂J =0 ∂d we finally obtain the optimal solution: ∗

d =

⎧ ⎨ ⎩

T 2K(K+2)

(Centr.)

T K[(K+1)2 +2]

(Distr.)

(15)

Now we should determine when is convenient to reduce the number of transmitted streams to maximize the sum rate in high SNR. The number of transmitted streams per user should satisfy the following:   2N d ≤ min d∗ , . K +1

The relation above can be specified, for the two cases studied in (15), as: ⎧   T 2N ⎪ (Centr.) , K+1 ⎪ min 2K(K+2) ⎨ d= (16)   ⎪ ⎪ T 2N ⎩ min (Distr.) , 2 K[(K+1) +2] K+1

From the equation above we can see that, for example in the centralized case, if 4N K(K + 2) T ≥ = 2Tovrhd K +1 then to optimize the DoF the number of transmitted streams should 2N be kept at its maximum d = K+1 . On the contrary, if the given con∗ dition is not satisfied then d streams per user should be transmitted. This implies that the number of antennas, used for transmission and reception, should be shrank to n≥

d∗ (K + 1) 2

with a consequent reduction of the time overhead for CSI acquisition. The same analysis can be done to study the case when output FB is used instead of channel FB. Calling D the number of time instants after which the FB transmission starts (in section 4 we used D = 1 ), the CSI acquisition phase lasts ⎧ Kd (Centr.) ⎨ 2 (K + 3) + D Tovrhd =TF B + D +TDL= ⎩ Kd (K(K + 1) + 2) + D (Distr.) 2 (17) Now solving the optimization problem (5) using the time overhead length derived above we obtain: ⎧ T −D (Centr.) ⎨ K(K+3) (18) d∗ = ⎩ T −D (Distr.) K[K(K+1)+2]

From the optimal number of transmitted streams above we can finally write : ⎧   T −D 2N ⎪ (Centr.) ⎪ ⎨ min K(K+3) , K+1 d= (19)   ⎪ ⎪ T −D 2N ⎩ min (Distr.) , K[K(K+1)+2] K+1

The analysis develop above is based on the assumption of symmetric MIMO links, in the following we extend the results to the asymmetric MIMO case where each transmitter has M antennas, and each receiver is equipped with N antennas. In concise notatio we consider the (M, N, d)K interference channel. To study this more general case we assume that the relationship between number of antennas and transmitted streams d≤

M +N K +1

(20)

derived also in [11] for such a system configuration, is still valid. This is true if the ratio M is not too far from 1. This is due to N the fact that, as recently shown in [13], for very rectangular MIMO links counting the total number of variables and constraints in the IA problem is not enough to determine the feasibility of the problem. In the analysis below we optimize w.r.t. the number of active transmitting and receiving antennas, m and n respectively, instead of a direct optimization of the number of transmitted streams.

We first study the case M > N . To simplify the analysis we consider that the overhead time for CSI acquisition is due to only DL training and CFB, then we obtain Tovrhd = 2Km. Expressing d as a function of the number of antennas we can rewrite as 2Km K(m + n) max J(n, m) = max(1 − ) log SN R (21) n,m n,m T K +1 for m ∈ [1, M ] and n ∈ [1, N ] and m ≥ n. The optimization problem above is linear in the variable n, then to maximize the cost function the optimal value for the number of receiving antennas falls in the extremum of the optimization interval: n∗ = N . To optimize w.r.t. m we need to equate the first order derivative of J w.r.t. m to zero obtaining: T N − . (22) 4K 2 ∗ From the solution above, and the constraint m = min{m , M }, then we can state that: ⎧ T ≥ 4KM + 2KN ⎨ M, m= (23) ⎩ T − N2 , 6KN ≤ T ≤ 4KM + 2KN 4K m∗ =

To conclude the analysis we should study the other regime M ≤ N . In this case the time overhead is Tovrhd = K(K+2) (m + n), where K+1 we also included the duration of the beamformed DL training phase. With this result the cost function that should be optimized is: K(m + n) 1 K(K + 2) (m + n)) log SN R. T K +1 K +1 (24) As we can see the cost function J depends only on the sum of the two optimization variables so we directly optimize w.r.t. y = (m + n). Then from the first order optimality condition we get: J(n, m) = (1 −

(m + n)∗ =

T K +1 . 2 K(K + 2)

From the optimization problem (24) there is nothing that we can infer about the behavior of the single variables m and n and how m+n is split over them as long as 1 ≤ n ≤ N and 1 ≤ m ≤ M ≤ N . On the other hand there is a slight preference to consider a square system since only for that case we are sure about the feasibility condition (12) [12]. Then : K(K + 2) K +1 Form the optimal antennas distribution is possible to determine the corresponding stream allocation just using the feasibility condition (20). In Fig. 4 we summarize all the results found in this section. It gives a qualitative description of the behavior of the antennas distribution (m + n) as a function of the coherence time T . In particular in Fig. 4(a) we describe the regime M ≥ N . When T is long enough m + n assumes its maximum value, then the number of Tx antenna starts to shrink up to the point where m = n = N . At this point the IFC becomes square and then the dimensions decrease as long as T decreases but the system remains square because the condition m ≥ n should be always satisfied. Fig. 4(b) depicts the situation where M ≤ N . There we should underline that only the behavior of m + n can be described but not how m and n behave separately. Also for the rectangular MIMO interference channel the analysis of the antennas and streams distribution as a function of the coherence time can be developed for the use of output FB instead of channel FB. These results are not provided here due to lack of space. m + n ≤ M + N,

T ≤ 2(M + N )

shorter FB delay as we do here, and as is possible in principle in FDD systems. 7. REFERENCES

(a)

(b)

Fig. 4: Behavior of the optimized antennas distribution 6. CONCLUDING REMARKS We optimized the sum rate of the MIMO IFC under investigation by focusing in particular on the resulting degrees of freedom. We showed that the optimal number of streams should vary as a function of the channel coherence time, just like in the single-user MIMO channel. We have considered here the use of output FB for the purpose of CSI acquisition. One may wonder whether the more general use of such Shannon feedback would allow to increase the DoF. A recent discussion on this can be found in [14] which appears to indicate that in the case of perfect CSIT, it is unlikely that output FB can help the DoF for the general MIMO IFC. However, [14] shows that in the case of delayed CSIT, (additional) output FB may allow to increase the DoF, depending on the number of antennas in the K = 2 MIMO IFC. Another aspect is that in the approach considered here, we focus on obtaining CSIT in an initial portion of the coherence interval, after which we apply coherent IA transmission. Some improvement can be obtained by adding retrospective IA during the training period. This has been explored for the K = 2 MISO IFC in [15], where an optimal combination of delayed CSIT and coherent transmission is proposed. One should note though that the improvements brought about by such further sophistication are only important when the coherence time becomes very short and/or the CSI FB delay becomes large. The approach of [15] (just like delayed CSIT in general) appears to be motivated by considering a substantial FB delay (time unit), e.g. corresponding to a slot in current wireless communication standards. The picture changes though if one considers much

[1] R. H. Etkin, D. N. C. Tse, and Hua Wang, “Gaussian interference channel capacity to within one bit,” IEEE Trans. on Inform. Theory, , no. 12, 2008. [2] V.R. Cadambe and S.A. Jafar, “Interference alignment and degrees of freedom of the K-user interference channel,” IEEE Trans. on Inform. Theory, Aug. 2008. [3] S.A. Jafar and M.J. Fakhereddin, “Degrees of freedom for the MIMO interference channel,” Information Theory, IEEE Transactions on, July 2007. [4] T. Gou and S.A. Jafar, “Degrees of freedom of the K user MxN MIMO interference channel,” 2008, http://arxiv.org/abs/0809.0099. [5] H. Bolcskei and I.J. Thukral, “Interference alignment with limited feedback,” in Proc. IEEE Int’l Symp. on Information Theory (ISIT), July 2009. [6] R.T. Krishnamachari and M.K. Varanasi, “Interference alignment under limited feedback for MIMO interference channels,” in Proc. IEEE Int’l Symp. Information Theory (ISIT), June 2010. [7] S.A. Jafar, “Exploiting Channel Correlations - Simple Interference Alignment Schemes with No CSIT,” in Proc. IEEE Global Telecommunications Conf. (Globecom), Dec. 2010. [8] O. El Ayach and R. W. Jr. Heath, “Interference alignment with analog channel state feedback,” in Proc. MILCOM, Oct. 2010, http://arxiv.org/abs/1010.2787. [9] F. Negro, U. Salim, I. Ghauri, and D.T.M. Slock, “The noisy MIMO interference channel with distributed CSI acquisition and filter computation,” in Proc. Asilomar Conf. on Signals, Systems, and Computers, Pacific Grove, CA, USA, Nov. 2011. [10] F. Negro, I. Ghauri, and D.T.M. Slock, “Deterministic annealing design and analysis of the Noisy MIMO Interference Channel,” in Proc. Information Theory and Applications Workshop (ITA), feb. 2011. [11] F. Negro, S. P. Shenoy, I. Ghauri, and D.T.M. Slock, “Interference Alignment Feasibility in Constant Coefficients MIMO Interference Channel,” in Proc. 11th IEEE Int’l Workshop on Signal Processing Advances in Wireless Comm’s (SPAWC), June 2010. [12] G. Bresler, D. Cartwright, and D. Tse, “Settling the feasibility of interference alignment for the MIMO interference channel: the symmetric square case,” 2011, http://arxiv.org/abs/1104.0888. [13] G. Bresler, D. Cartwright, and D. Tse, “Geometry of the 3-user MIMO interference channel,” 2011, http://arxiv.org/abs/1110.5092. [14] C.S. Vaze and M.K. Varanasi, “The Degrees of Freedom Region of the MIMO Interference Channel with Shannon Feedback,” Trans. Information Theory, subm., Oct. 2011, arXiv:1109.5779v2. [15] X. Yi, D. Gesbert, S. Yang, and M. Kobayashi, “The DoF Region of the Multiple-Antenna Time Correlated Interference Channel with Delayed CSIT,” Subm. to IEEE Trans. on Information Theory, Apr. 2012, http://arxiv.org/pdf/1204.3046.pdf.

LOCATION AIDED WIRELESS COMMUNICATIONS Dirk Slock EURECOM 2229 route des Crˆetes, BP 193, 06904 Sophia Antipolis Cedex, FRANCE Email: [email protected] ABSTRACT The availability of location information of mobile terminals, relays, femto cells and primary units provides opportunities to greatly enhance the operation of wireless communication systems. We provide an overview of some of the possibilities, starting with physical layer considerations for a single link. However, most of the opportunities concern resource allocation aspects. Especially for multi-user systems, for which recent information theory progress has shown that an optimized handling may lead to significant system capacity increase. But the optimization of multi-user systems requires very precise Channel State Information at the Transmitter (CSIT). The problem is compounded when taking furthermore user selection into account. CSIT is typically obtained by feedback (FB), which leads to transmission overhead. Channel reciprocity based TDD systems only represent a limited alternative in multi-cell settings, or for user selection. For single-cell multi-user communications, we argue for a revival of SDMA (Spatial Division Multiple Access). We then consider the multi-cell problem, and cognitive radio. Some (but not all) of the location aided techniques require substantial databases, which have come into vogue in the context of flexible spectrum access. Location aided techniques may furthermore exploit location prediction through mobility trajectory information. This would allow slow fading (and even connectivity) predictibility, something that is difficult to achieve without location information. Of course, proposals for location aided techniques need to be weighted against classical approaches (CSIT learning) in order to assess their definitive value. Index Terms— Wireless communications, location, SDMA, mobility, multi-user, multi-cell. 1. INTRODUCTION Wireless network based localization offers an alternative and/or complement to GNSS based localization. Satellite connectivity may pose problems in urban canyons and indoor, and not all mobile terminals (MTs) are GNSS equipped. Wireless network based localization is now part of LTE-A, based on the following techniques: Enhanced Cell Id = Cell Id + RSS (Received Signal Strength), OTDoA (Observed Time Difference of Arrival), and AoA (Angle of Arrival at the base station (BS)). The availability of location information offers in turn opportunities to enhance the wireless communications. The position based information that can be exploited comprises slow fading channel characteristics of various links: EURECOMs research is partially supported by its industrial members: ORANGE, BMW Group, Swisscom, Cisco, SFR, ST Ericsson, Symantec, SAP, Monaco Telecom, and also by the EU FET project CROWN and FP7 projects SACRA and WHERE2.

• LOS/NLOS ((Non) Line of Sight) • attenuation

• delay spread, frequency selectivity

• angular spreads, MIMO channel characteristics (rank)

• speed, direction of movement, acceleration (predictibility of movement), trajectory Some of these aspects may require the use of databases (containing these characteristics as a function of position), compatible with a cognitive radio setting. Compared to feedback (FB) based approaches: some of these characteristics can not easily be determined from isolated channel estimates, or not predicted at all (e.g. slow fading prediction). What can not be inferred on the basis of position (as generally believed) is the fast fading state, the instantaneous complex channel impulse response. However, Nokia-Siemens in [1] work with a database of channel impulse responses directly (which 0 are claimed to be stable over 40 in some measurements), to overcome the problem of delay in channel FB. They consider a combination of FB + location aided approaches as realistic. 2. SINGLE-USER ASPECTS On the receiver (Rx) side: position information can lead to information about the channel statistics via a database, which can be used to improve channel estimation. This could be compared to learning of the channel statistics from previous channel estimates (which is hardly possible though in short packet mode!) or with sparse techniques. On the transmitter (Tx) side: adapt AMC and resource allocation (see further). Location and Database aided Channel Estimation/Prediction These days, optimized LMMSE channel estimation and tracking is often considered [2], which requires 2D covariance information in the form of the Power Delay Doppler Profile (PDDP). In multiantenna systems the space dimension could also be added to that profile. For fast fading channel estimation and short-term prediction, the channel PDDP an be (1) learned from consecutive channel estimates, but knowledge will often come a bit late in this way and may require long data and stationarity for extensive PDDPs, or (2) determined from position information + (extensive) database, leading to instantaneous knowledge & extended (short-term) channel prediction range. A Kalman filter performing integrated position tracking and channel tracking is one solution here. Approach (2) allows furthermore longer-term prediction, but of channel statistics only. If the database content is limited, a combination of both approaches could be considered.

Position based Adaptive Modulation and Coding (AMC) and (OFDMA) Resource Allocation (Position information leads to) Environment information which in turn leads to information on the channel diversity structure, on the channel frequency selectivity and would allow to adapt frequency allocation/interleaving. One could consider adapting the (OFDM) Cyclic Prefix (CP) and pilot structure on the basis of environment parameters. This would lead to minimized overhead and would avoid to design for the worst case. Information on the MIMO channel richness (e.g. rank) allows to adapt the spatial multiplexing and the (linear) space-time coding. Information on the mobility provides temporal diversity information, which can be used to adapt interleaving in time. All these adaptations can take into account channel non-Rayleigh aspects (e.g. LOS/NLOS, LOS leads to reduced or no fading). 3. SINGLE-CELL MULTI-USER COMMUNICATIONS 3.1. Location aided Multi-User Resource Allocation Some possibilities are: • Multi-user MIMO: Use environment information to preselect users, to limit channel feedback to a reduced set of preselected users. The user preselection can e.g. involve: users with similar attenuation, users with rank 1 MIMO channels (close to LOS), ... • Multicell aspects (interference coordination) or for Cognitive Radio (interference from secondary to primary systems): the interference level can be predicted from position information. A transversal aspect is also that location tracking can lead to location prediction. This leads in turn to slow fading predictibility (and not just fast fading prediction, which can in principle be done also from past channel response estimates). Another aspect is that user selection (multi-user diversity) potentially leads to an explosion of CSIT requirements and associated overhead. Location based covariance CSIT might offer a (partial) solution. In this section, we shall focus on the Spatial Division Multiple Access (SDMA) problem, which in Information Theory is called the Broadcast Channel (BC). The SDMA terminology dates from the early nineties. These days it is referred to as the multi-user MISO (or MIMO) communications problem, and we shall particularly focus on the more difficult downlink. 3.2. SDMA considerations Whereas single user (SU) MIMO communications represented a big breakthrough and are now integrated in a number of wireless communication standards, the next improvement is indeed multi-user MIMO (MU MIMO). This topic is nontrivial as e.g. illustrated by the fact that 3gpp had a lot of difficulty to get it included in the LTE standard. MU MIMO is a further evolution of SDMA, which was THE hot wireless topic in the early nineties. The MU MIMO area has now sufficiently evolved to allow us to understand the following key elements: • SDMA is a suboptimal approach to MU MIMO, with transmitter precoding limited to linear beamforming, whereas optimal MU MIMO requires Dirty Paper Coding (DPC). • Channel feedback has gained much more acceptance, leading to good CSIT, a crucial enabler for MU MIMO, whereas SDMA was either limited to TDD systems (channel CSIT

through reciprocity) or Covariance CSIT. In the early nineties, the only feedback that existed was for slow power control. • Since SDMA, the concepts of multiuser diversity and user selection have emerged and their impact on the MU MIMO sum rate is now well understood. Furthermore, it is now known that user scheduling allows much simpler precoding schemes (such as Zero-Forcing (ZF) beamforming (BF)) to be close to optimal. • Whereas SU MIMO allows to multiply transmission rate by the spatial multiplexing factor, when mobile terminals have multiple antennas, MU MIMO allows to reach this same gain with single antenna terminals. • Whereas in SU MIMO, various degrees of CSIT only lead to a variation in coding gain (the constant term in the sum rate), in MU MIMO however CSIT affects the spatial multiplexing factor (multiplying the log(SNR) term in the sum rate). In the process attempting to integrate MU-MIMO into the LTE-A standard, a number of LTE-A contributors had at some point become quite sceptical about the usefulness of the available MU-MIMO proposals. The issue is that they consider MU-MIMO in the same spirit as SU-MIMO, i.e. with FB of CSI limited to just a few bits! However, MU-MIMO requires very good CSIT! Some possible solutions are: • Increase CSI FB enormously (possibly using analog transmission); LTE-A went recently a bit in this direction. • Exploit channel reciprocity in TDD (there may be an electronics calibration issue though [3]). • Limit MU-MIMO (SDMA) to NADA (see below) users and extract essential CSIT from position information (or from DoA estimates - in both cases the knowledge of the antenna araay manifold is (eventually) required). Narrow AoD Aperture (NADA) case The idea here is to focus on the category of mobiles for which the angular spread seen from the BS is limited [4]. This is a small generalization of the LOS case. In the NADA case, the MIMO channel H (assumed frequency-flat here or we assume a narrowband case (e.g. an OFDM subcarrier)) is of the form h i X H= hr (θi )hTt (φi ) = B AT , A = ht (φ) h˙ t (φ) (1) i

where hr (.) is the receive side antenna array response, ht (.) is the transmit side antenna array response, θi is the Angle of Arrival (AoA) of path i and φi is the Angle of Departure (AoD) of path i. In the case of narrow AoD spread, we have φi = φ + ∆φi where φ is the nominal (LOS) AoD and ∆φi is small. Hence ht (φi ) ≈ ht (φ) + ∆φi h˙ t (φ) .

(2) (3)

This leads to the second equality in (1). Hence H is of rank 2 (regardless of the AoA spread). The LOS case is a limiting case in which the power of the h˙ t (φ) term becomes negligible and the channel rank becomes 1. The factor A in H depends straightforwardly on position (which translates into LOS AoD), only B remains random. In what follows, we shall focus on the LOS limit for considerations of location based processing. We propose that location based MU MIMO transmission involves position based user selection (attenuation, nominal AoD, AoD spread) and associated beamforming (BF) and power control (PC).

3.3. Location Based SDMA

a first restriction in the SDMA user selection process is that for MUMISO purposes, users to be considered need to be in LOS mode. So in this case we get for the downlink channel to user k:

3.3.1. Sum Rate Lower Bound In [5] one can find a discussion of the importance of CSIT in MU MISO and of the state of the art on this. The analysis in [5] concerns optimization of the CSIT FB. We shall work here with the same lower bound of the sum rate attained by ZF BF based on approximate channel knowledge. The frequency-flat system we consider consists of a BS having nt transmit antennas and K (K ≤ nt ) single-antenna user terminals. In the DL, the signal received by k-th user can be expressed as yk = hH k x + nk , k = 1, 2, . . . , K

(4)

where hk is the (complex conjugated) channel vector of user k, x denotes the nt -dimensional signal transmitted by the BS and nk is independent complex Gausian noise with zero mean and unit variance. We omit the time index for simplicity. The concatenation of the K user channels is HH = [h1 h2 · · · hK ]. The channel input from the BS must satisfy an (average) transmit power constraint of P , i.e. E[||x||2 ] ≤ P . In this setting, the transmit power P equals the (transmit) SNR at each user due to the normalized noise variances. We will assume the BF to be based on an approximate (knowledge) b j of the channel vectors. In ZF precoding, the unit-norm BF vector h for the k-th user (denoted as v ¯k ) is chosen to be orthogonal to the bH channel vectors of all other selected users, i.e., h ¯k = 0 , j 6= k. j v b i.e. If W is the pseudo-inverse of H,  −1 bH H bH bH W=H , (5) ¯ = [¯ then the precoding matrix V v1 v ¯2 · · · v ¯K ] can be obtained from W by normalizing all of its columns. The channel for user k can be bk + h e k where the entries of the error term h ek decomposed as hk = h are modeled as i.i.d. Gaussian with zero mean and variance σh2 . If u represents the vector of Gaussian information symbols (uk intended ¯ and the signal for user k), the transmitted signal x becomes x = Vu received by the k-th selected user (4) can be expressed as follows: yk

= = = =

¯ hH k Vu + nk P ¯j uj + nk hH ¯k uk + j6=k hH k v k v P H bH e e H ¯j uj + nk h v ¯ u + h v ¯ u + k k k k k k j6=k hk v P K H H bk v ek v h ¯k uk + j=1 h ¯j uj + nk .

(6)

eH The rate lower bound comes from relegating the signal part h ¯ k uk k v into the interference and by treating all the interference terms as additional independent Gaussian noise.The SINR of the k-th user can be written as bH bHv p|h ¯ k |2 p|h ¯ k |2 k v Xk (7) SINRk = = H 2 1 + pKσh2 ek v 1+p E e |h ¯j | hk

j∈S

P in the case of uniform power control. This leads to where p = K the sum rate lower bound ! K P bH X ¯ k |2 |hk v P K SRLB = EH = RZF (K, nt , ). b log 1+ 1 + P σh2 1+P σh2 k=1 (8)

3.4. Location based SDMA: ZF BF sum rate Although some extension to the more general NADA case could probably be considered, we shall focus here on the LOS case. So

jψk hH hTt (φk ) k = γk e

(9)

where ht (.) is the (unit norm) BS antenna array response, φk is the AoD for user k, which in the LOS case can be computed from the user’s position, γk > 0 is a complex attenuation factor, and ψk is a phase that is unimportant for transmitter considerations. There are a variety of ways in which the information of γk can be obtained: • User feedback of just the scalar γk .

• Infer γk from the uplink. Not only in TDD but even in FDD, in the case of a LOS channel, the channel gain should be reciprocal (because there is no frequency-dependent superposition of multipath contributions). • Determine the attenuation from the position and simple (e.g. free space (LOS!)) propagation laws. 3.4.1. Effect of LOS deviation on ZF BF sum rate In this case we can model the user’s channels as jψk eH hTt (φk ) + h hH k k = γk e

(10)

e k could in a first instance be modeled as random with i.i.d. where h γ2 zero mean components with variance σh2 . The ratio n kσ2 could be t h considered as a Ricean factor. The reasoning leading to the sum rate LB (8) can be adapted to yield the following sum rate LB for location based ZF BF (for uniform transmit power over the set S of |S| selected users)   X 1 P 2 T 2 LBRice = E log 1 + γ |h (φ )¯ v | (11) k k k t 1 + P σh2 |S| k∈S

where the expectation is over the distribution of the φk and the γk . Hence 1 los LBRice = RZF (|S|, nt , P) (12) 1 + P σh2 where the perfect LOS case would be obtained by putting σh2 = 0. In contrast to the training based approach, here the performance increases with the number K of users to choose from as then they can be better chosen to have close to orthogonal antenna array responses (note that K should grow with SNR if sum rate saturation at high SNR is to be avoided). Another contrast to the training based approach in which σh2 is due to channel estimation error, in which case σh2 in (7) decreases with the UL SNR, here σh2 , which is now due to LOS approximation error, is independent of SNR. The result of this is that at high SNR the sum rate will saturate and the spatial multiplexing factor will be lost. This only happens though at SNR above which the interference resulting from channel approximation error dominates the noise, i.e. when P > σ12 . h

One remark is in order here about antenna spacing. For the purpose of DoA estimation, and considering a uniform linear array (ULA) of antennas, it is generally considered that an antenna spacing of λ/2 is good. However, for the purpose of SDMA, in which we would like the antenna array responses between different angles to be easily orthogonal, it is preferable that the antenna spacing is larger. Indeed, the larger the antenna spacing, the larger the number of angles within a sector for which the array response is orthogonal

to the array response at a given angle in the same sector. This multiplicity of ”orthogonal” angles on the other hand leads to ambiguities in the DoA estimation problem. In the case where the DoA is not estimated from received signal data but is computed on the basis of the position, these ambiguity problems are irrelevant and then antenna spacing should indeed be as large as possible (although not too large to invalidate the far field and narrowband assumptions). 3.4.2. Effect of position error on ZF BF sum rate

4. MULTI-CELL COMMUNICATIONS

Assume a (2D) position error ∆pk for user k, with mean square value σp2 = E k∆pk k2 (assuming also the position error to be isotropic). The position error will lead to a AoD error ∆pk √ ∆φk = (13) dk 2 √ where dk is the distance of user k from the BS, and 2 is not an exact representation but leads to the correct AoD error variance, accounting for the fact that AoD error only depends on the component of ∆pk orthogonal to the LOS direction. The AoD error will lead to an error in the steering vector, which for small AoD error we can approximate by a first order Taylor series expansion (similar to the NADA case) ht (φk + ∆φk ) ≈ ht (φk ) + ∆φk h˙ t (φk ) .

with BF done with knowledge (from location information) of the LOS components only, and on the other hand on quantized CSIT according to codebooks used in LTE. It can be concluded that the location based precoders are capable to achieve higher system capacity in most scenarios than a LTE system due to the limited codebook size (FB rate) in the LTE system. The capacity enhancement is significant already for a 2-user MISO system.

(14)

Paralleling the reasoning in the previous cases, we can obtain a ZF BF sum rate LB   T 2 P X γ |h (φ ) v ¯ | k k k t |S|   LBloc = E log 1 +  . σ2 P P 2 ˙ Tt (φk ) v ¯ | | h 1 + |S| γk 2 dp2 k∈S j j∈S k

(15) The effect of the position error is hence to reduce the SNR for user k by a factor σp2 X ˙ T P 1+ γk |ht (φk ) v ¯j |2 . (16) |S| 2 d2k j∈S 3.4.3. From MU MISO to MU MIMO Downlink

In MU MISO, all ZF has to be done by the Tx. In MU MIMO however, the ZF can be shared between Tx and Rx. All possible distributions of the ZF task between Tx and Rxs lead to many possible local optima of the sum rate at high SNR, hence providing potential for improved performance while complicating the task of TX/RX design. For a location-aided approach, with limited CSIT, consider restricting MU-MIMO to NADA users, and base the Tx design on the LOS components only. The interference due to angular spread around the LOS can then be handled by the multiple Rx antennas at the MT. In the NADA model, the MIMO channel is of rank two, hence the received signal lives in a two-dimensional subspace, which is independent of the BF design. Two Rx antennas are sufficient to allow the Rx to suppress all interference, regardless of the number of users. A further evolution would be to consider mixed CSIT [6], in which NADA users with location based CSIT get mixed with other users which have FB based CSIT. Another interesting recent development appears in [7] where blind ZF is proposed, interweaving PDP (or PDDP) polyphase components. 3.4.4. Comparative Simulations of Location based SDMA vs LTE Quantization-FB based SDMA In [8, Section6.5] one can find some comparative evaluations of sum rate for ZF BF, based on the one hand on a Ricean channel model

Whereas single cell designs are applicable even in a multi-cell context, for users in the interior of the cell, intercell interference needs to be considered for the cell edge users. In the single antenna case: the multi-cell aspect requires Tx power coordination, which can fairly easily be done location-aided (locations translate into distances and attenuations; databases could be used for further statistical characteristics (e.g. slow fading)). Multi-antenna techniques: require downlink channel knowledge, in principle of all channels at all transmitters (cells). Several approaches are possible, in increasing complexity: • single-cell Tx, multi-cell Rx: the BS perform single-cell Tx; inter-cell interference gets handled by the MT Rx antennas. The CSIT requirements remain local, per cell. In the LOS case, the MT needs to have a number of antennas at least equal to the number of cells (BS signals) to be handled (ZF). In the NADA case, the required number of antennas gets doubled. • multi-cell coordinated beamforming: also called the MISO or MIMO Interference Channel (IFC) in the case of one MT per cell. In the MISO case, the BSs need to ZF towards the users in other cells. In the MIMO case, this ZF can be shared between Txs and Rxs (interference alignment (IA)). The case of multiple MTs per cell, with interfering cells, is called the Interfering Broadcast Channel (IBC), or sometimes also simply the multi-cell problem. The IFC/IBC models are applicable also when the interfering cells correspond to heterogeneous systems (e.g. macro-femto coexistence). • network MIMO: also called Coordinated Multi-Point Tx (CoMP): requires not only global CSIT at all Txs (BSs) but furthermore distribution of all Tx signals over the BSs. Whenever we mention ZF BF above, this refers to the high SNR case, and could be replaced by optimized BF at finite SNR. Also BF could be replaced by DPC or other more optimal Tx techniques. 4.1. MIMO Interference Channel (IFC) The joint Tx/Rx design is plagued by numerous local optima. In [9], we proposed a deterministic annealing approach for guaranteeing the global optimum of the weighted sum rate (WSR). At high SNR, the optimum WSR design becomes ZF (IA), with typically many possible solutions due to the nonlinearity of the ZF conditions. Nevertheless, we may remark, as in [9], [10], that the ZF problem simplifies enormously in the LOS case. Indeed, let fi,n be the Rx spatial filter for stream n of user i and gk,m the Tx filter for stream m of BS k, and Hi,k the MIMO channel from BS k to MT i, then the ZF (IA) requirement for this particular cross link is fi,n Hi,k gk,m = 0. These ZF condistions need to be considered jointly for all cross links and hence they are coupled through the Tx and Rx filters. Stating the solutions for the filters analytically is impossible in general. However, consider the case in which all MIMO channels would be in LOS and hence of rank one: Hi,k = ui,k vH i,k . Then the ZF condition just considers becomes H fi,n ui,k vH i,k gk,m = 0 iff fi,n ui,k = 0 or vi,k gk,m = 0 . (17)

Hence, apart from the distribution of the ZF roles over Txs and Rxs, the design of the Tx and Rx filters becomes decoupled, and their design only requires knowledge of the channels connected to them (in general the design of a Tx or Rx filter in the MIMO IFC problem requires the knowledge of all channels appearing in the IFC). Furthermore, the factors ui,k depend only on the antenna array of BS k and the location of MT i. Hence the design of the Tx filters can be carried out on the basis of the location information of the various MTs. To go beyond LOS, the NADA and mixed CSIT cases could be considered. Another issue is the strength of the interfering links. In a ZF/IA approach, all link strengths are considered of equal order of magnitude, but in reality not all interfering links equally important. In [11], the concept of generalized degrees of freedom (gdof) is introduced. The dof are the prelog of user rates at high SNR. In a MIMO IFC, the dof of a link correspond to the number of streams for which ZF/IA is feasible. Those dof become gdof when one models the Interference to Noise Ratios (INRs) as evolving with the SNR to a certain power, e.g. smaller than one for the case of weak interference. Whereas such analysis may lead to qualitative insights into the relative effect of certain interference terms, the gdof results are quantitatively of limited use since in practice one needs to work at a finite SNR, at which one cannot unambiguously define α and β in a relation of the form INR = β SNRα . The problem is due to only considering exponents in asymptotic analysis. Analysis needs to evolve from gdof or tier 1 interferers only (a model introduced in [12] in which interferers beyond tier one are ignored for dof analysis) to location (distance & propagation) dependent interference strengths. 4.2. Femto Cells Femto cells are clearly a potentially important application for positioning: an operator needs to know (e.g. 911) the position of its BSs, including femto cells. Intercell Interference Coordination (ICIC) is part of LTE and has been shown to be greatly improved when exploiting location information, see [13, section 4]. ICIC is of crucial importance in the macro-femto coexistence. However, femtos are static, so all the time is available to perform communications based measurements of the attenuations of various links, so the relative advantage brought by location information is less clear. 4.3. Relays Relays are affected by resource allocation aspects in the form of relay and cell handover, cell-center to cell-edge transitions, association of (which and how many) relays etc. Position information can play a crucial role here to reduce handover dead times and significantly reduce handover hysteresis. The use of relays allows to overcome near-far effects to a large extent and minimize slow fading variations. Relays may hence constitute an essential ingredient in the recent and necessary tendency towards green wireless. However, since relays serve mainly users at the cell edge, intercell interference is going to be strong and needs to be dealt with. In any case, location information may be usefully exploited to shortcut heavy communication overhead required in the coordination of relay resource allocation. See [13, section 2] for examples of work in this direction. 5. COGNITIVE RADIO 5.1. Single Receive Antenna Case 5.1.1. Location Aided Underlay Cognitive Radio Underlay Cognitive Radio (CR) is a popular CR design problem, in which a secondary network is allowed to operate in the presence of a

primary system with interference limits at the primary Rxs, and this without any collaboration or even awareness of the primary system. To make underlay feasible, the exploitation of position information to determine attenuations constitutes probably the only realistic approach. In the MISO case, the location information could also be translated to Direction of Departure (DoD) based ZF BF. The cases of LOS and NADA need to be explored. 5.1.2. Weighted Sum Rate (WSR) Maximization in the Underlay Cognitive MISO IFC In [14] we study a CR MISO IFC with K secondary MISO BS-MT pairs and an additional set of L single-antenna Primary Users (PUs). This setting is relevant in the case of a network of two or more cognitive femto cells, that represent the secondary system, where each femtocell BS is serving a single user in the time-frequency unit of interest. The femto cells are deployed in the same area of a macro cell (primary system) and they want to coexist with L mobile users that belong to one or more macro cells. The picture is as in Fig. 1 except that the Rxs have only a single antenna and hence no receive filters. In [14] the objective is to find the set of BF vectors {gi } that maximize the WSR of the secondary IFC network, under Tx power constraints for the secondary BS, and interference level constraints at the primary Rxs. Unfortunately, this problem is non-convex. The proposed solution, which is an iterative algorithm based on augmenting the set of variables and performing alternating optimization, converges to a local optimum. Deterministic Annealing (DA) could be added as in [9] to find the global optimum. In [15] the alternative problem formulation of SINR balancing is considered. 5.2. Multi-Antenna Case 5.2.1. Multi-Antenna Cognitive Radio Paradigms The extension of a number of standard cognitive radio paradigms to the multi-antenna case is not as straightforward and unambiguous as it may seem at first. Here we propose some possible multi-antenna extensions for these paradigms. Spatial Overlay: MISO/MIMO Interference Channel In the overlay paradigm, primary and secondary collaborate. This collaboration could be interpreted at multiple levels, at the level of an exchange of Tx signals (as in network MIMO), or just at the level of CSIT, which in the single antenna case translates to coordinated power control. In the case of multiple antennas, if we limit cooperation to CSIT, this would lead to the exploitation of the multiple antennas for coordinated BF to achieve parallel interference-free channels. Coordinated BF applies to multiple antennas at the Tx side (MISO IFC). In the case of multiple antennas at the Rxs, we can have coordinated Rxss. The case of the coordination of the multiple antennas on both sides corresponds to the (noisy) MIMO IFC which was discussed earlier in the multi-cell setting. The recent Authorized Shared Access (ASA) proposal by Qualcomm and Nokia-Siemens Networks fits in the realm of overlay cognitive radio. Spatial Underlay: In the underlay paradigm, interference caused by a secondary Tx to a primary Rx is acceptable as long as the interference remains under a maximum tolerance level. One possible definition of spatial underlay then would be that the primary Rx equipped with multiple antennas allows primary interference as long as it has enough antennas to handle it. Hence the primary Rx needs to be active. So, the primary Rx allows an interference subspace of maximum dimension equal to the excess of its number of antennas over the number of primary streams it needs to receive. The primary system is secondary-aware.

Of course, the secondary Txs need to align the interference caused to primaries in subspaces of limited dimension. Spatial Interweave: In the interweave paradigm, the primary system should not be disturbed at all, and is not required to exhibit any cooperation with the secondary systems. So in a spatial interweave version, with multiple primary Rx antennas also, the secondary systems need to zero-force to all primary Rx antennas individually. In this case there is still room for secondary Tx if the secondary Txs have more antennas than the combined primary Rxs. The spatial interweave paradigm requires significant CSIT and can be reciprocity based in TDD, or location based in the case of LOS secondary-primary cross channels. In the LOS case, the number of primary Rx antennas becomes irrelevant (assuming they are in the far field from the secondary). In the case of NLOS, the secondary Tx needs to have more antennas than the number of propagation paths to all primary Rxs. 5.2.2. Spatial Interweave for a MIMO Secondary IFC with Multiple Primary Users Secondary System

1

1

1

...

F1

N1

M1

d1

...

G1

H11

...

...

1

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H1K

...

... Hk1 1

1

... MK

HK+LK

FK

NK

...

dK

1

GK

HKK HK+1K

...

...

1

dK

HK+L1 1 1

...

...

FK+1

NK+1

dK+1

HK+L1

... 1 1

...

...

FK+L

NK+L

dK+L

Primary System

Fig. 1. MIMO IFC spatial interweave.

This CR setting is depicted in Fig. 1. It can be used to model the coexistence of a set of K femto cells (MIMO IFC) in the presence of L primary macro-users (PRs). The objective considered in [16] is to design IA BF matrices at the secondary Txs such that the interference received at the primary Rxs is confined in a subspace of proper dimension. To solve this optimization problem we propose an iterative algorithm that is based on the reciprocity of IA. The proposed algorithm iterates between the downlink (DL) and its dual uplink (UL) problem, determining the Tx and Rx filters such that the leakage interference is minimized. In addition we propose a set of feasibility conditions for the combined primary and secondary IA. 6. REFERENCES [1] W. Zirwas and W. Mennerich, “Main Enablers for Advanced Interference Mitigation,” in Proc. IEEE Int’l Workshop on Multi-Carrier Systems & Solutions (MCSS), Herrsching, Germany, May 2011, EU FP7 Project Session 7: ARTIST4G LTE & LTE Advanced.

[2] D.T.M. Slock, “Signal Processing Challenges for Wireless Communications,” in Proc. IEEE Int’l Symp. on Control, Communications and Signal Processing (ISCCSP), Hammamet, Tunisia, March 2004. [3] M. Guillaud, D. Slock, and R. Knopp, “A Practical Method for Wireless Channel Reciprocity Exploitation Through Relative Calibration,” in Proc. IEEE Int’l Symp. on Signal Processing and its Applications (ISSPA), Sydney, Australia, Sept. 2005. [4] D. Astely and B. Ottersten, “The Effects of Local Scattering on Direction of Arrival Estimation with MUSIC,” IEEE Trans. on Signal Processing, Dec. 1999. [5] D.T.M. Slock and U. Salim, “How Much Feedback is Required for TDD Multi-Antenna Broadcast Channels with User Selection?,” EURASIP Journal on Advances in Signal Processing (JASP), vol. 2010. [6] Rizwan Ghaffar, Umer Salim, Irfan Ghauri, and Raymond Knopp, “Mixed CSIT DL Channel : Gains with Interference Aware Receivers,” in Proc. 17th European Wireless Conf. (EW), Vienna, Austria, April 2011. [7] H.C. Papadopoulos, S. Mukherjee, and S.A. Ramprashad, “Semi-Blind MU-MIMO based on Limited Features of the User Multi-Path Intensity Profiles,” in Proc. IEEE Information Theory and Applications workshop (ITA), La Jolla, CA, USA, Feb. 2011. [8] WHERE consortium, “Location Based Cross-Layer Optimisation for PHY/MAC: Final,” Deliverable D3.5, FP7 project ICT-217033 WHERE, 2010, http://www.kns.dlr.de/where/documents/Deliverable-D3.5.pdf. [9] Francesco Negro, Irfan Ghauri, and Dirk T M Slock, “Deterministic Annealing Design and Analysis of the Noisy MIMO Interference Channel,” in Proc. IEEE Information Theory and Applications workshop (ITA), La Jolla, CA, USA, Feb. 2011. ´ Gonz´alez and I. Santamar´ıa, “Interference Alignment in [10] O. Single-Beam MIMO Networks via Homotopy Continuation,” in Proc. IEEE Int’l Conf. on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic, May 2011. [11] R. Etkin, D.N.C. Tse, and H. Wang, “Gaussian Interference Channel Capacity to within one Bit,” IEEE Trans. on Information Theory, Dec. 2008. [12] M. Guillaud and D. Gesbert, “Interference Alignment in the Partially Connected K-user MIMO Interference Channel,” in Proc. European Signal Processing Conf. (EUSIPCO), Barcelona, Spain, Aug. 2011. [13] WHERE2 consortium, “Coordination and Cooperation between Network Nodes: Intermediate,” Deliverable D3.1, FP7-ICT-2009-4 project WHERE2, 2012, http://www.kns.dlr.de/where2/documents deliverables.php. [14] L. Gallo, F. Negro, I. Ghauri, and D.T.M. Slock, “Weighted Sum Rate Maximization in the Underlay Cognitive MISO Interference Channel,” in Proc. IEEE Int’l Symp. Personal Indoor and Mobile Radio Comm. (PIMRC), Sept. 2011. [15] F. Negro, M. Cardone, I. Ghauri, and D.T.M. Slock, “SINR Balancing and Beamforming for the MISO Interference Channel,” in Proc. IEEE Int’l Symp. Personal Indoor and Mobile Radio Communications (PIMRC), Sept. 2011. [16] F. Negro, I. Ghauri, and D.T.M. Slock, “Spatial Interweave for a MIMO Secondary Interference Channel with Multiple Primary Users,” in Proc. 4th Int’l Conf. Cognitive Radio and Advanced Spectrum Management (CogART), Oct. 2011.

MIMO Broadcast and Interference Channels with Location based Partial CSIT Dirk Slock‡ EURECOM Campus SophiaTech, 450 route des Chappes, 06410 Biot Sophia Antipolis, FRANCE Email: [email protected]

Abstract—Multiple antennas facilitate the coexistence of multiple users in wireless communications, leading to spatial multiplexing and spatial division and to significant system capacity increase. However, this comes at the cost of very precise channel state information at the transmitters (CSIT). We advocate the use of channel propagation models to transform location information into (possibly incomplete) CSIT. We investigate the resulting multi-user sum rate from a DoF (Degree of Freedom, high SNR rate prelog, spatial multiplexing factor) point of view. For singlecell multi-user communications, we argue for a revival of SDMA (Spatial Division Multiple Access). In the MIMO case, the receive antennas can suppress the Non Line of Sight (NLoS) channel components to transform the MIMO channel into a MISO LoS channel, allowing the CSIT to be limited to LoS information. For the multi-cell problem, we consider the feasibility of interference aligment in the case of reduced rank MIMO channels. We then focus on the LoS components. Whereas in general MIMO multicell coordinated beamforming, the transmitters require global CSIT due to the coupling between transmit and receive filters, in the LoS case decoupling arises, permitting location based transmit beamforming. We also discuss the transceiver design based on Partial LoS CSIT by essentially maximizing a weighted sum rate at finite SNR and finite Ricean factor.

I. I NTRODUCTION In TDD single-cell systems, channel reciprocity can turn CSIR (Receiver) into CSIT. In multi-cell systems however, TDD reciprocity is of limited interest as it only leads to only local CSIT. In FDD systems, CSIT needs to be acquired by feedback, which increases with the MIMO, multi-cell and Doppler dimensions. The problem is compounded when taking furthermore user selection into account. Wireless network based localization offers an alternative and/or complement to GNSS based localization. Satellite connectivity may pose problems in urban canyons and indoor, and not all mobile terminals (MTs) are GNSS equipped. Wireless network based localization is now part of LTE-A, based on the following techniques: Enhanced Cell Id = Cell Id + RSS (Received Signal Strength), O-TDoA (Observed Time Difference of Arrival), and AoA (Angle of Arrival at the base station (BS)). The availability of location information offers in turn opportunities to enhance the wireless communications. The position ‡ EURECOM’s research is partially supported by its industrial members: ORANGE, BMW Group, Swisscom, SFR, ST Microelectronics, Symantec, SAP, Monaco Telecom, iABG, and also by the EU FP7 projects WHERE2 and NEWCOM#.

based information that can be exploited comprises slow fading channel characteristics of various links: • LOS/NLOS ((Non) Line of Sight) • attenuation • delay spread, frequency selectivity • angular spreads, MIMO channel characteristics (rank) • speed, direction of movement, acceleration (predictibility of movement), trajectory Some of these aspects may require the use of databases (containing these characteristics as a function of position), compatible with a cognitive radio setting. Compared to feedback (FB) based approaches: some of these characteristics can not easily be determined from isolated channel estimates, or not predicted at all (e.g. slow fading prediction). What can not be inferred on the basis of position (as generally believed) is the fast fading state, the instantaneous complex channel impulse response. In what follows, we consider a number of problem formulations in which fast fading state information can essentially be avoided. In this paper, Tx may denote transmit/transmitter/transmission and Rx may denote receive/receiver/reception. II. P ROPAGATION C HANNEL M ODEL

Fig. 1.

MIMO transmission with M transmit and N receive antennas.

A. Specular Wireless MIMO Channel Model Consider a MIMO transmission configuration as depicted in Fig. 1. We get for the matrix impulse response of the timevarying channel h(t, τ ) [1] h(t, τ ) =

Np X i=1

Ai (t) ej2π fi t hr (φi ) hH t (θi ) p(τ − τi ) .

(1)

The channel impulse response h has per path a rank 1 contribution in 4 dimensions (Tx and Rx spatial multi-antenna dimensions, delay spread and Doppler spread); there are Np pathwise contributions where •

•

• • •

•

•

Ai : complex attenuation fi : Doppler shift θi : direction of departure (AoD) φi : direction of arrival (AoA) τi : path delay (ToA) h∗t (.), hr (.): M/N × 1 Tx/Rx antenna array response p(.): pulse shape (Tx filter)

The fast variation of the phase in ej2π fi t and possibly the variation of the Ai (when the nominal path represents in fact a superposition of paths with similar parameters) correspond to the fast fading. All the other parameters (including the Doppler frequency) vary on a slower time scale and correspond to slow fading. We shall assume here OFDM transmission, as is typical for 4G systems, with the Doppler variation over the OFDM symbol duration being negligible. We then get for the channel transfer matrix at any particular subcarrier of a given OFDM symbol H=

Np X

Ai hr (φi ) hH t (θi )

(2)

i=1

where with some abuse of notation we use the same complex amplitude Ai in which we ignored the dependence on time (particular OFDM symbol), through at least the Doppler shift, and on frequency (subcarrier), through the Tx (and Rx) filter(s). B. Narrow AoD Aperture (NADA) case The idea here is to focus on the category of mobiles for which the angular spread seen from the BS is limited [2]. This is a small generalization of the LoS case. In the NADA case, the MIMO channel H is of the form h i X H ˙ t (θ) . H= Ai hr (φi )hH (θ ) ≈ B A , A = h (θ) h i t t i

In the case of narrow AoD spread, we have θi = θ + ∆θi

(3)

(4)

where θ is the nominal (LoS) AoD and ∆θi is small. Hence ht (θi ) ≈ ht (θ) + ∆θi h˙ t (θ) .

(5)

This leads to the second equality in (3). Hence H is of rank 2 (regardless of the AoA spread). The LOS case is a limiting case in which the power of the h˙ t (θ) term becomes negligible and the channel rank becomes 1. The factor A in H depends straightforwardly on position (which translates into LOS AoD), only B (which depends on the Ai hr (φi ) and the ∆θi ) remains random.

C. Partial CSIT LoS Channel Model Assuming the Tx disposes of not much more than the LoS component information, we shall consider the following MIMO channel model e H = hr hH t (θ) + H

(6)

where θ is the LoS AoD and the Tx side array response is normalized: ||ht (θ)||2 = 1. Since the orientation of the MT is random, and the LoS case can be considered as a limiting NADA case in which a multitude of AoAs could appear, we shall model the Rx side LoS array response hr as a vector of i.i.d. complex Gaussian variables µ ) and hr i.i.d. ∼ CN (0, µ+1 1 1 e i.i.d. ∼ CN (0, H µ+1 M ) , independent of hr ,

(7)

e represents the aggregate NLoS compowhere the matrix H nents. Note that E||H||2F = Etr{HH H} =

||ht (θ)||2 E||hr ||2 + E||H||2F =

µN µ+1

+

N µ+1

=N,

(8)

reflecting that Rx power augments proportionally with N , and ( E||hr hTt (θ)||2F )/( E||H||2F ) = µ which can be considered as a Rice factor. In fact the only parameter additional to the LoS AoD θ assumed in (6) is µ. III. S INGLE -C ELL M ULTI -U SER C OMMUNICATIONS In this section, we shall focus on the downlink (DL) of Spatial Division Multiple Access (SDMA) problem, which in Information Theory is called the Broadcast Channel (BC). The SDMA terminology dates from the early nineties. These days it is referred to as the multi-user MISO (or MIMO) communications problem. A. Location Based SDMA The MISO case was treated in [3], where we proposed that location based MU MIMO transmission involve position based user selection (attenuation, nominal AoD, AoD spread) and associated beamforming (BF) and power control (PC). For the location aided MISO case, we need to essentially consider users with LoS channels. The effect of location error or of weak multipath on the resulting sum rate was also investigated. In the MIMO BC case, the multiple Rx antennas at the MTs cannot help to augment the totale number of streams, which are limited by the number of BS antennas. They allow to vary the number of streams per user though and thus to combine SU MIMO with MU MIMO. In the case of partial CSIT (as in LTE-A), it may seem beneficial to augment the number of streams per user. This is because in comparison the CSIR can be considered as as good as perfect (semi-blind channel estimation can be performed at the Rx). This means that at least the interference due to CSIT imperfections coming from other streams of the same user can be handled by the Rx, in effect reducing the number of undecoded interfering streams. Ignoring CSIT imperfections, on the basis of diversity considerations it may be beneficial to have some MIMO aspect

per user (to distribute the Zero-Forcing (ZF) or Minimum Mean Squared Error (MMSE) task between Tx and Rx) in case of a rich channel model [4], whereas in the perhaps more realistic case of poorer multipath a single stream per user is to be preferred [5]. The effect of user selection may play a role also. In the context of location aided, we shall consider good but incomplete CSIT. As a result, it may be beneficial to focus on the case of a single stream per user. B. MIMO BC with Incomplete CSIT The concept of incomplete CSIT was considered in [6] for the MIMO IC with a single stream per link. What is shown in [6] is that in the MIMO IC case, ZF may be possible with less than global CSIT. However, this only occurs for cases of very non-uniform antenna numbers over the Txs and Rxs. Incomplete CSIT differs from partial CSIT, which usually means that the Tx has a noisy (possibly quantized) version of the channel. In incomplete CSIT, the knowledge is (close to) perfect, but only of part of the channel (with the rest being unknown). Consider MIMO BC with a single stream per user. We shall show that it is sufficient for ZF BF (and hence for DoF) that the BS knows for each user a vector in the row span of its MIMO channel. Let Hk be the N × M MIMO channel of user k and let ck Hk be the equivalent MISO channel that the BS is aware of for user k, where ck is a 1 × N vector (the number of receive antennas can vary with user but we shall keep the notation as N ). For ZF BF, the BS shall use for user k a spatial filter gk such that ⊥ ⊥ /||ck Hk P(cH) || gkH = ck Hk P(cH) k k

(9)

⊥ where PX = I − PX and PX = XH (XXH )−1 X are projection matrices and (cH)k denotes the stacking of ci Hi for users i = 1, . . . , M, i 6= k. The N × 1 received signal at user k is

yk = Hk gk xk +

M X

Hk gi xi + vk

(10)

i=1,6=k

where xi is the signal intended for user i, and vk is additive noise. For the reception, user k shall use a linear filter fk with corresponding Signal-to-Interference Ratio (SIR) (for ZF and DoF considerations) SIRk = PM

|fk Hk gk |2 σk2

i=1,6=k

|fk Hk gi |2 σi2

(11)

where σi2 is the power of xi . Maximizing SIRk w.r.t. fk leads to fk ∼ ck if Hk is full row rank (and to fk Hk ∼ ck Hk otherwise) with maximum SIR max SIRk = SIRk (fk = ck ) = ∞ fk

(12)

since the interference power becomes zero. This leads to: Theorem 1: Sufficiency of Incomplete CSIT for Full DoF in MIMO BC In the MIMO BC with perfect CSIR, it is sufficient that the BS knows for each of the K users any vector in the row space of its MIMO channel (as long as the resulting

vectors are linearly independent) in order for ZF BF to produce min(M, K) DoF. C. Location Based MU-MIMO Consider now a propagation channel model as in (2), combined with the NADA model, in which a cluster of paths contributes the equivalent of two paths. Counting paths in this way, assume that the total number Np 0 of equivalent paths satisfies Np 0 ≤ N (again, the number of Rx antennas could be variable with user but we shall omit this notation). Assume one of the paths is the LoS path which is known by the BS (location aided). The situation that arises now is similar to chip equalization in the 3G downlink: due to the synchronicity of the downlink, 3G systems use CDMA with orthogonal codes such that a simple correlator at the Rx would suffice to suppress all intracell interference. This ideal scenario is perturbed by the multipath propagation channel whose frequency-selectivity perturbs the orthogonality of the spreading codes. However, since in the downlink from the BS to a particular user all intracell signals pass through the same channel of that user, it suffices for the user to equalize that channel to restore the code orthogonality and to allow a correlator to suppress the interference. In SDMA, the temporal spreading of CDMA is replaced by spatial filtering at the BS. This spatial filtering gk is based on the hypothesis of a LoS channel. Hence, for the reception at the user through the LoS path, all interference will be supressed. But the interference arrives at the user through the multipath components. However, regardless of the beamforming employed at the BS, all interference received by user k passes through the same multipath components of the channel of that user. Now, if Np 0 ≤ N , the user can employ Rx spatial filtering fk to suppress all paths, except for the LoS path, so that fk Hk only contains the LoS path. Combined with the LoS based BF gk design, this allows to suppress all interference and hence to produce full DoF. For the previous reasoning to work, it would have been sufficient (in terms of DoF) that the Bs knows any vector in the row space of Hk , but clearly the LoS path is typically much stronger than the other paths. Hence the knowledge of the LoS path leads to better performance at finite SNR. When there is no LoS path, it suffices to use another path, preferably the strongest path. Whereas the LoS path can be computed on the basis of only the user position (and a calibrated antenna array), in case another (and hence single- or multi-bounce) path needs to be used, this will typically require a database containing the information of the AoD of the strongest path, as a function of the position of the user. When Np 0 > N , there is no guarantee that the LoS Tx antenna array response lies in the row space of the MIMO channel matrix. D. Location Based MU-MIMO: from ZF to BF design at finite SNR and Rice factor In the previous subsection we considered the attainable DoF with LoS CSIT, attained by ZF Tx BF design on the LoS components. Note in passing that in practical multipath

scenarios, even if only the interference passing through the LoS paths would be handled, this would already lead to a substantial SINR increase. Here we shall explore how to go beyond the asymptotics of high SNR and high Ricean factor: even if the Tx ignores the multipath and the Rx can handle it, it would be better to have a multipath aware Tx design. To this end, various intermediate forms of CSIT could be considered beyond the LoS knowledge only. Here we shall consider the perhaps simplest model, the partial CSIT LoS model of (6). Note that the Ricean factor µ satisfies uplink/downlink (UL/DL) reciprocity, even in a FDD system, and hence can easily be estimated. D.1. Perfect CSI Case So consider the signal Rx’d by user k in (10) where we shall now assume that the K ≤ M signal streams xi have unit 2 variance and the noise is white with vk ∼ CN (0, σv,k INk ) (for Nk Rx antennas). Consider as a starting point for the optimization the weighted sum rate (WSR) W SR = W SR(g) =

K X

uk ln

k=1

1 ek

(13)

where g represents the collection of BFs gk , the uk are rate weights, the ek = ek (g) are the Minimum Mean Squared Errors (MMSEs) 1 −1 H H −1 −1 = 1 + gkH HH k Rk Hk gk = (1 − gk Hk Rk Hk gk ) ek Rk = Rk + Hk gk gkH HH k P 2 Rk = i6=k Hk gi giH HH k + σv,k INk ) , (14) Rk , Rk are the total and interference plus noise Rx covariance matrices resp. and ek is the MMSE obtained at the output x bk = fkH yk of the optimal (MMSE) linear Rx fk , fk = R−1 k Hk gk .

(15)

For a general Rx filter fk we have the MSE

ek (fk , g) = (1 − fkH Hk gk )(1 − gkH HH k fk ) P H H H 2 + i6=k fk Hk gi gi Hk fk + σv,k ||fk ||2 = P H H H 2 2 1−fkH Hk gk −gkH HH k fk + i fk Hk gi gi Hk fk +σv,k ||fk || . (16) The W SR(g) is a non-convex and complicated function of g. In [7], [8], we introduced an augmented cost function, the Weighted Sum MSE, W SM SE(g, f , w) =

K X

k=1

uk (wk ek (fk , g) − ln wk ) + λ(

K X

k=1

||gk ||2 − P ) (17)

where λ is a Lagrange multiplier and P is the Tx power constraint. After optimizing over the aggregate auxiliary Rx filters f and weights w, we get the WSR back: min W SM SE(g, f , w) = −W SR(g) . f ,w

(18)

The advantage of the augmented cost function is however that alternating optimization for one of the three sets of quantities,

g, f , w, keeping the other two fixed, leads to solving simple quadratic or convex functions min W SM SE ⇒ wk = 1/ek wk X 2 −1 min W SM SE ⇒ fk = ( Hk gi giH HH Hk gk k +σv,k INk ) fk

i

min W SM SE ⇒ gk P −1 H H Hk fk uk wk gk = ( i ui wi HH i fi fi Hi +λIM ) (19) Indeed, after substituting (16) into (17), one can notice the UL/DL duality, leading to a duality between Tx and Rx filters and the optimal Tx filter gk in (19) is indeed of the form of a MMSE linear Rx for the dual UL in which λ plays the role of Rx noise variance. The optimal λ inP each iteration can be K found using a (bisection) line search on k=1 ||gk ||2 −P = 0 P H ∂W SM SE or as in [7], [8] by exploiting k gk = 0. ∂g∗ k

D.2. Partial CSIT Case

Now, so far we have assumed that the channel H is known. The scenario of interest however is that of perfect CSIR but partial LoS CSIT. Once the CSIT is imperfect, various optimization criteria could be considered, such as outage capacity. Here we shall consider the ergodic weighted sum rate EH W SR(g, H) = X −1 (20) EW SR(g) = EH uk ln(1 + gkH HH k Rk Hk gk ) k

where we now underlign the dependence of various quantities on H. The EWSR in (20) corresponds to perfect CSIR since the optimal Rx filters fk as a function of the aggregatePH have been substituted, namely W SR(g, H) = maxf k uk (− ln(ek (fk , g))). However, EW SR(g) is again difficult to maximize directly. As observed in [9], it appears much more attractive to consider EH ek (fk , g, H) since ek (fk , g, H) is quadratic in H. Hence in [9], the cost function optimized is EH W SM SE(g, f , w, H) where W SM SE(g, f , w, H) appears in (17). However, minf ,w EH W SM SE(g, f , w, H) ≥ EH minf ,w W SM SE(g, f , w, H) = −EW SR(g) .

(21) So now only a lower bound to the EWSR gets maximized, which corresponds in fact to the CSIR being equally partial as the CSIT. The EWSR gap can be reduced by following the optimization over the Tx filters gk with an optimization over the Rx filters fk for full CSIR, namely by taking the fk as in (15). D.3. Partial LoS CSIT Case Consider now the partial LoS CSIT case (6), namely Hk = µk 2 e hr,k hH t,k + Hk and introduce the variances σk = µk +1 for the 1 1 2 ek elements of hr,k and σ ek = µk +1 M for the elements of H (which may also reflect link attenuations). However, the problem in applying this approach to the partial LoS CSIT case (6) is that EHk = 0 and hence the first order terms fkH Hk gk in the last expression of (16) disappear,

making the minimization of EH ek (fk , g, H) meaningless. A solution to this problem can be find by reexamining the (fictitious) dual Rx problem to which the BF gk was the optimal Rx solution: P gkH yek = gkH HH ek + gkH ( i6=k HH fi x ei + vek ) iX k fk x H eH +g ( H f x e + HH ei + vek ) = gkH ht,k hH f x e k k k i fi x r,k k k k |{z} | {z } i6=k source zk | {z } noise interference (22) where the fictitious signals x ei have variance ui wi , Ee vk vekH = λIM , we integrate the random hH r,k into the source zk which e H fk x now has variance σk2 ||fk ||2 , and the multipath part H ek k is counted in the interference. This dual Rx problem leads to the SINR H 2 2 ] k = |gk ht,k | σk αk , αi = ui wi ||fi ||2 SINR e k gk gkH R K X X e k = (λ + R σ ei2 αi )IM + σi2 αi ht,i hH t,i i=1 i6=k

(23)

with maximizing solution

e −1 ht,k . gk = R k

(24)

This Tx filter solution only depends on the Rx filters through the ||fk ||2 . In order to determine these (approximately), cone sider the MSE in a first instance only averaged over the H, minfk EH e (f , g, H) (where E {.}), leading {.} = E e k k e H|hr H to !−1 K X H 2 H 2 2 2 ei ||gi || I fk = σv,k I + {|ht,i gi | hr,i hr,i + σ hr,k hH t,k gk i=1

(25)

We then can obtain

2 2 −2 ||fk ||2 ≈ Ehr ||fk ||2 ≈ |hH } t,k gk | σk Ehr tr{(.) H 2 2 −2 ≈ |ht,k gk | σk tr{( Ehr .) } σ 2 |hH gk |2 Nk P k2 t,k = 2 2 (σv,k + i (σi |hH ei2 ||gi ||2 ))2 t,i gi | + σ

(26)

and similarly using (19), (14) wk ≈

1−

2 + σv,k

P

2 σk2 |hH t,k gk | Nk

2 H 2 i (σi |ht,i gi |

+σ ei2 ||gi ||2 )

!−1

(27)

2 which depend on the gk through ||gk ||2 and |hH t,i gi | . The solution for the Tx filters gk requires alternating between solving for the gk from (24), (23), with PKadjustment of the Lagrange multiplier λ by line search for k=1 ||gk ||2 −P = 0, and solving for the ||fk ||2 , wk from (26), (27). ek In the case of high Ricean factor and high SNR, R ] in the denominator of SINRk is dominated by the term P 2 2 H ] i6=k σi ||fi || ht,i ht,i and hence the SINRk gets maximized H by enforcing ht,i gk = 0, i 6= k which is the ZF of the LoS components considered earlier. Again, in the end the Rxs use the full CSIR solutions (15).

IV. MIMO I NTERFERENCE C HANNEL (IC) A. IA feasibility singular MIMO IC This subject was treated by [10] for the general K = 2 user case and for certain symmetric cases with K = 3. Related work also appears in [11] where for the case of no relay (as considered here) only some bounds were provided. Interference Alignment (IA) is joint Tx/Rx ZF BF and allows to attain the correct DoF in an IC. For dk streams of user k, a Mk × dk Tx filter Gk and a dk × Nk Rx filter Fk is used. In the rank deficient case, if 0 ≤ rik ≤ min(Ni , Mk ) denotes the rank of MIMO channel Hik then we can factor Hik = Bik Aik for some full rank Ni × rik Bik and rik × Mk Aik . The ZF from BS k to MT i requires Fi Hik Gk = Fi Bik Aik Gk = 0

(28)

which involves min(di dk , di rik , rik dk ) constraints to be satisfied by the (Ni − di )di /(Mk − dk )dk variables parameterizing the row/column subspaces of Fi /Gk . The overall IA feasibility gets determined by verifying whether the system is proper [6]: for each subset of MTs and subset of BSs, the total number of Tx/Rx variables involved needs to be at least equal to the total number of constraints in the corresponding conditions (28). When the rank constraints are active (number of constraints involves rik ), counting the # of variables vs. the # of ZF constraints gives the complete answer since we have traditional (one-sided) Tx or Rx ZF (Fi Bik = 0 or Aik Gk = 0). When the rank constraints are not active (min attained for di dk ) then counting arguments may not be sufficient in very rectangular (non-square) MIMO channel cases [12], [13]. Note also that the full rank requirement on Fk Hkk Gk leads to 1 ≤ dk ≤ rkk ≤ min(Nk , Mk ) (the first inequality reflects that we consider only active links). Consider now some examples that were also considered in [10]. In the full rank case with K links of N × M , we have +N that dk = M K+1 is feasible in the not too rectangular case. In the uniform singular K = 2 case with (M, N, r)2 , d = M +N −r ) is possible (with d1 = d2 = d). For the min(r, 2 uniform square K = 3 case (M, M, r)3 , d = min(r, M/2) is feasible. Still in the K = 3, M × M case with   r0 , i = k r1 , i > k rik = (29)  r2 , i < k min(M, r1 + r2 ) ). 2 B. IA feasibility singular MIMO IC with Tx/Rx decoupling we get d = min(r0 , M −

In this case we shall insist that (28) be satisfied by Fi Bik = 0 or Aik Gk = 0 .

(30)

This leads to a possibly increased number of ZF constraints rik min(di , dk ) and hence to possibly reduced IA feasibility. Of course, the task of ZF of every cross link now needs to be partitioned between all Txs and Rxs, taking into account the limited number of variables each Tx or Rx has. The main goal

of this approach however is that it leads to Tx/Rx decoupling. Whereas in the general case (28) the design of the Txs depends on the Rxs and vice versa, in (30) the ZF constraints are linear and involve Tx or Rx but not both. The ZF constraints for a Tx (or a Rx) only require local channel knowledge (of the channel connected to it). Of course, the gobal ZF task partitioning needs to be known. This leads to a category of IA feasibility with incomplete CSIT, different from the one appearing in [6] as described earlier. In the uniform case (M, N, r)K with d ≤ r per user, (30) leads to 1 (31) d ≤ (M + N − (K − 1)r) 2 whereas the general coupled case (28) would have led to d ≤ 1 2 (M + N − (K − 1)d). There is no loss if d = r, in which +N case d = r ≤ M K+1 . In the case of general rank distribution but with a single stream per user (dk ≡ 1), we get K X X (Mk + Nk ) ≥ 2K + rik . i=1

(32)

i6=k

The non-decoupled case would correspond to replacing all the rik in (32) by 1. C. LoS Case In what follows, we shall focus on the LoS limit for considerations of location based processing. This is a special case of (31) with d = r = 1 and leads to the requirement M +N ≥K +1

(33)

for IA feasibility with a single stream per user. In the MISO or SIMO cases this becomes M ≥ K or N ≥ K. The meaning of (33) is: (M − 1) + (N − 1) ≥ K − 1: that each BS performs ZF towards M − 1 MTs. As a result, each MT still receives interference from (K − 1) − (M − 1) cross links but with its N antennas it can ZF N − 1 streams. In the decoupled approach, the design of any Tx gk only depends on the factors Aik of the channels connected to it and in general even only on a subset of this local CSIT (e.g. in the LoS case, only M − 1 cross link Aik are required to be known for any given BS). In the LoS case, the Aik are clearly only a function of the positions of the BS and MTs (and the BS antenna array response). One can go somewhat beyond the LoS case by considering (LoS) NADA and other multipath components. The number of components (and hence the rik ) to be considered could vary with the cross links. An issue that arises here is that different cross links may have multipath components with the same AoD from a certain BS, because the paths may bounce on the same scatterer. In this case the multiple paths get ZF’d simultaneously, leading to a reduction in required Tx antennas.

D. BF Design in the Finite SNR and Rice Factor Case with Partial LoS CSIT In the case of a centralized design, the approach of subsection III.D.3 can be followed with a few minor modifications: the channels Hik now have two indices, and now there is a Tx power constraint per BS leading to ||gk ||2 = Pk (with associated Lagrange multiplier λk ). As a result the LoS and 2 2 NLoS variances σik and σ eik now also have two indices, and they should not only reflect the Ricean factors µik but also link attenuations. Consider now the case of a decoupled Tx/Rx design, which should be based on Local Partial LoS CSIT only. In the dual UL (22), the LoS components of only M − 1 cross links should be accounted for, namely the ones that the particular BS considered is supposed to reduce its interference over. For the K − M other cross links, the LoS component can be 2 handled like a NLoS component, with the σik absorbed in 2 the corresponding σ eik . This means that the number of terms e in (23) shrinks from K −1 to M −1. For in the last sum for R the determination of the ||fk ||2 , wk from (26), (27), a number of assumptions will need to be made on the values for the Pi , 2 2 2 ,σ eik and σv,k involved. In any case, we can take for sure σik 2 ||gi || = Pi and assuming an isotropic distribution of the gi 2 compared to the ht,i , we can set |hH t,i gi | = Pi /M . R EFERENCES [1] D. Shutin and B. Fleury, “Sparse Variational Bayesian SAGE Algorithm With Application to the Estimation of Multipath Wireless Channels,” IEEE Trans. on Signal Proc., Aug. 2011. [2] D. Astely and B. Ottersten, “The Effects of Local Scattering on Direction of Arrival Estimation with MUSIC,” IEEE Trans. on Signal Processing, Dec. 1999. [3] D. Slock, “Location Aided Wireless Communications,” in Proc. IEEE Int’l Symp. on Control, Comm’s and Signal Proc. (ISCCSP), Rome, Italy, May 2012. [4] Y. Lejosne, D. Slock, and Y. Yuan Wu, “User Selection in the MIMO BC,” in European Signal Proc. Conf. (EUSIPCO), Bucharest, Romania, Aug. 2012. [5] E. Bj¨ornson, M. Kountouris, M. Bengtsson, and B. Ottersten, “Receive Combining vs. Multistream Multiplexing in Downlink Systems with Multi-Antenna Users,” IEEE Trans. on Signal Proc., subm., 2012, arxiv1207.2776v1. [6] P. de Kerret and D. Gesbert, “Interference Alignment with Incomplete CSIT Sharing,” Nov. 2012, arxiv1211.5380. [7] F. Negro, S. Shenoy, I. Ghauri, and D. Slock, “On the MIMO Interference Channel,” in Information Theory and Applications Workshop (ITA), Feb. 2010. [8] F. Negro, I. Ghauri, and D. Slock, “Deterministic Annealing Design and Analysis of the Noisy MIMO Interference Channel,” in IEEE Information Theory and Applications Workshop (ITA), San Diego, CA, USA, Feb. 2011. [9] F. Negro, I. Ghauri, and D. Slock, “Sum Rate Maximization in the Noisy MIMO Interfering Broadcast Channel with Partial CSIT via the Expected Weighted MSE,” in IEEE Int’l Symp. on Wireless Commun. Systems (ISWCS), Paris, France, Aug. 2012. [10] S. Krishnamurthy and S. Jafar, “Degrees of Freedom of 2-user and 3-user Rank-Deficient MIMO Interference Channels,” in Proc. IEEE Globecom, Dec. 2012. [11] S. Chae, S.-W. Jeon, and S.-Y. Chung, “Cooperative Relaying for the Rank-Deficient MIMO Relay Interference Channel,” IEEE Communications Letters, Jan. 2012. [12] G. Bresler, D. Cartwright, and D. Tse, “Geometry of the 3-User MIMO Interference Channel,” in Proc. Allerton Conf., Sept. 2011. [13] ——, “Feasibility of Interference Alignment for the MIMO Interference Channel: the Symmetric Square Case,” in Proc. Information Theory Workshop (ITW), 2011.

DEGREES OF FREEDOM OF DOWNLINK SINGLE- AND MULTI-CELL MULTI-USER MIMO SYSTEMS WITH LOCATION BASED CSIT Wa¨el Guibene and Dirk Slock EURECOM Campus SophiaTech, 450 route des Chappes, 06410 Biot Sophia Antipolis, FRANCE Email: {guibene,slock}@eurecom.fr ABSTRACT Multiple antennas facilitate the coexistence of multiple users in wireless communications, leading to spatial multiplexing and spatial division and to significant system capacity increase. However, this comes at the cost of very precise channel state information at the transmitters (CSIT). We advocate the use of channel propagation models to transform location information into (possibly incomplete) CSIT. We investigate the resulting multi-user sum rate from a DoF (Degree of Freedom, high SNR rate prelog, spatial multiplexing factor) point of view. For single-cell multiuser communications, we argue for a revival of SDMA (Spatial Division Multiple Access). In the MIMO case, the receive antennas can suppress the Non Line of Sight (NLoS) channel components to transform the MIMO channel into a MISO LoS channel, allowing the CSIT to be limited to LoS information. For the multi-cell problem, we consider the feasibility of interference aligment in the case of reduced rank MIMO channels. We then focus on the LoS components. Whereas in general MIMO multi-cell coordinated beamforming, the transmitters require global CSIT due to the coupling between transmit and receive filters, in the LoS case decoupling arises, permitting location based transmit beamforming. Location aided techniques may furthermore exploit location prediction through mobility trajectory information. This would allow slow fading (and even connectivity) predictibility, something that is difficult to achieve without location information.

Strength), O-TDoA (Observed Time Difference of Arrival), and AoA (Angle of Arrival at the base station (BS)). The availability of location information offers in turn opportunities to enhance the wireless communications. The position based information that can be exploited comprises slow fading channel characteristics of various links:

Index Terms— Wireless communications, location, SDMA, MIMO, multi-user, multi-cell.

II. PROPAGATION CHANNEL MODEL

• • • • •

LOS/NLOS ((Non) Line of Sight) attenuation delay spread, frequency selectivity angular spreads, MIMO channel characteristics (rank) speed, direction of movement, acceleration (predictibility of movement), trajectory

Some of these aspects may require the use of databases (containing these characteristics as a function of position), compatible with a cognitive radio setting. Compared to feedback (FB) based approaches: some of these characteristics can not easily be determined from isolated channel estimates, or not predicted at all (e.g. slow fading prediction). What can not be inferred on the basis of position (as generally believed) is the fast fading state, the instantaneous complex channel impulse response. In what follows, we consider a number of problem formulations in which fast fading state information can essentially be avoided. In this paper, Tx may denote transmit/transmitter/transmission and Rx may denote receive/receiver/reception.

I. INTRODUCTION In TDD single-cell systems, channel reciprocity can turn CSIR (Receiver) into CSIT. In multi-cell systems however, TDD reciprocity is of limited interest as it only leads to only local CSIT. In FDD systems, CSIT needs to be acquired by feedback, which increases with the MIMO, multi-cell and Doppler dimensions. The problem is compounded when taking furthermore user selection into account. Wireless network based localization offers an alternative and/or complement to GNSS based localization. Satellite connectivity may pose problems in urban canyons and indoor, and not all mobile terminals (MTs) are GNSS equipped. Wireless network based localization is now part of LTE-A, based on the following techniques: Enhanced Cell Id = Cell Id + RSS (Received Signal EURECOM’s research is partially supported by its industrial members: ORANGE, BMW Group, Swisscom, SFR, ST Microelectronics, Symantec, SAP, Monaco Telecom, iABG, and also by the EU FP7 projects SACRA and WHERE2.

Fig. 1. MIMO transmission with M transmit and N receive antennas.

II-A. Specular Wireless MIMO Channel Model Consider a MIMO transmission configuration as depicted in Fig. 1. We get for the matrix impulse response of the time-varying

channel h(t, τ ) [1] h(t, τ ) =

Np  i=1

III. LOCATION AIDED MULTI-USER RESOURCE ALLOCATION

Ai (t) ej2π fi t hr (φi ) hTt (θi ) p(τ − τi ) .

(1)

The channel impulse response h has per path a rank 1 contribution in 4 dimensions (Tx and Rx spatial multi-antenna dimensions, delay spread and Doppler spread); there are Np pathwise contributions where • • • • • • •

Ai : complex attenuation fi : Doppler shift θi : direction of departure (AoD) φi : direction of arrival (AoA) τi : path delay (ToA) ht (.), hr (.): M/N × 1 Tx/Rx antenna array response p(.): pulse shape (Tx filter)

The fast variation of the phase in ej2π fi t and possibly the variation of the Ai (when the nominal path represents in fact a superposition of paths with similar parameters) correspond to the fast fading. All the other parameters (including the Doppler frequency) vary on a slower time scale and correspond to slow fading. We shall assume here OFDM transmission, as is typical for 4G systems, with the Doppler variation over the OFDM symbol duration being negligible. We then get for the channel transfer matrix at any particular subcarrier of a given OFDM symbol H=

Np 

Ai hr (φi ) hTt (θi )

Some possibilities are: Multi-user MIMO (MU MIMO): Use environment information to preselect users, to limit channel feedback to a reduced set of preselected users. The user preselection can e.g. involve: users with similar attenuation, users with rank 1 MIMO channels (close to LOS), ... MU-MIMO is in the context of a single cell, and the DL problem is referred to in information theory as the Broadcast Channel (BC). • Multicell aspects (interference coordination) or for Cognitive Radio (interference from secondary to primary systems): the interference level can be predicted from position information. The multi-cell DL problem is referred to in Information Theory as the Interference Channel (IC). In the IC, each Tx has a signal at the intention of one corresponding Rx, in contrast to the Network MIMO (NW MIMO) or Coordinated Multi-Point (CoMP) in which all Txs possess the signals at the intention of all the Rxs. Hence NW MIMO is a form of MU MIMO with distributed Txs. The use of linear Txs in MIMO/MISO IC is also referred to as Coordinated Beamforming (BF). A transversal aspect is also that location tracking can lead to location prediction. This leads in turn to slow fading predictibility (and not just fast fading prediction, which can in principle be done also from past channel response estimates). Another aspect is that user selection (multi-user diversity) potentially leads to an explosion of CSIT requirements and associated overhead. Location based covariance CSIT might offer a (partial) solution. •

(2)

i=1

where with some abuse of notation we use the same complex amplitude Ai in which we ignored the dependence on time (particular OFDM symbol), through at least the Doppler shift, and on frequency (subcarrier), through the Tx (and Rx) filter(s). II-B. Narrow AoD Aperture (NADA) case The idea here is to focus on the category of mobiles for which the angular spread seen from the BS is limited [2]. This is a small generalization of the LoS case. In the NADA case, the MIMO channel H is of the form  T  Ai hr (φi )hTt (θi ) ≈ B A , A = ht (θ) h˙ t (θ) . H= i

(3)

In the case of narrow AoD spread, we have θi = θ + Δθi

(4)

where θ is the nominal (LoS) AoD and Δθi is small. Hence ht (θi ) ≈ ht (θ) + Δθi h˙ t (θ) .

(5)

This leads to the second equality in (3). Hence H is of rank 2 (regardless of the AoA spread). The LOS case is a limiting case in which the power of the h˙ t (θ) term becomes negligible and the channel rank becomes 1. The factor A in H depends straightforwardly on position (which translates into LOS AoD), only B (which depends on the Ai hr (φi ) and the Δθi ) remains random.

IV. SINGLE-CELL MULTI-USER COMMUNICATIONS In this section, we shall focus on the Spatial Division Multiple Access (SDMA) problem, which in Information Theory is called the Broadcast Channel (BC). The SDMA terminology dates from the early nineties. These days it is referred to as the multiuser MISO (or MIMO) communications problem, and we shall particularly focus on the more difficult downlink. IV-A. SDMA considerations Whereas single user (SU) MIMO communications represented a big breakthrough and are now integrated in a number of wireless communication standards, the next improvement is indeed multiuser MIMO (MU MIMO). This topic is nontrivial as e.g. illustrated by the fact that 3gpp had a lot of difficulty to get it included in the LTE standard. MU MIMO is a further evolution of SDMA, which was THE hot wireless topic in the early nineties. The MU MIMO area has now sufficiently evolved to allow us to understand the following key elements: • SDMA is a suboptimal approach to MU MIMO, with transmitter precoding limited to linear beamforming, whereas optimal MU MIMO requires Dirty Paper Coding (DPC). • Channel feedback (FB) has gained much more acceptance, leading to good CSIT, a crucial enabler for MU MIMO, whereas SDMA was either limited to TDD systems (channel CSIT through reciprocity) or Covariance CSIT. In the early nineties, the only feedback that existed was for slow power control. • Since SDMA, the concepts of multiuser diversity and user selection have emerged and their impact on the MU MIMO

•

•

sum rate is now well understood. Furthermore, it is now known that user scheduling allows much simpler precoding schemes (such as Zero-Forcing (ZF) beamforming (BF)) to be close to optimal. Whereas SU MIMO allows to multiply transmission rate by the spatial multiplexing factor, when mobile terminals have multiple antennas, MU MIMO allows to reach this same gain with single antenna terminals. Whereas in SU MIMO, various degrees of CSIT only lead to a variation in coding gain (the constant term in the sum rate), in MU MIMO however CSIT affects the spatial multiplexing factor (multiplying the log(SNR) term in the sum rate).

In the process attempting to integrate MU-MIMO into the LTEA standard, a number of LTE-A contributors had at some point become quite sceptical about the usefulness of the available MUMIMO proposals. The issue is that they consider MU-MIMO in the same spirit as SU-MIMO, i.e. with FB of CSI limited to just a few bits! However, MU-MIMO requires very good CSIT! Some possible solutions are: • • •

Increase CSI FB enormously (possibly using analog transmission); LTE-A went recently a bit in this direction. Exploit channel reciprocity in TDD (there may be an electronics calibration issue though [3]). Limit MU-MIMO (SDMA) to NADA users and extract essential CSIT from position information (or from DoA estimates - in both cases the knowledge of the antenna array manifold is (eventually) required).

IV-B. Location Based SDMA The MISO case was treated in [4], where we proposed that location based MU MIMO transmission involve position based user selection (attenuation, nominal AoD, AoD spread) and associated beamforming (BF) and power control (PC). For the location aided MISO case, we need to essentially consider users with LoS channels. The effect of location error or of weak multipath on the resulting sum rate was also investigated. In the MIMO BC case, the multiple Rx antennas at the MTs cannot help to augment the totale number of streams, which are limited by the number of BS antennas. They allow to vary the number of streams per user though and thus to combine SU MIMO with MU MIMO. In the case of partial CSIT (as in LTE-A), it may seem beneficial to augment the number of streams per user. This is because in comparison the CSIR can be considered as as good as perfect (semi-blind channel estimation can be performed at the Rx). This means that at least the interference due to CSIT imperfections coming from other streams of the same user can be handled by the Rx, in effect reducing the number of undecoded interfering streams. Ignoring CSIT imperfections, on the basis of diversity considerations it may be beneficial to have some MIMO aspect per user (to distribute the ZF/MMSE task between Tx and Rx) in case of a rich channel model [5], whereas in the perhaps more realistic case of poorer multipath a single stream per user is to be preferred [6]. The effect of user selection may play a role also. In the context of location aided, we shall consider good but incomplete CSIT. As a result, it may be beneficial to focus on the case of a single stream per user.

IV-C. MIMO BC with Incomplete CSIT The concept of incomplete CSIT was considered in [7] for the MIMO IC with a single stream per link. What is shown in [7] is that in the MIMO IC case, ZF may be possible with less than global CSIT. However, this only occurs for cases of very non-uniform antenna numbers over the Txs and Rxs. Incomplete CSIT differs from partial CSIT, which usually means that the Tx has a noisy (possibly quantized) version of the channel. In incomplete CSIT, the knowledge is (close to) perfect, but only of part of the channel (with the rest being unknown). Consider MIMO BC with a single stream per user. We shall show that it is sufficient for ZF BF (and hence for DoF) that the BS knows for each user a vector in the row span of its MIMO channel. Let Hk be the N × M MIMO channel of user k and let ck Hk be the equivalent MISO channel that the BS is aware of for user k, where ck is a 1 × N vector (the number of receive antennas can vary with user but we shall keep the notation as N ). For ZF BF, the BS shall use for user k a spatial filter gk such that ⊥ ⊥ gkH = ck Hk P(cH) /||ck Hk P(cH) || k k

(6)

⊥ = I − PX and PX = XH (XXH )−1 X are projection where PX matrices and (cH)k denotes the stacking of ci Hi for users i = 1, . . . , M, i = k. The N × 1 received signal at user k is

yk = Hk gk xk +

M 

Hk gi xi + vk

(7)

i=1,=k

where xi is the signal intended for user i, and vk is additive noise. For the reception, user k shall use a linear filter fk with corresponding Signal-to-Interference Ratio (SIR) (for ZF and DoF considerations) |fk Hk gk |2 σk2 2 2 i=1,=k |fk Hk gi | σi

SIRk = M

(8)

where σi2 is the power of xi . Maximizing SIRk w.r.t. fk leads to fk ∼ ck if Hk is full row rank (and to fk Hk ∼ ck Hk otherwise) with maximum SIR max SIRk = SIRk (fk = ck ) = ∞ fk

(9)

since the interference power becomes zero. This leads to: Theorem 1: Sufficiency of Incomplete CSIT for Full DoF in MIMO BC In the MIMO BC with perfect CSIR, it is sufficient that the BS knows for each of the K users any vector in the row space of its MIMO channel (as long as the resulting vectors are linearly independent) in order for ZF BF to produce min(M, K) DoF. IV-D. Location Based MU-MIMO Consider now a propagation channel model as in (2), combined with the NADA model, in which a cluster of paths contributes the equivalent of two paths. Counting paths in this way, assume that the total number Np  of equivalent paths satisfies Np  ≤ N (again, the number of Rx antennas could be variable with user but we shall omit this notation). Assume one of the paths is the LoS path which is known by the BS (location aided). The situation that arises now is similar to chip equalization in the 3G downlink: due to the synchronicity of the downlink, 3G systems use CDMA with orthogonal codes

such that a simple correlator at the Rx would suffice to suppress all intracell interference. This ideal scenario is perturbed by the multipath propagation channel whose frequency-selectivity perturbs the orthogonality of the spreading codes. However, since in the downlink from the BS to a particular user all intracell signals pass through the same channel of that user, it suffices for the user to equalize that channel to restore the code orthogonality and to allow a correlator to suppress the interference. In SDMA, the temporal spreading of CDMA is replaced by spatial filtering at the BS. This spatial filtering gk is based on the hypothesis of a LoS channel. Hence, for the reception at the user through the LoS path, all interference will be supressed. But the interference arrives at the user through the multipath components. However, regardless of the beamforming employed at the BS, all interference received by user k passes through the same multipath components of the channel of that user. Now, if Np  ≤ N , the user can employ Rx spatial filtering fk to suppress all paths, except for the LoS path, so that fk Hk only contains the LoS path. Combined with the LoS based BF gk design, this allows to suppress all interference and hence to produce full DoF. For the previous reasoning to work, it would have been sufficient (in terms of DoF) that the Bs knows any vector in the row space of Hk , but clearly the LoS path is typically much stronger than the other paths. Hence the knowledge of the LoS path leads to better performance at finite SNR. When there is no LoS path, it suffices to use another path, preferably the strongest path. Whereas the LoS path can be computed on the basis of only the user position (and a calibrated antenna array), in case another (and hence single- or multi-bounce) path needs to be used, this will typically require a database containing the information of the AoD of the strongest path, as a function of the position of the user. When Np  > N , there is no guarantee that the LOS Tx antenna array response lies in the row space of the MIMO channel matrix. Related work appears in [8], [9] where a not so rich propagation environment leads to subspaces (slow CSIT) for the channel vectors so that the fast CSIT can be reduced to the smaller dimension of the subspace. A further evolution would be to consider mixed CSIT [10], in which NADA users with location based CSIT get mixed with other users which have FB based CSIT. V. MIMO INTERFERENCE CHANNEL (IC) V-A. IA feasibility singular MIMO IC This subject was treated by [11] for the general K = 2 user case and for certain symmetric cases with K = 3. Related work also appears in [12] where for the case of no relay (as considered here) only some bounds were provided. Interference Alignment (IA) is joint Tx/Rx ZF BF and allows to attain the correct DoF in an IC. For dk streams of user k, a Mk × dk Tx filter Gk and a dk × Nk Rx filter Fk is used. In the rank deficient case, if 0 ≤ rik ≤ min(Ni , Mk ) denotes the rank of MIMO channel Hik then we can factor Hik = Bik Aik for some full rank Ni × rik Bik and rik × Mk Aik . The ZF from BS k to MT i requires Fi Hik Gk = Fi Bik Aik Gk = 0

(10)

which involves min(di dk , di rik , rik dk ) constraints to be satisfied by the (Ni − di )di /(Mk − dk )dk variables parameterizing the row/column subspaces of Fi /Gk . The overall IA feasibility gets

determined by verifying whether the system is proper [7]: for each subset of MTs and subset of BSs, the total number of Tx/Rx variables involved needs to be at least equal to the total number of constraints in the corresponding conditions (10). When the rank constraints are active (number of constraints involves rik ), counting the # of variables vs. the # of ZF constraints gives the complete answer since we have traditional (one-sided) Tx or Rx ZF (Fi Bik = 0 or Aik Gk = 0). When the rank constraints are not active (min attained for di dk ) then counting arguments may not be sufficient in very rectangular (non-square) MIMO channel cases [13], [14]. Note also that the full rank requirement on Fk Hkk Gk leads to 1 ≤ dk ≤ rkk ≤ min(Nk , Mk ) (the first inequality reflects that we consider only active links). Consider now some examples that were also considered in [11]. In the full rank case with K links of N × M , we have that dk = M +N is feasible in the not too rectangular case. In the uniform K+1 M +N −r ) singular K = 2 case with (M, N, r)2 , d = min(r, 2 is possible (with d1 = d2 = d). For the uniform square K = 3 case (M, M, r)3 , d = min(r, M/2) is feasible. Still in the K = 3, M × M case with ⎧ ⎨ r0 , i = k (11) rik = r1 , i > k ⎩ r2 , i < k we get d = min(r0 , M −

min(M, r1 + r2 ) ). 2

V-B. IA feasibility singular MIMO IC with Tx/Rx decoupling In this case we shall insist that (10) be satisfied by Fi Bik = 0 or Aik Gk = 0 .

(12)

This leads to a possibly increased number of ZF constraints rik min(di , dk ) and hence to possibly reduced IA feasibility. Of course, the task of ZF of every cross link now needs to be partitioned between all Txs and Rxs, taking into account the limited number of variables each Tx or Rx has. The main goal of this approach however is that it leads to Tx/Rx decoupling. Whereas in the general case (10) the design of the Txs depends on the Rxs and vice versa, in (12) the ZF constraints are linear and involve Tx or Rx but not both. The ZF constraints for a Tx (or a Rx) only require local channel knowledge (of the channel connected to it). Of course, the gobal ZF task partitioning needs to be known. This leads to a category of IA feasibility with incomplete CSIT, different from the one appearing in [7] as described earlier. In the uniform case (M, N, r)K with d ≤ r per user, (12) leads to 1 (13) d ≤ (M + N − (K − 1)r) 2 whereas the general coupled case (10) would have led to d ≤ 1 (M + N − (K − 1)d). There is no loss if d = r, in which case 2 +N . d=r≤ M K+1 In the case of general rank distribution but with a single stream per user (dk ≡ 1), we get K  i=1

(Mk + Nk ) ≥ 2K +



rik .

(14)

i=k

The non-decoupled case would correspond to replacing all the rik in (14) by 1.

V-C. LoS Case In what follows, we shall focus on the LoS limit for considerations of location based processing. This is a special case of (13) with d = r = 1 and leads to the requirement M +N ≥K+1

(15)

for IA feasibility with a single stream per user. In the MISO or SIMO cases this becomes M ≥ K or N ≥ K. The meaning of (15) is: (M − 1) + (N − 1) ≥ K − 1: that each BS performs ZF towards M −1 MTs. As a result, each MT still receives interference from (K − 1) − (M − 1) cross links but with its N antennas it can ZF N − 1 streams. In the decoupled approach, the design of any Tx Gk only depends on the factors Aik of the channels connected to it and in general even only on a subset of this local CSIT (e.g. in the LoS case, only M − 1 cross link Aik are required to be known for any given BS). In the LoS case, the Aik are clearly only a function of the positions of the BS and MTs (and the BS antenna array response). One can go somewhat beyond the LoS case by considering (LoS) NADA and other multipath components. The number of components (and hence the rik ) to be considered could vary with the cross links. An issue that arises here is that different cross links may have multipath components with the same AoD from a certain BS, because the paths may bounce on the same scatterer. In this case the multiple paths get ZF’d simultaneously, leading to a reduction in required Tx antennas. VI. FURTHER DIRECTIONS See [15] for location aided Tx/Rx design with partial CSIT. The location aided BF can be extended to 2D antenna arrays for BF in 3D. The antenna array calibration can also be made location aided. In the time domain, another interesting recent development appears in [16] where blind ZF is proposed, interweaving Power Delay (Doppler) Profile (PDP/PDDP) polyphase components. The exploitation of different user Doppler spectrum supports (different Doppler shifts/spreads) has already been exploited in certain forms of blind IA (BIA), see e.g. [17]. Location based LoS array responses which determine the LoS channel up to a scalar are sufficient for BC or IC, but the construction of beamformers for Network MIMO or CoMP would still require the feedback of these scalars. Finally, whereas LoS/NADA models may be appropriate for macrocells in many environments, the development of small cells may pose a problem for the ideas presented here. VII. REFERENCES [1] D. Shutin and B. Fleury, “Sparse Variational Bayesian SAGE Algorithm With Application to the Estimation of Multipath Wireless Channels,” IEEE Trans. on Signal Proc., Aug. 2011. [2] D. Astely and B. Ottersten, “The Effects of Local Scattering on Direction of Arrival Estimation with MUSIC,” IEEE Trans. on Signal Processing, Dec. 1999. [3] M. Guillaud, D. Slock, and R. Knopp, “A Practical Method for Wireless Channel Reciprocity Exploitation Through Relative Calibration,” in Proc. IEEE Int’l Symp. on Signal Processing and its Applications (ISSPA), Sydney, Australia, Sept. 2005. [4] D. Slock, “Location Aided Wireless Communications,” in Proc. IEEE Int’l Symp. on Control, Comm’s and Signal Proc. (ISCCSP), Rome, Italy, May 2012.

[5] Y. Lejosne, D. Slock, and Y. Yuan Wu, “User Selection in the MIMO BC,” in European Signal Proc. Conf. (EUSIPCO), Bucharest, Romania, Aug. 2012. [6] E. Bj¨ornson, M. Kountouris, M. Bengtsson, and B. Ottersten, “Receive Combining vs. Multistream Multiplexing in Downlink Systems with Multi-Antenna Users,” IEEE Trans. on Signal Proc., subm., 2012, arxiv1207.2776v1. [7] P. de Kerret and D. Gesbert, “Interference Alignment with Incomplete CSIT Sharing,” Nov. 2012, arxiv1211.5380. [8] H. Yin, D. Gesbert, M. Filippou, and Y. Liu, “A coordinated approach to channel estimation in large-scale multiple-antenna systems,” IEEE J. on Selected Areas in Comm’s (JSAC), Special Issue on: Large Scale Antenna Systems, Jan. 2013. [9] A. Adhikary, J. Nam, J.-Y. Ahn, and G. Caire, “Joint Spatial Division and Multiplexing,” 2012, arxiv1209.1402. [10] R. Ghaffar, U. Salim, I. Ghauri, and R. Knopp, “Mixed CSIT DL Channel : Gains with Interference Aware Receivers,” in Proc. 17th European Wireless Conf. (EW), Vienna, Austria, April 2011. [11] S. Krishnamurthy and S. Jafar, “Degrees of Freedom of 2-user and 3-user Rank-Deficient MIMO Interference Channels,” in Proc. IEEE Globecom, Dec. 2012. [12] S. Chae, S.-W. Jeon, and S.-Y. Chung, “Cooperative Relaying for the Rank-Deficient MIMO Relay Interference Channel,” IEEE Communications Letters, Jan. 2012. [13] G. Bresler, D. Cartwright, and D. Tse, “Geometry of the 3User MIMO Interference Channel,” in Proc. Allerton Conf., Sept. 2011. [14] ——, “Feasibility of Interference Alignment for the MIMO Interference Channel: the Symmetric Square Case,” in Proc. Information Theory Workshop (ITW), 2011. [15] D. Slock, “MIMO Broadcast and Interference Channels with Location based Partial CSIT,” in Proc. European Wireless (EW), Surrey, UK, Apr. 2013. [16] H. Papadopoulos, S. Mukherjee, and S. Ramprashad, “SemiBlind MU-MIMO based on Limited Features of the User Multi-Path Intensity Profiles,” in Proc. IEEE Information Theory and Applications workshop (ITA), La Jolla, CA, USA, Feb. 2011. [17] S. Chae and S.-Y. Chung, “Blind Interference Alignment for a Class of K-user Line-of-Sight Interference Channels,” IEEE Trans. Communications, May 2012.

A.6

Location aware CoMP transmission synchronization

This appendix includes the following published paper: • Armin Dammann and Ronald Raulefs, “Exploiting Position Information for Synchronization in Coordinated Multipoint Transmission”, IEEE 77th Vehicular Technology Conference (VTC2013Spring), Dresden, Germany, 2-5 June 2013.

161

Exploiting Position Information for Synchronization in Coordinated Multipoint Transmission Armin Dammann and Ronald Raulefs

Institute of Communications and Navigation German Aerospace Center (DLR) Oberpfaffenhofen, 82234 Wessling, Germany Email: {Armin.Dammann, Ronald.Raulefs}@DLR.de Abstract—Cellular communications systems suffer from interference in particular at cell edge regions. This is also the case for downlink synchronization signals. Such synchronization signals are base station specific and superimpose at a mobile terminal with different delays and amplitudes. This causes inter cellular interference depending on the cross correlation properties of the particular synchronization signals. Assuming knowledge about the positions of the serving and interfering base stations and having available a position estimate of the mobile terminal, there is a-priori information about the different signal propagation delays at the mobile terminal’s position. Using this information, synchronization signals received from adjacent base stations can be timely related. For this reason, former interference can at least partly be turned into useful signal and exploited for improving synchronization performance especially at the critical cell edge regions. Within this paper we evaluate the benefit of position information for a mobile terminal in order to improve mobile terminal synchronization performance. The analysis is based on calculating the Cram´er-Rao lower bound for this particular problem. In particular, we will derive additional Fisher information about OFDM symbol timing from position information about the mobile terminal.

I.

I NTRODUCTION

Wireless communications systems face an increasing data throughput demand. Therefore, multicarrier modulation techniques like orthogonal frequency division multiplexing (OFDM) [1] have been adopted to communications systems beyond 3G, e.g., the UMTS1 successor standard 3GPP-LTE2 [2], [3]. To achieve high service coverage, terrestrial mobile communication systems are based on a cellular layout of base stations, where each base station is serving mobile terminals located in the surrounding area. In order to use the available spectrum efficiently, such systems usually target at a frequency reuse factor of one. Adjacent cells are accessing the same time-frequency resources. At the cell border, downlink signals from adjacent base stations are received with similar power levels. This results in severe interference. Therefore, it is difficult to achieve high data rates at cell edges if there is no coordination between the serving and interfering base stations at all. To overcome this problem, concepts like interference coordination [4], which reduce interference by coordinated resource management at the cell border, or macro diversity, where mobile terminals at the cell edge are served from multiple base stations, have been proposed. Coordinated multiopoint (COMP) transmission is a main element of LTE beyond Release 9 [5]. It aims to improve cell edge data rates 1 UMTS:

Universal Mobile Telecommunications System 3rd Generation Partnership Project - Long Term Evolution

2 3GPP-LTE:

but comes along with additional challenges such as accurate synchronization of base stations. One of the first signal processing steps at the mobile terminal receiver is synchronization. In this process, local oscillator frequency offset as well as frame and symbol timings have to be estimated in order to detect data symbols correctly. For synchronization purposes a common approach is to transmit signals, which are known to the receiver. For instance in 3GPPLTE such signals are the so-called primary and secondary synchronization signals (PSS, SSS) [6]. Similar to data symbols, synchronization signals transmitted from adjacent base stations interfere significantly at the cell edge. In [7] the authors investigated the effect of cyclic delay diversity (CDD) on synchronization. CDD is a transmit antenna diversity technique which transmits cyclically shifted replicas of an OFDM symbol over different antennas, providing channel fading characteristics with sufficiently low mutual correlation. Thus, the probability for all transmit signals being deeply faded is lower compared to a single transmit antenna system. CDD can be considered as a macro diversity approach where the transmitters are located in close proximity. Because of this co-location of the TX antennas, the signal propagation delay differences from different TX antennas to the mobile terminal do not depend significantly from the position of the mobile terminal with respect to the base station. For the macro diversity principle, where signals are transmitted from different sites, we obtain a strong dependency of these delay differences from system geometry, i.e., the location of base stations and the mobile terminal. In this paper we analyze the potential gains in mobile terminal synchronization performance by exploiting COMP. We derive the Cram´er-Rao lower bound for mobile terminal synchronization in a perfectly synchronized COMP network. The key issue is to calculate additional Fisher information about OFDM symbol timing from position information about the mobile terminal. Sufficient accuracy of such position information is essential to achieve synchronization performance gains. II.

C OORDINATED M ULTIPOINT S YNCHRONIZATION

A. Principle Particularly at cell edge areas of a mobile communications system with frequency reuse of one signals are received from different base stations (BSs) with similar power levels. Depending on the signal properties this may cause high interference levels. Fig. 1 illustrates the situation, where 3

BS2 (x2, y2)

B. Signal Model At BSp we transmit a multicarrier time domain signal denoted in baseband as

s2 t BS1 (x1, y1)

st)

s1

st)

st)

1 sp (t) = √ N

t

MT (x, y)

rMT t BS3 (x3, y3)

t 

Fig. 1. The principle of exploiting position information in CoMP transmission: With knowledge about the position of the MT, propagation delays of signal components coming from different BS can be related to each other.

BSs synchronously transmit different synchronization signals. Accurate BS synchronization is a key requirement in coordinated multipoint transmission. These signals are received with different propagation delays at the mobile terminal (MT), depending on the location of the MT with respect to the BSs. We assume BS1 being the serving BS for the MT. If there is no additional information about the mutual relation of the signal propagation delays, the synchronization signals of the adjacent, non-serving BSs appear as interference. Using estimation algorithms which estimate the propagation delays of the synchronization signals, received from both the serving BS and the interfering BSs, jointly can combat these interference. However, the performance remains worse compared to the single link case, where only the serving BS1 is transmitting. The situation changes if we can relate the signal propagation delays of the interfering base stations to that of the serving BS1 . Using such a relation the signals from non-serving BSs provide information about the signal propagation delay between BS1 and the MT. Such additional information can be obtained from position information of the MT with respect to the BSs. A positioning entity like a Global Positioning System (GPS) module at the MT can provide a position estimate for instance. The quantity of mutual information between the signal propagation delays depends strongly on the position estimation accuracy. With position information becoming more and more accurate, synchronization signals from non-serving BSs turn from interference into useful signals. Therefore, we can expect a synchronization performance gain even compared to the single BS case, especially at cell border areas. On the one hand we gain from additional signal energy which is available from adjacent BSs. On the other hand there is also a diversity gain if there are fading effects in signal propagation. Here, the probability of multiple signals being deeply faded is lower compared to the single BS case, where we have only one signal available for synchronization.

Sp (`) ej2π ` fSC t

(1)

`=− N 2

N BS X p=1



X

with subcarrier spacing fSC which we generate from N corresponding subcarrier symbols Sp (`) located around but not using the zero subcarrier ` = 0. At the mobile terminal (MT) we receive a signal rMT (t) =

s3

+N 2

αp sp (t − τp ) + n(t)

(2)

which consists of signal components transmitted from different BSs and additive white Gaussian noise (AWGN). The signal components sp are received with propagation delays τp depending on the distance between BSp and the MT and influenced by flat fading coefficients αp . We denote the received signal in frequency domain and obtain R(`) =

N BS X

αp Sp (`) e−j2π ` fSC τp + N (`)

(3)

p=1

2 with n AWGN o N (`) having zero mean and variance σ = 2 E |N (`)| .

We may justify the frequency domain representation by using OFDM with a cyclic prefix as guard interval. The length of the guard interval has to be chosen such that the received OFDM symbol components sp (t − τp ) are free of inter-symbol interference for an LTE OFDM symbol length of TOFDM = 1/fSC = 1/15 kHz = 66.67 µs. The usual guard interval length of 3GPP-LTE for instance is Tg = 4.56 µs. This corresponds to a maximum tolerable distance between base stations of about 1367 m which is sufficient for the scenario we consider in this paper. C. Propagation Model For our investigations we use a WINNER channel model [8] for obtaining the large scale parameters path loss   fc [GHz] (4) PLp [dB] = A log (dp [m]) + B + C log 5.0

and shadow fading SFp . The large scale channel model parameters for a typical urban environment are summarized in Table I, where the model parameters have been calculated for the default heights of the BS (hBS = 25 m) and the MT (hMT = 1.5 m). The model distinguishes between line-of-sight (LOS) and non-LOS propagation conditions. The probability for LOS propagation between BSp and the MT    dp dp 18 m ,1 1 − e− 63 + e− 63 (5) PLOSp = min dp is dependent on the distance dp between BSp and MT. For LOS propagation there is a breakpoint distance, which separates two applicability ranges with different path loss parameters. This breakpoint distance is calculated from carrier wavelength λc as shown in Table I. The shadow fading
SFp [dB] ∼ N 0, σSFp (6)

TABLE I.

L ARGE SCALE CHANNEL MODEL PARAMETERS FOR A TYPICAL URBAN MACRO CELL (WINNER C2).

Propagation Condition

Applicability Range

LOS

10 m < dp < 48 m2 /λc 48 m2 /λc < dp < 5 km 50 m < dp < 5 km

non-LOS

A. Fisher Information for Synchronization from the Received Signal

A

B

C

σSFp

26 40 35.7

39 12.4 42.6

20 6 23

4 dB 6 dB 8 dB

The useful signal part in the complex valued AWGN signal model in Eq. (3) is ˜ = S(`)

N BS X

αp Sp (`) e−j2π ` fSC τp .

(10)

p=1

in dB is drawn from a normal distribution with zero mean and standard deviation σSFp . For links between a MT and different BSs p and q, the shadow fading values are correlated with correlation coefficient

For a complex AWGN signal model, the Fisher information is a NBS × NBS matrix with components [9, Ch. 15.7]  N  +2 ∗ X ˜ ˜ 2 ∂ S (`) ∂ S(`)  (11) [Fsig ]p,q = 2 Re  σ ∂τp ∂τq N `=−

ρp,q

Cp,q = 0.5 =p Cp,p Cq,q

(7)

where Cp,q denotes the covariance between SFp and SFq . Note 2 Cp,p = σSF is the variance of shadow fading value SFp . The p correlation coefficients ρp,q do not depend on the distance dp between BSs and the MT. We relate the path loss and shadow fading to the flat fading coefficients αp in Eq. (3) as |αp | = 10−

PLp +SFp 20

.

(8)

arg (αp ) ∼ U[0, 2π)

(9)

We draw the phase

of fading coefficient αp identically, independently and uniformly distributed from the interval [0, 2π).

III. T HE C RAM E´ R -R AO L OWER B OUND FOR S YNCHRONIZATION IN C OORDINATED M ULTIPOINT T RANSMISSION We assume coordinated multipoint transmission with perfectly synchronized BSs. At the MT we receive a superposition of NBS signals from adjacent BS according to the signal model in Eq. (3). Let us assume that BS1 is the serving BS. So we are primarily interested in estimating the signal propagation delay τ1 . First of all, the other NBS − 1 signal components appear as interference, since the applied signal model does not provide a relation of signal propagation delays τp , p = 2, . . . , NBS to τ1 . Taking care of this interference we have to analyze a vector parameter estimation problem for the signal propagation T delays τ = (τ1 , . . . , τNBS ) . For such a problem, the Cram´erRao lower bound is a fundamental bound for the variance of any unbiased estimator. It is based on the so-called Fisher information about the parameters which we wish to estimate. Subsequently, we calculate the Fisher information for estimation of the vector parameter τ based on the received signal samples R(`). As an optimum estimation approach for achieving this bound we could estimate the NBS propagation delays τp jointly by applying the maximum likelihood criterion for instance. In a second step, we calculate additional Fisher information about the signal propagation delays T τ = (τ1 , . . . , τNBS ) from a MT position estimate.

2

n o 2 at row p and column q where σ 2 = E |N (`)| denotes the ˜ with AWGN variance. The derivative of the useful signal S(`) respect to signal propagation delay τp in Eq. (11) is

˜ ∂ S(`) = [Jsig ]`,p = (−j2π ` fSC ) αp Sp (`) e−j2π ` fSC τp ∂τp (12) and can be identified as a Jacobian matrix component. With ˜ the N × NBS Jacobian matrix Jsig for signal S(`) and its Hermitean we can express Eq. (11) in matrix form as   2 Fsig = 2 Re JH (13) sig Jsig . σ B. Fisher Information for Synchronization from Position Information

There is a functional dependency between the position of T T the mobile terminal x = (x, y) = (f1 (τ ), f2 (τ )) = f (τ ) T and the signal propagation delays τ = (τ1 , . . . , τNBS ) , obtained at that position. With this vector valued functional T dependency and an error vector (x , y ) , consisting of zero mean AWGN components, we can express a signal model for a MT position estimate as      x ˆ = f (τ ) + x . (14) yˆ y  We assume a circular position error with variance E 2x =  σ2 E 2y = pos 2 . With this AWGN signal model we obtain the Fisher information about the signal propagation delays from a MT position estimate as 2 Fpos = 2 JT Jf . (15) σpos f The components of the real valued 2 × NBS Jacobian matrix Jf are ∂ [Jf ]k,p = fk (τ ). (16) ∂τp For calculating the Jacobian matrix, and finally the Fisher information, we require the function f (τ ) analytically. Unfortunately, obtaining this function is not an easy problem. In navigation research the calculation of this function actually means solving the positioning problem for time of arrival based positioning [10]. In this paper we follow another approach and assume that function f : RNBS 7→ R2 is invertible at least locally around

the MT position. Its inverse function is g = f −1 . The inverse function g : R2 7→ RNBS maps the position of the MT to the T appropriate signal propagation delays τ = (τ1 , . . . , τNBS ) . We can easily calculate the components of function g (x) in an analytic way from the positions of the BSs and the MT as 1 q (x − xBSp )2 + (y − yBSp )2 (17) τp = gp (x) = c0 | {z } = dp and the corresponding Jacobian matrix as  x−x1  ∂ (g1 , . . . , gNBS ) 1   Jg = = ∂ (x, y) c0  

d1 x−x2 d2

y−y1 d1 y−y2 d2

x−xNBS dNBS

y−yNBS dNBS

.. .

.. .



   . (18)  

If we apply the result of function g (x) to function f (τ ), we obtain the identity function id (x) = f ◦g (x) = f (g (x)) = x. The 2 × 2 Jacobian matrix for the identity function Jid = I2×2 = Jf ◦g = Jf Jg

(19)

is the identity matrix. The last equation above follows from applying the chain rule to the concatenation of the functions f and g. From Eq. (19) we observe that the product of Jacobian matrices for function f and its inverse g is the identity matrix. This property is fulfilled if we build
−1 T Jf = J T Jg (20) g Jg

as the Moore-Penrose pseudo inverse of the Jacobian matrix Jg , which we can easily calculate according to Eq. (18). Inserting this result into Eq. (15) yields the Fisher information about τ from position estimation Fpos =

2 2 σpos

Jg JT g Jg


−2

JT g.

(21)

For convenience we skipped the arguments of the Fisher information and Jacobian matrices. C. Bound and References Since the AWGN for the signal models in Eq. (3) and Eq. (14) is statistically independent, the Fisher information matrices for the received signal and the position estimate can be added for obtaining the overall Fisher information about the signal propagation delays. We build the NBS × NBS Cram´erRao lower bound matrix −1

CRLB = (Fsig + Fpos )

(22)

by inverting the overall Fisher information matrix. The first main diagonal element of this matrix provides a lower bound for the variance VAR {ˆ τ1 } of an unbiased estimator for propagation delay τ1 . Equivalently we express this bound in terms of the standard deviation q p VAR {ˆ τ1 } ≥ στ1 = [CRLB]1,1 . (23) As a reference σref =

lim

σpos →∞

q q  [CRLB]1,1 = Fsig −1 1,1 .

(24)

we use the bound above for Fpos → 0 or equivalently σpos → ∞, which means that no position information is available. The appropriate reference for the single BS case is 1 . σsingle = q [Fsig ]1,1 IV.

(25)

R ESULTS

A. Parameters and Environment For the evaluation of the synchronization performance, we consider an arrangement of three BSs as shown in Fig. 1 with a BS-to-BS distance of 1000 m. The MT is located at the cell √ border. Thus, its distance to the BSs is 1000 m/ 3 = 577.4 m. We take into account large scale fading effects as introduced in Sec. II-C. The carrier frequency is fc = 2.6 GHz. At this spectrum range, 140 MHz are allocated for LTE FDD (Frequency Division Duplex) in Europe. We use the 3GPP-LTE Secondary Synchronization Signals (SSSs) as specified in [3]. These binary sequences are defined in frequency domain and occupy the 62 core subcarriers except subcarrier zero with an overall bandwidth of 63 × fSC = 63 × 15 kHz = 945 kHz. 3GPP-LTE specifies 504 SSSs in total. For our evaluations we have randomly chosen the SSSID set (142, 411, 472). Several simulation runs have shown only slight differences for different choices of SSS-IDs. The overall transmit power of PTX is equally distributed over the 62 subcarriers which yields a subcarrier power of n o P TX 2 E |Sp (`)| = . (26) 62 With the LTE subcarrier spacing fSC = 15 kHz, Boltzmann constant kB = 1.38 × 10−23 Ws/K and a noise temperature of T = 300 K we can expect a subcarrier noise power level of n o 2 E |N (`)| = σ 2 = kB T fSC = −132.1 dBm. (27) B. Synchronization Accuracy

Subsequently, we evaluate the Cram´er-Rao lower bound (CRLB) for the synchronization error at the MT, i.e., the standard deviation for estimation of signal propagation delay τ1 between the MT and BS1 . Since signal propagation contains random components according to Eq. (8) and Eq. (9), the CRLB is a random process as well. We draw the cumulative distribution function (CDF) for the synchronization error from 105 realizations of the fading coefficients αp , p = 1, . . . , 3. Fig. 2 shows these CDFs for a transmit power of PTX = 30 dBm and different values for positioning standard deviation σpos . For the reference case, where no position information is available (σpos → ∞), we get a synchronization error of less than 60 ns with a probability of 0.9. Note this bound is suitable for joint estimation of the signal propagation delays τp , p = 1, . . . , 3 which aims to get rid of inter cellular interference. A genie joint estimation algorithm would be able to completely cancel inter cellular interference. With such a genie algorithm we could approach the CRLB for the single BS case, which we have drawn for comparison. Having available perfect position information (σpos → 0) improves the synchronization performance to 21 ns. The synchronization performance gradually improves for positioning accuracy in the range of σpos = 20, . . . , 2 m in this example. By mul-

3

10

σpos → ∞ σpos = 100m σpos = 30m σpos = 10m σpos = 3m σpos → 0 Single BS

0.9 0.8

CRLB for Sync. Error [ns]

Prob(CRLB < Synchronization Error)

1

0.6 σpos → ∞ σpos = 100m σpos = 30m σpos = 10m σpos = 3m σpos → 0 Single BS

0.4

0.2

0 0

10

20 30 40 50 Synchronization Error [ns]

60

1

10 10

70

Fig. 2. CDF of the CRLB for synchronization error (standard deviation) at the cell border between 3 adjacent BSs. PTX = 30 dBm. SSS-IDs are 142, 411, 472.

tiplying with the speed of light, c0 = 3 × 108 m/s, we can express the synchronization performance values in units of meters as c0 ×21 ns = 6.3 m, . . . , c0 ×60 ns = 18 m. Thus, we can state that we obtain a synchronization gain from position information, if the position estimation accuracy is in the same order of magnitude as the synchronization performance itself, expressed in meters. This characteristics can also be observed from Fig. 3. Here we have drawn the 90 % synchronization accuracy versus the transmit power PTX for different values of positioning accuracy σpos . A synchronization error of 100 ns corresponds to c0 × 100 ns = 30 m. Around this order of magnitude the performance for σpos = 30 m shifts between the asymptotic performances. Furthermore, we can observe that the asymptotic performance graphs show a steepness of 1 decade per 20 dB of transmit power difference. The horizontal shift between the asymptotic graphs σpos → ∞ (no position information) and σpos → 0 (perfect position information) indicates that we can gain up to 8 dB in transmit power by exploiting sufficiently accurate position information at the cell border compared to the performance without position information. It should be mentioned that we have considered the channel coefficients αp , p = 1, . . . , NBS as a random variable as discussed in Sec. II-C. However, we have assumed that we know those values for the derivation of the Cram´er-Rao lower bound. With this assumption, the resulting bound is still a lower bound. If we assume the αp , p = 1, . . . , NBS as unknown parameters, which we have to estimate as well, we may get a tighter lower bound for our estimation problem.

20 25 30 Transmit Power PTX [dBm]

35

40

tion estimation accuracy is in the same order of magnitude compared to the synchronization performance expressed in meters. For the considered scenario, up to 8 dB in transmit power can be gained by exploiting position information at the cell border compared to the performance of optimum joint estimation without position information. ACKNOWLEDGMENT This work has been performed in the framework of the FP7 project ICT-248894 WHERE2 (Wireless Hybrid Enhanced Mobile Radio Estimators - Phase 2) which is partly funded by the European Union. R EFERENCES [1]

[2] [3] [4] [5]

S UMMARY

In this paper, we have investigated the benefit of position information for synchronization in a multi cellular signal propagation environment using the secondary synchronization signals of 3GPP-LTE. We have derived and evaluated the Cram´er-Rao lower bounds for synchronization (timing estimation) taking into account information about signal propagation delays coming from an estimation of the mobile terminal’s position. The evaluations have shown that a synchronization gain from position information can be obtained, if the posi-

15

Fig. 3. CRLB for the synchronization error (standard deviation) versus the base station transmit power PTX . SSS-IDs are 142, 411, 472.

[6]

V.

2

10

[7] [8] [9] [10]

S. B. Weinstein and P. M. Ebert, “Data transmission by frequency division multiplexing using the Discrete Fourier Transform,” IEEE Transactions on Communications Technology, vol. 19, no. 5, pp. 628– 634, Oct. 1971. LTE; Evolved Universal Terrestrial Radio Access (E-UTRA); Long Term Evolution (LTE) physical layer; General description (3GPP TS 36.201 version 8.3.0 Release 8), ETSI, Apr. 2009, ETSI TS 136 201 V8.3.0. LTE; Evolved Universal Terrestrial Radio Access (E-UTRA); Physical channels and modulation (3GPP TS 36.211 version 8.7.0 Release 8), ETSI, Jun. 2009, ETSI TS 136 211 V8.7.0. D. Ast´ely, E. Dahlman, A. Furusk¨ar, Y. Jading, M. Lindstr¨om, and S. Parkvall, “LTE: The evolution of mobile broadband,” IEEE Communications Magazine, vol. 47, no. 4, pp. 44–51, Apr. 2009. R. Irmer, H. Droste, P. Marsch, M. Grieger, G. Fettweis, S. Brueck, H.-P. Mayer, L. Thiele, and V. Jungnickel, “Coordinated multipoint: Concepts, performance, and field trial results,” Communications Magazine, IEEE, vol. 49, no. 2, pp. 102–111, Feb. 2011. Y. Tsai, G. Zhang, D. Grieca, F. Ozluturk, and X. Wang, “Cell search in 3GPP long term evolution systems,” IEEE Vehicular Technology Magazine, vol. 2, no. 2, pp. 23–29, Jun. 2007. W.-C. Huang, C.-L. Tsai, and P.-A. Ting, “A novel timing synchronization method for CDD-OFDM systems with spatially correlated channel,” in IEEE Vehicular Technology Conference (VTC Fall 2011), Sep. 2011. “WINNER II Deliverable D1.1.2: WINNER II Channel Models,” Sep. 2007. [Online]. Available: http://www.ist-winner.org/deliverables.html S. M. Kay, Fundamentals of Statistical Signal Processing — Estimation Theory. Prentice Hall, 1993. P. Misra and P. Enge, Global Positioning System — Signals, Measurements and Performance, 2nd ed. Ganga-Jamuna Press, 2005, ISBN 0-9709544-1-7.

A.7

Downlink femto-macro ICIC with location-based long-term power setting

This appendix includes the following published paper: • J. Guillet, L. Brunel, N. Gresset, “Downlink Femto-Macro ICIC with Location-Based Long-Term Power Setting”, 17th International Workshop on Computer Aided Modeling and Design of Communication Links and Networks (CAMAD 2012), Barcelona, Spain, 17-19 September 2012.

167

Downlink Femto-Macro ICIC with Location-Based Long-Term Power Setting Julien Guillet, Lo¨ıc Brunel and Nicolas Gresset Mitsubishi Electric R&D Centre Europe 1 All´ee de Beaulieu, CS 10806, 35708 Rennes Cedex, France Email: {j.guillet, l.brunel, n.gresset}@fr.merce.mee.com Abstract—Inter-cell interference is a major issue in current wireless cellular systems, in particular with the development of femto-cells. Efficient macro-femto inter-cell interference coordination (ICIC) is crucial and should be performed with minimum communication between macro and femto base stations. We propose an ICIC approach, in which each femto base station informs a server about its position, obtains relevant information from mobile terminal measurements stored in a database maintained by the server and configures its transmission power according to this information. This power setting aims at maintaining a controlled impact of the femto base station on macro-cell performance, independent of the femto-cell location. In a 3GPP-LTE context, this approach exhibits a good femtomacro performance trade-off and is robust against power and positioning measurement errors.

I. I NTRODUCTION In current mobile cellular networks, like 3GPP Long Term Evolution (LTE) networks, heterogeneous deployments mixing macro base stations (MBS) and home base stations or femto base stations (FBS) are foreseen as an effective way to ensure both mobility within a large geographical area and high data throughput at home [1][2]. As in homogeneous macro deployments, fairness between cell-center and cell-edge users [3] must be sought and inter-cell interference coordination (ICIC) [3][4] appears as a proper way to mitigate the interference impact. In heterogeneous co-channel deployments, FBSs may strongly interfere with MBSs and even create coverage holes in downlink (DL). In order to secure the operator MBS traffic, priority should be put on minimizing the interference created by FBSs on MBSs. However, the FBS throughput inside home should remain reasonably high. Furthermore, due to the high number of FBSs under the MBS coverage, macro-femto ICIC minimizing the MBS-FBS exchanges is desirable. As depicted in Fig. 1, for the No ICIC case, the area where macro mobile terminals (MTs) are strongly interfered by the FBS varies, depending of the FBS position relative to MBSs. In a DL macro-femto ICIC approach presented in [5], the FBS independently sets its long-term transmit power [6], [7] according to its knowledge of the additive white Gaussian noise (AWGN) level and the received power from neighboring MBSs. In [5], received powers are obtained through measurements performed by the FBS on MBS DL signals. From an operator point-of-view, it is desirable that the impact of a FBS on surrounding macro MTs (MMTs) is independent of its location in the MBS coverage. The power setting

Step1: FBS position transmitted to the server

Server

Step2: Information about power measurements of MMTs in HIRZ transmitted to FBS No ICIC

HIRZ Impact of the FBS on the MMTs is set constant

FBS MBS

Step3: FBS transmit power computed

FBS ICIC

Fig. 1: ICIC providing macro-degradation equalization (single cell, no shadowing).

in [5] achieves this property, which we call here macrodegradation equalization. In addition to VoIP and data services, mobile cellular networks also propose positioning services [8]. Positioning is also implemented in most MTs through Global Navigation Satellite System (GNSS). In this paper, we investigate how the MT and FBS location information, together with the supply of an appropriate database, can benefit to the long-term ICIC power setting, by providing precise information on received powers at MMTs surrounding a given FBS. After describing several key concepts of long-term power setting in Section II, we detail the proposed location-based FBS power setting in Section III. Finally, Section IV presents evaluation results for a 3GPP-LTE system and provides comparison with constant FBS transmit power and the FBS measurement based power setting approach of [5], including errors on measurements and propagation models. II. P OWER SETTING PRINCIPLES A. Inter-cell interference definition We consider a planned macro-cellular system, serving MMTs, and FBSs with closed-subscriber group (CSG), e.g., private home base stations, serving femto mobile terminals (FMTs). We denote Pt,F the transmit power of the most interfering FBS for a given MMT, GF the path gain from this FBS to the MMT, PM the received power at the MMT from the MBS serving the MMT, I the level of the interference received from other MBSs and FBSs plus AWGN at the MMT. The signal to interference plus noise ratio (SINR) for the MMT

is

PM SINRM (Pt,F ) = I + Pt,F GF

.

(1)

Let us define a performance metric as an increasing function of the SINR. There is a trade-off between femto and macro performance driven by the FBS transmit power Pt,F . Longterm FBS power setting must ensure a controlled macro-femto performance trade-off for a high number of MMT and FMT SINR realizations. B. Macro-degradation equalization For the sake of macro-degradation equalization, we introduce a high interference reference zone (HIRZ) [5], as depicted in Fig. 1, which is a given area in which the level of MMT performance degradation is controlled. When the same HIRZ and the same definition and level of MMT performance degradation are considered for all FBSs, all FBSs are expected to have the same impact on the MMTs and macro-degradation equalization is achieved. The HIRZ, denoted ZMMT , is a ring encompassing the femto building. We define the macro performance degradation as a function g(·) being the ratio of the MMT performance metric with and without FBS transmission. As the path gain properties are not the same for all positions in ZMMT , we consider the outage probability of the degradation function sol g(·). The FBS transmit power is set to Pt,F
such that, in sol ZMMT , the probability that g PM , I, GF Pt,F is lower than or equal to a threshold gth equals POU T :

sol Pr g PM , I, GF Pt,F ≤ gth |ZMMT = POU T . (2)

sol such that, It is equivalent to find the FBS transmit power Pt,F   1 −1 sol g (PM , I, gth ) |ZMMT = POU T , (3) Pr Pt,F ≤ GF

where g −1 (PM , I, gth ) /GF is the appropriate power setting value for a given realization of PM , GF and I. Function g −1 (·) denotes the inverse function of g(·). Thus, the transmit power sol can be expressed as a quantile function: setting solution Pt,F sol Pt,F = Q G1

F

g −1 (PM ,I,gth )|ZMMT

(POU T ) ,

(4)

where the quantile Qu|ZMMT (P ) denotes the input value of the cumulative distribution function (CDF) of function u(·) such as the CDF evaluated on the area ZMMT equals P . Thus, the long-term power setting is defined by a choice of the function g(·), of the HIRZ ZMMT and of the parameters gth and POU T . C. Power setting based on spectral efficiency degradation We adopt a performance metric related to spectral efficiency S. The macro performance degradation is defined as g (PM , I, GF Pt,F ) = S (Pt,F ) /S (0) ,

(5)

where S (Pt,F ) = a log2 (1 + b × SINRM (Pt,F )). Parameters a and b are chosen in order to accurately compute the obtained spectral efficiency from the large-scale SINR. For each MT, we compute the spectral efficiency, taking into account smallscale channel effects and scheduling, and the large-scale SINR.

Finally, a and b are chosen in order to fit the obtained cloud of (large-scale SINR, spectral efficiency) couples. Using (1) in (5), we obtain   1 bPM g −1 (PM , I, gth ) − I . (6) = GF GF (1 + bPM /I)gth − 1

The path gain GF is modeled with a log-normal distribution and the exact distribution is obtained with FMT measurements or through a predefined path loss model. In the latter case, the variance is the shadowing variance and the mean is for instance obtained from a log-distance path loss model, using the mean radius of ZMMT and assuming a given wall penetration loss Aw . III. FBS TRANSMIT POWER COMPUTATION WITH POSITION INFORMATION

In the proposed location-based approach depicted in Fig. 1, the statistical model for PM and I powers received from MBSs at MMTs in ZMMT is based on the FBS position information and the use of a geo-referenced database. The georeferenced database has been constructed in advance thanks to MMT reports to their serving MBS, containing received power from neighboring base stations and the MMT location. Upon installation or reinitialization, a FBS obtains its own location information, e.g., through GNSS, and transmits it to the server maintaining the database (step 1). Thanks to this information, the server can transfer appropriate information about MMTs located in ZMMT to the FBS (step 2). This information allows accurate power setting at FBS (step 3). This database approach induces different types of errors: FBS position error, MMT position errors, MMT power measurement errors and quantization errors. The FBS position error may be lower than the MMT position error since the FBS location remains unchanged for a long duration. The information transferred by the server to the FBS may be obtained in at least two ways from measurements performed by MMTs in ZMMT . It may be, in increasing order of accuracy, 2 of the in• the mean g inv |dB and variance σg inv | dB   −1 ˆ verse degradation function g PM,i , Iˆi , gth |dB over •

all samples i in ZMMT , or directly the samples   of the inverse degradation function −1 ˆ ˆ PM,i , Ii , gth |dB , g

where PˆM,i and Iˆi are the database sample i for PM and I, respectively, and x|dB is the expression of x in dB. In the first approach, considering a log-normal distribution for g −1 (PM , I, gth ) and GF and using (4), the quantile of a sol normal distribution has to be evaluated in order to get Pt,F in dB: sol Pt,F |dB

=

Q−GF |dB +g−1 (PM ,I,gth )|dB |ZMMT (POU T )

= −GF |dB + g inv |dB + σ|dB QN (POU T ) ,(7)

where QN is the quantile function of the standard normal distribution. Assuming independence between the FBSMMT path gain and the received power from MBS we obtain, q 2 σ|dB = σG + σg2inv |dB , (8) F |dB

2 where GF |dB and σG are the mean and variance of F |dB GF |dB in area ZMMT , respectively. In the second approach, still considering a log-normal distribution for GF , independent of PˆM,i and Iˆi , (4) results in the computation of the quantile of a Gaussian mixture. Indeed, the distribution is the mixture of Gaussian distributions, the   mean and variance of distribution i 2 , respecbeing g −1 PˆM,i , Iˆi , gth |dB + GF |dB and σG F |dB 2 tively. With σGF |dB being large compared to the variance   on database samples g −1 PˆM,i , Iˆi , gth , the first approach

is a good approximation of the second one. This condition is satisfied in scenarios of interest and, in the sequel of this paper, we use the first approach. Therefore, with (7) and (8), the solution for femto transmit power setting is in log scale, sol Pt,F |dB

inv

= −GF |dB + g |dB q 2 + σg2inv |dB QN (POU T ) + σG F |dB

(9)

Parameters g |dB , and POU T are provided to the FBS by the database server. The model for the FBS-to-FMT path gain GF may also be provided by the database server based on typical values assumed by the operator. Alternatively, they are estimated at each FBS based on MT measurements. In [5], the FBS power is set according to PM and I values measured at FBS, assuming that the values of PM and I are the same for MMTs in ZMMT , except for the wall penetration loss. Equation (9) can be used for setting the FBS power according to FBS power measurements, setting σginv |dB to a common value, function of the assumed path gain model from MBS to MMT in ZMMT . Thus, σginv |dB is common to several FBSs, whereas in the proposed location-based approach, σginv |dB is specific to each FBS. However, as in the location-based approach, g inv |dB is specific to each FBS. It is obtained from F BS and IˆF BS of the DL signals FBS power measurements PˆM from neighbouring MBSs:   F BS Aw , IˆF BS Aw , gth |dB (10) g inv |dB ≈ g −1 PˆM inv

σg2inv |dB

Thus, the location-based approach provides more information on actual PM and I values experienced at MMTs and avoids wall penetration loss error effects on these variables. For situations where the indoor and outdoor received powers from MBS are very different, a better macro-femto performance trade-off can be achieved by the power setting thanks to the additional information provided by the database. Furthermore, an error on penetration loss has more impact on the FBS measurement based power setting approach [5] since Aw appears in (10) in addition to (9), where it impacts GF |dB . This performance advantage has some costs: maintaining a database, adding some MBS-to-server signaling in the core network and having a positioning capability in FBSs and many MTs. However, we note that the positioning capability is already well spread among MTs. Furthermore, the database size is relatively small. For instance, for a database density of 0.1 MMT measurement (sample) per m2 , around 1011 samples are needed to cover 106 km2 . Thus, the database size is of the order of magnitude of one terabyte.

TABLE I: Simulated propagation model for MBS. Total MBS transmit power Distance dependent mean path loss (dB) MBS antenna type MBS Antenna gain Shadowing standard deviation Shadowing correlation for two MBSs Shadowing correlation distance Wall penetration loss Aw |dB Small-scale channel

43 dBm 128.1 + 37.6 log10 (d), d in km directional (for 3-sectorized sites) with vertical selectivity 14 dB 8 dB 0.5 50 m 10 dB SCM Urban Macro low-spread

TABLE II: Simulated propagation model for FBS. Maximum FBS transmit power Distance dependent mean path loss for indoor (dB) Distance dependent mean path loss for outdoor (dB) FBS antenna type FBS antenna gain Shadowing standard deviation for FBS Shadowing correlation distance Wall penetration loss Aw |dB Small-scale channel

20 dBm 37 + 30 log10 (d), d in m 37 − 6.7 log10 (r) + Aw |dB −36.7 log10 (d), d in m Omni-directional 5 dB 10 dB Uncorrelated 10 dB ITU-InH

IV. P ERFORMANCE RESULTS A. Simulation scenario We simulate an LTE system with 2 GHz carrier frequency, using a static multi-cell system-level simulator. MBSs are deployed with 1732 m inter-site distance according to the 3GPP case 3 [9]. Nineteen tri-sectorized sites (3 cells per site) are simulated with wrap-around. The indoor femto propagation model is the 3GPP LTE-A femto-cell model and the indoorto-outdoor femto propagation model uses the attenuation coefficient of the ITU-UMi NLOS model [9]. This approach with double slope more realistically models the difference between indoor-to-indoor and indoor-to-outdoor propagation, which is important for our study. These models include the shadowing on path gain, the Rice factor, the delay spread and the angular spread at base stations and MTs. The small-scale Rayleigh channels follow the 3GPP-SCM-Urban Macro model with low angular spread for MBS and the ITU-InH channel model [9] for FBS. Model details are gathered in Tables I and II. We consider different deployment scenes, each scene corresponding to one realization of FBS positions and shadowing. For each scene, we consider random drops of MMTs and FMTs. There are 10 MMTs per macro-cell and 2 FMTs per FBS. In each base station, an equal number of sub-carriers is allocated to all MTs and all base stations have full load. Round-Robin scheduling is used, allocating to a MT nonadjacent physical resource blocks (PRBs) of 12 sub-carriers. Multi-stream 2x2 multiple-input multiple-output (MIMO) transmission is performed on a 10 MHz system bandwidth as described in Table III. We use a link level to system level interface which takes into account small-scale effects,

TABLE III: Simulated 3GPP-LTE physical layer. Modulation waveform Bandwidth FFT size Useful sub-carriers Sub-carrier spacing MMT/FMT allocation granularity Maximum spectral efficiency

OFDM 10 MHz 1024 600 15 kHz one PRB = 12 sub-carriers 7 b/s/Hz (MIMO 2x2, 64-QAM, coderate 1, 43% overhead)

computing the spectral efficiency with true small-scale interference modeled using a frequency-selective and spatially colored additive Gaussian noise covariance matrix, from largescale parameters generated by the system level simulation. The spectral efficiency is computed as the outage capacity based on Shannon capacity and is limited here to a maximum 2-stream LTE spectral efficiency, i.e., 7 bits/s/Hz. Circular FBS buildings with radius r = 6 m are assumed. The HIRZ is defined as a ring centered on FBS with 6 m inner radius and 16 m outer radius. B. Error model used for power and localization measurements We assume a zero-mean iid Gaussian error model for positioning and for received power measurements PˆM,i and Iˆi in dB. Without any power measurement and positioning errors and with a high database density, the distribution of PM and I estimated from the database exactly matches the long-term reality. With positioning errors smaller than the shadowing correlation distance, this distribution remains an accurate estimate. We observed from our simulations that for positioning errors higher than the shadowing correlation distance (up to 100 m RMSE), the variance of the distribution becomes over-estimated whereas its mean value remains reliable. Furthermore, practical errors on power estimates (root mean square error (RMSE) smaller than 3 dB) do not strongly impact the performance if there are many MMT measurements available in the database for HIRZ. Indeed, with our scenario, the standard deviation in HIRZ without any power or positioning error is around 4 dB. As the proposed location-based FBS power setting approach is long-term, a high density database is easily built. Thus, in the sequel, we consider 0.1 sample per m2 for all simulations, i.e., on average 70 MMT measurements in HIRZ. Furthermore, in the path gain model between FBS and an MMT located in HIRZ, we consider a Gaussian error, iid among FBSs, between the actual wall penetration loss in the FBS building and the assumed wall penetration loss Aw |dB in the algorithm. When not specified, no error is considered. For comparison, we consider the approach based on the measurement of received powers PM and I at FBS [5]. FBS measurements suffer from a iid Gaussian error, with a RMSE different from MMT measurements, in order to take into account the positive impact of time averaging and the negative impact of shadowing decorrelation between indoor and outdoor.

Fig. 2: Global FMT-MMT performance trade-off in term of cell-edge spectral efficiency. Blue: 25 FBS/km2 , red: 125 FBS/km2 , green: 250 FBS/km2 .

C. Simulation results We simulate 20 realizations of FBS positions and shadowing map for each FBS density and 50 MMT drops for each realization. We compare three approaches: the constant FBS transmit power, the FBS power setting based on FBS power measurement [5] and the proposed location-based FBS power setting (denoted by NoICIC, ICIC Pow. and ICIC Loc., respectively). In order to compare their effect on FBS and MBS performances, many power setting parameter values and fixed transmit powers are tested. We evaluate the global FMT-MMT performance trade-off, i.e., the 5%-ile FMT spectral efficiency over all FBSs as a function of the 5%-ile MMT spectral efficiency over all outdoor MMTs. We consider typical measurement errors, namely 10 m RMSE for the location-based approach and 5 dB (resp. 3 dB) RMSE on FBS (resp. MMT) power measurement. Three FBS densities are considered: 25, 125 and 250 FBSs per km2 , i.e., 22, 109 and 217 FBSs per MBS sector, respectively. We observe in Fig. 2 non-negligible femto-femto interference when the FBS density increases since the maximum FBS performance strongly depends on the FBS density. Figure 2 also shows that the proposed location-based power setting exhibits a better FMT-MMT performance trade-off than the two other approaches, the relative gain increasing with the FBS density. We note that, for FBS, the localization is done once and for all and a good accuracy can be reached even for indoor FBS. For MMT positions, only high quality location information (e.g., with GNSS, using a quality metrics) can be stored in the database. However, an interesting aspect is the sensitivity to localization errors. Figure 3 shows, for the three approaches and in medium FBS density, the FMT celledge spectral efficiency for a 10 % degradation of MMT cell-edge spectral efficiency (i.e., a 0.42 b/s/Hz spectral efficiency) as a function of positioning RMSE. With typical FBS

FBS transmit power approach whereas the proposed locationbased approach still exhibits a 300 % gain over the constant FBS transmit power approach. With 7 dB wall penetration loss RMSE, the location-based approach still outperforms the two other approaches. V. C ONCLUSION

Fig. 3: Localization error effects: Femto performance for 10 % cellular cell-edge decrease with 125 FBS/km2 .

Long-term power setting for femto-macro ICIC can take benefit from positioning. The concept of HIRZ for controlling the macro degradation due to FBS transmission is used, resulting in an equalization of the macro-degradation among FBSs. The positioning information is used in conjunction with a database available in the core network, providing relevant information to each FBS on powers measured by MMTs in its vicinity. This information guarantees efficient power setting. In the simulated 3GPP-LTE context, the proposed power setting relying on positioning and database improves the global FMT-MMT performance trade-off compared to constant FBS transmit power and the FBS power setting based on FBS power measurement proposed in [5] and proves robustness against relatively high positioning error. Compared to the FBS power setting in [5], higher robustness against wall penetration loss error is also observed. ACKNOWLEDGMENT This work has been performed in the framework of the FP7 project ICT-248894 WHERE2 (Wireless Hybrid Enhanced Mobile Radio Estimators - Phase 2) which is partly funded by the European Union. R EFERENCES

Fig. 4: Penetration loss error effects: Femto performance for 10 % cellular cell-edge decrease with 125 FBS/km2 . power measurement RMSE of at least 3 dB, the proposed location-based approach outperforms the simpler FBS power measurement based approach of [5] for positioning RMSE lower than 30 m. For a 20 m RMSE, the FMT cell-edge spectral efficiency is increased by more than 50 % (resp. 10 %) over the FBS power measurement based approach with a 5 dB (resp. 3 dB) RMSE on FBS power measurement. Compared to the constant transmit power approach, it is increased whatever the positioning accuracy (RMSE lower than 100 m) by up to 400 %. Considering now the sensitivity to wall penetration loss error and assuming typical 10 m, 3 dB and 5 dB RMSE for positioning, MMT power measurements and FBS power measurements, respectively, and medium FBS density, Fig. 4 confirms the lower sensitivity of the proposed location-based approach compared to the FBS power measurement based approach. For 3 dB wall penetration loss RMSE, the power measurement based approach does not outperform the constant

[1] V. Chandrasekhar, J. G. Andrews, and A. Gatherer, “Femtocell networks: A survey,” IEEE Commun. Mag., vol. 46, no. 9, pp. 59–67, Sep. 2008. [2] D. L´opez-P´erez, A. Valcarce, G. de la Roche, and J. Zhang, “OFDMA femtocells: A roadmap on interference avoidance,” IEEE Commun. Mag., vol. 47, no. 9, pp. 41–48, Sep. 2009. [3] V. D’Amico, A. Dekorsys, A. Gouraud, S. Kaiser, B. L. Floch, P. Marsch, and H. Schneich, “ARTIST4G: A way forward to the interference problem in future mobile networks,” in Future Network and Mobile Summit 2010 Conference Proceedings, Jun. 2010. [4] G. Fodor, C. Koutsimanis, A. R´acz, N. Reider, A. Simonsson, and W. Muller, “Intercell interference coordination in OFDMA networks and in the 3GPP long-term evolution system,” Journal of Communications, vol. 4, no. 7, pp. 445–453, Aug. 2009. [5] J. Guillet, L. Brunel, and N. Gresset, “Downlink femto-macro ICIC with blind long-term power setting,” in Proc. IEEE Personal, Indoor and Mobile Radio Communications, PIMRC, vol. 22, Toronto, Canada, Sep. 2011, pp. 72–76. [6] 3GPP, “TDD Home eNode B (HeNB) radio frequency (RF) requirements analysis,” 3GPP TSG-RAN - E-UTRA, Tech. Rep. 36.922 V9.0.0, Apr. 2010. [7] V. Chandrasekhar, M. Kountouris, and J. G. Andrews, “Coverage in multi-antenna two-tier networks,” IEEE Trans. Wireless Commun., vol. 8, no. 10, pp. 5314–5327, Oct. 2009. [8] S. Plass and R. Raulefs, “Combining wireless communications and navigation - the WHERE project,” in Proc. IEEE Vehicular Technology Conference, VTC, vol. 68, Calgary, Canada, Sep. 2008. [9] 3GPP, “Further advancements for E-UTRA physical layer aspects,” 3GPP TSG-RAN - E-UTRA, Tech. Rep. 36.814, Mar. 2010.

A.8

Location-aided HeNB SON System

This appendix includes the following technical report: • D. Conde¸co, A. Gomes, W. Lages, “HeNB Self-Organised Network System”, Technical Report, Aveiro, Portugal, October 2013.

173

HeNB Self-Organised Network System Technical Report Diogo Condeço Instituto Telecomunicações Campus Santiago 3810-193 Aveiro, Portugal Email: [email protected]

24th July 2013 Abstract Increasing demand on mobile networks lead operators to use other means for extending their capacity and coverage than the traditional evolved Node-B. Such solutions include the use of Home evolved NodeB as access points to the operator’s network, which can be freely placed by users. The existence of more cells in the network produces intercellular interference problems between cells, specially when referring to cells without any control in terms of network planning. This causes a decrease on both the system capacity and coverage resulting on a lower QoS. Assuming knowledge about the cells position and configuration parameters, which the network has access to, it is possible to minimise the inter-cellular interference problems with a careful study of the best configuration parameters for the each cell at the given location, even thought it cannot be predicted "a priori". Within this report we address the research carried out on a Self-Organise Network System which is able to configure Home evolved Node-B. The system is based on a dedicated radio network planning for a new cell considering its position in the existing network. The planning procedure takes into account all the relevant information surrounding the cell to obtain the optimal results. A final evaluation of the system is then carried out

1

using monitor capabilities embedded on the cells, which report back the data to the network for evaluation purposes.

1

Introduction

Wireless networks face constant tests to their limitations in terms of capacity and coverage demands. Users tend to spend more and more time on-line with higher volumes of transferred data. On top of this, while moving, users seek for higher coverage areas to keep their "on-line" status, being available as long as possible. At last, the low number of users in remote locations does not generate enough revenues to overcome the high operational costs of this oversized network, highlighting the need for new solutions. Following this need, operators start to adopt other solutions to extend their networks for better QoS, user experience and lower operational costs. In this context appears a new type of cells - Home evolved Node-Bs (HeNBs). HeNBs are small cells, comparable to Access Points in the WiFi technology, that provide radio access to the operator’s network, acting as normal Base Stations (BSs) apart some performance differences. The interface between the core network and the users’ equipment (UEs) is routed through this cells instead of the normal eNBs, which connect to the core through high speed internet connections. HeNBs are characterised for having a lower transmitting power and processing capabilities, which reduce substantially the physical dimensions of the device, the energy consumption and the cooling requirements, allowing for an easier placement an mobility of the device and reducing its operational costs. These limitations also reduce the number of users that can be connected to the cell both in an idle or active communication. Such solution is, however, scalable, meaning that it is possible to overcome the reduction in the number of users by deploying more cells. Furthermore, the number of users can be ultimately influenced by the internet connection speed through which the cell communicates with the network. The limitations on the transmitting power help the reduction of Inter-Cell Interference (ICI) problems, but in a crowed environment that may not be enough. With a limited spectrum window available and multiple cells operating in a confined spatial area it may not be possible to grant a carrier for each one of them. Every time a carrier is re-used there will be an interaction between them as the ICI problems increase and the Signal to Interference plus Noise Ratio (SINR) deteriorates, consequently decreasing the coverage 2

area. These problems are unavoidable but predicted and minimised in advance by a radio network planning that operators perform before deploying eNBs. While this may be valid for eNBs and even for HeNBs deployed by the operators, it is not a solution for HeNBs contracted by users, for which the operator has minimal control and knowledge over. A user can easily place a HeNB device in a functional network and jam it, simply because it is operating at the same carrier of another cell, in a close by location. Since these are devices with a certain freedom in terms of mobility, it is not possible for the operator to predict where it is going to be placed, and make that regular radio planning study of the environment, mainly because its position is unknown. There are already some solutions in the market that address this problematic by using monitoring capabilities embedded in cells, but as the attenuation effects over the signals are not constant the retracted sense of the environment may not be a reliable representation of the environment. Furthermore, there can also be some temporal variations on the sensed spectrum which may lead to false assumptions on the signals levels of the cell. These are usually passive methods which do not allow for interaction with other cells for security reasons leading to a control over the network by the first devices configured in a given area.

2

System Description

To configure a new cell the system executes five actions (Fig.1) to gather the relevant information, process the data, configure the cell, and evaluate the final solution in the real scenario.

2.1

Network’s Information Identification

A vital information for the system is the location of the new cell, since it is the starting point for the entire process. Once connected to a high speed internet connection the system will have to be able to report back accurate information about its location, whether it is placed in an outdoor or indoor environment. It is this location that allows to determine the relevant information that is required for the entire process. The relevance of the information is a direct consequence of the new HeNB’s location, and consequently its surroundings. The location, reported back to the system Fig.1(1.), allows to identify close-by cells (both MBSs and other FBSs), and from there the 3

key parameters of each of them, like: maximum transmitting power, carrier, antenna gain, antenna tilt, antenna direction, etc. Hence, a need for the presence of a good positioning system, able to provide accurate location estimations for indoor or outdoor environments, depending on where the cell is deployed. An error in the location may lead to a wrong identification of the cells (neglecting key information about the scenario), or to a wrong recreation of the scenario. The identification process filters irrelevant information to the system, since in large scale networks it can be huge, which only would delay the process without adding any value to the system.

2.2

Radio Network Planning

The previous data is the starting point for the simulations carried out by a Radio Network Planning Tool Fig.1(2.). In this stage a software tool uses that data to recreate a model of the network disposal as accurate as possible. The accuracy is a direct consequence of the location systems used to obtain the cells position. Any location errors made in the previous stage will propagate to this step and throughout the system. The tool evaluates the geographical characteristics of the environment and uses further ahead described models for the signal attenuation calculation. Using the position of the new HeNB, the system gathers the relevant information to recreate the scenario, namely: • Other cells location, which can be either eNBs or HeNBs. It is imperative to assess also eNB cells, to prevent cases where the carriers are shared between HeNB and eNB; • Cells carriers, to access if there are free carriers, or which one is the most convenient to use in the new cell; • Cells maximum transmitting power, which impose the carrier effect in the new cell location. Once this information is obtained it is possible to recreate the scenario to be processed by the RNP tool. Thus, the system takes the collected data, recreates the practical scenario in a computational model, and determines the best carrier and maximum transmit power that the new cell can use. These are the parameters which are going to be configured in the new cell, in stage 3. It may also occur, in some cases, that nearby HeNB need to see their power decreased, so it is also in this stage that those adjustments are estimated. 4

These kind of adjustments may be essential for the correct operation of the network. Stage 4 and 5 correspond to the verification of the results where the system validates the obtained solution, where the monitoring is made according with [1]. First (stage 4), the new cell checks if the estimated values allow it to present the expected SINR, and thus, the QoS intended. Finally, other cells (including eNB), proceed in a similar way to evaluate the new cell’s effect in the network, and more specifically in the service they provide. During the entire process there is no kind of interaction with the eNBs configuration process or values modification. Those are macro entities which are configured and planned when the network is deployed. Interfering with such configuration at this point would cause serious coverage and/or ICI problems, seriously affecting the network performance.

2.3

Configuration

The optimal values obtained by the system are sent to the the corresponding cell, which will start using those parameters. The parameters can be a valid carrier and transmitting power, or a notification preventing the cell to be turned on, in a scenario which its placement would be highly adverse for the existent network. Once the configuration information is received in the new HeNB, it should have the capability of auto-configuring itself and start operating at the corresponding carrier with a maximum transmitting power equal to the optimal value. If there was not an error in the location leading to a wrong choice of the optimal values to be configured, the cell should be performing as expected apart from some small variations characteristic of mobile communications, like the users’ movements, building constrains, etc. These effects will ultimately manifest in the new cell coverage, and not by any means of interference in the existent cells, when compared with the expected results.

2.4

System Evaluation

An evaluation is carried out by the system, in this case by the new HeNB and the other cells identified as being in a closely neighbourhood. Firstly the new HeNB evaluates if the solution results are accordingly with the expected, by evaluating the SINR at its location, and reporting it back to the system (Fig.1-4.). Such analysis, allows to decide if there is a real gain with the introduction of a new cell, if a new re-organisation is required, or if the new 5

cell is irrelevant for the network operation and should be turned off. With the same purpose, other cells monitor the network to evaluate the effects caused by the presence of the new cell. Once again, this data is sent back to the system (Fig.1-5.) to be evaluated and correctly dealt with, either to complete the process, re-call a configuration process, or to turn off the cell. The monitor process is used to monitor the entire spectrum since the monitor capabilities allows cells to monitor carriers which they are not configured on, so these can be used to access the network performance by measuring the SINR in different locations. The possibility of moving the cell is always present, if the configuration process takes into account that it should be executed every time it is powered on, this scenarios are usually predicted because there is also the need to unplug the cell from the energy source. For small distances there are no important changes expected for the configuration, but most certainly the user will not unplug the HeNB anyway, so there is no reason to schedule a new configuration process.

Figure 1: System Block Diagram

6

3

RNP

To implement the various algorithms, responsible for the identification of the optimal parameters to configured on the new system, a in-house RNP tool was used. This software [2] is implemented in Matlab and is used for simulations on mobile networks to test networks planning, optimisations, smart solutions for mobile networks, etc. It has been used in various research projects like: C2POWER, Cogeu, Green-T, amongst others. It is implemented in a modular configuration to allow an easy integration of new solutions/tests. For this particular project, two modules (as the follow descriptions highlight) were developed: one responsible for the carrier identification; and another to control the maximum transmitting power.

3.1

Carrier Selection Procedure

The first procedure in the process addresses the choice of the carrier to be configured in the new HeNB. Given an array of available carriers to the operator for that location, the system evaluates them and determines the one with lower SINR in the scenario. By evaluating the signal distribution in that area, it is possible to obtain the carrier with the lowest average amount of interference, which leads the minimal ICI problems for the given region where the cell is going to be deployed. The area to be considered can be configured according with the scenario, namely network parameters and restrictions, environmental conditions, etc. Operators may opt to use dedicated carriers for HeNBs, in which case the eNB effects on the HeNBs coverage areas would come out minimised, or to share them resulting on possible interferences between them. Either way, the system is prepared to deal with both scenarios. Interference problems can come from nearby cells, but also from UEs that are connected to more remote cells which by themselves do not present a serious threat for the new cell coverage. Hence the need to address no only direct interferences but also possible problems caused by devices that may be in a further away neighbourhood plausible to cause interference problems. For that reason the system addresses not only the effect of the first ring of cells surrounding the new one, but also looks more deep into further away cells where active communications can influence the new cell. Once again, this is a two-way precaution, since it ensures the integrity of the results for the new cell, but also assures the preservation of already deployed means on the scenario, being those other cells or users 7

devices. Such procedure always reports back to the power control algorithm the best carrier, even if the obtained results are not sufficient to achieve the operators standards in terms of QoS for the user. Thus, we assure that a opportunity for a possible re-arrangement of the network exists, and we test if it is possible to accommodate the new cell by minor configuration tweaks on other cells, instead of rejecting ä priori" new cells.

3.2

Power Control Procedure

A module to find the maximum transmitting power on the HeNB was developed based on the measurement of the interference interactions with neighbour cells. Existent cells, either owned by users or the operator prevail over new HeNBs, and should not see their service noticeable affected in a negative way, unless their service is way above the minimal values. Example of such scenario is a cell transmitting at its full power in a indoor urban environment, where it is expectable that its useful coverage area is substantially lower. This means that there are some limits the existing cells have to keep achieving in order to a new HeNB can be connected, but it also can give up some transmitting power to allow the allocation of more cells into the network. Thus, the first test on this module is to determine the action to take, depending on the faced situation, the system tests if it is possible to implement the new cell (which means the minimal requirements are valid), or if a decrease on the transmitting power. By addressing this initial test the systems determines which action has to be made: • Increase maximum transmitting power - to obtain the maximum coverage area of the cell possible, without degrading the already deployed means. This action happens whenever the minimum value of the SINR for the new HeNB is achieved, and keeps running until the new cell is at its maximum transmitting power, or it starts to significantly interfere with other cells. • Decrease of power in neighbour cells. The highest jammer of the new HeNB are successively evaluated to test for a possible decrease of maximum transmitting power in the new cell. If possible, the systems decreases the transmitting power until the new cell can achieve the minimum configuration parameters. Each existing cell has to maintain a minimum SINR at defined distance of the existing cell in direction to the new one. Only then it is possible to decrease the transmitting 8

power of an existing cell. If a single decrease is not sufficient, the system keeps to test de existent HeNBs for possible reduction in the maximum transmitting power, until it comes to one of two conclusions: or the cell is able to be configured, which in that case will try to increase its maximum transmitting power; or it is no plausible to install the new cell without decreasing the QoS of the other cells, and in which case, it has to be turned off. For a case where the new cell is not installed, the existent cells that saw their maximum transmit power affected, by the test for the new HeNB, will keep their settings as they were in the beginning of the process.

Figure 2: Power Control Algorithm 9

4 4.1

System Evaluation Testing scenario

The simulation scenario is based on a LTE system operating at the 2.6GHz sub-band, and was chosen according with other partners simulations to give more coherence to the results comparisons within the project. MBSs are deployed with an inter-site distance of 1732m according with 3GPP case 3 [3]. A total of nineteen cells are is evaluated in a tri-sectorised arrangement - three cells per site (Table 1). Has stated before the simulation scenario and tests are carried out on a PTIN’s RNP tool. The propagation models implemented on the tool were the 3GPP LTE-A femtocell model for indoor-to-indoor environments, while in a indoor-to-outdoor scenario the attenuation is obtained from the ITU-UMi NLOS model[3]. Using such approach (double slope) like this, allows a more realistic recreation of the attenuation effects for indoor and outdoor environments. HeNBs were installed on a single central ring of eNBs to avoid tedious and extend periods of simulation, since the simulation scenario is somehow extensive both in terms of entities and spatial area. Furthermore, the simulation of the process in other locations would not bring any added value to the results and system analysis, as it is mere replication of the results through other locations, since the distance between HeNBs in different rings of HeNBs would highly minimise the interference interactions between them. The expectation in terms of available carriers for HeNB’s use are low, since they most certainly be reserved for the exclusive use on eNBs due to an highly crowded spectrum. Thus, we carried out simulations for two distinct scenarios: one using two carriers for the HeNBs cells; and the other considering an availability of five carriers. All the simulations carried out to evaluate the system consider that there is no co-operation of different type of cells in the same carriers, meaning that the carriers of the eNBs are different from the ones for HeNBs. This assumption was made to prevent high data volume in the simulations, however the system was defined to support shared carriers, in which case, the influence of the eNBs would also have to be taken into account. A considerable number of HeNBs (60) were deployed to see the system operating in crowed environments, and to promote the occurrence of interference interactions between cells. All HeNBs are installed on a indoor environment represented by an indoor propagation model up to a six meters radius, which is then replaced by an outdoor propagation model for radius higher than that value (Table. 2). 10

Number of Sites eNB Maximum Power eNB Antenna Type

Transmitting

Antenna Gain Path Loss Model [dB]

19 43dBm Directional Tri-sectorised Antenna Array 15dB 128.1 + 37.6 ∗ log10 (d), d in km

Table 1: eNB Scenario Information Number of Sites eNB Maximum Transmitting Power eNB Antenna Type Antenna Gain Indoor Path Loss Model [dB] Outdoor Path Loss Model [dB]

60 20dBm Omni-Directional 5dB 37 + 30 ∗ log10 (d), d in m 37 − 6.7 ∗ log10 (τ ) + 36.7 ∗ log10 (d), d in m

Table 2: HeNB Scenario Information

5

Results

To decide the number of carriers to use, some preliminary simulations were executed to access the number of carriers to use in the simulations. As stated before, the system is prepared to use a restricted spectrum window to allocate the HeNBs, and it was important to know which simulations would be interesting to analyse. After performing such research we realised three important facts that lead us to choose de two carrier scenario and the five carrier one. First, two carriers is the lowest number to ensure that the system executes both modules. With only one carrier the system would not have a carrier to choose from and it would directly proceed to a tuning on the transmitting power parameters. Then, when using four carriers, we noticed that users would have have about 0% probability (Fig.3) of getting a call blocked. Finally, when the carriers used increased to five, the cell vacancy still increases about 5%, and to get another 5% off-load from the cells we have 11

to increase that value up to 8 carriers - Fig.4. When comparing the gain vs the cost we realised that an operator would spend 62.5% more money on spectrum (assuming that it is not yet rented) to obtain 5% more capacity on the network, which seems highly unlikely to happen. For those stated reasons, we decided to go with a minimal (2 carriers) and a cost/efficiency optimal solution (5 carrieres) for the simulations to evaluate our system.

Figure 3: Average Call Block Rate vs Number of Carriers.

5.1

Figure 4: Cell Occupancy vs Number of Carriers.

System with 2 dedicated carriers for HeNBs

Fig.5 and Fig.6 present the results for the coverage of each cell for the two carrier test case. Each color represents de entity with coverage responsibility in such area. It doesn’t not necessary mean that other cells do not have coverage in a specific point, but which is the cell with best SINR on that specific point and thus, the main provider in that region.

12

Figure 5: Network Coverage without SON.

5.2

Figure 6: Network Coverage with SON.

System with 5 dedicated carriers for HeNBs

Fig.7 and Fig.8 represent the same test, but now for the five carrier case. Again the colors highlight the cell with main responsibility in terms of coverage for that area.

Figure 7: Network Coverage.

Figure 8: Network Coverage with SON.

13

5.3

Coverage Statistics

Figure 9: HeNB coverage enhancements.

Figure 10: Overall Network Coverage enhancement. 14

2 Carriers 5 Carriers

Coverage Area HeNB Total HeNB Total

Without SON 4093.13 245588 4093.13 314678

With SON 4695.02 281701 4695.02 357602

Improvement 14.70% 13.64%

Table 3: Coverage Statistics Results.

5.4

Result Analysis

The cell’s coverage is represented by a coloured region, for which each cell has better SINR than the other cells in the scenario. To better understand this representation, each colour represents the region where each cell is the primary access entity to the network, since it has a better SINR, and as a consequence is able to provide better services. An actual increase of the coloured regions represent an increase of the SINR in that region of the given cell, either by an increase on the transmitting power or a decrease of interferences from other cells. Furthermore, as the various eNBs in the scenario are operating in a different group of carriers than the HeNBs, there is no interaction effect between them. Since the interferences on this analysis occur only between HeNBs, and the coverage on these areas is assured by the eNBs, once this effect is minimised that areas are then covered by the HeNBs. A general look over an average HeNB (Fig.9) reveals that in both cases (for two and five dedicated carriers) the cells coverage increases. This increment, on the HeNBs coverage area, is conquered from the eNBs through a reduction on inter-cell interferences, resulting on an increment of the SINR of the closest HeNB. Furthermore, user terminals located in the new part of the coverage area, are going to communicate with the network core through the corresponding HeNB, instead of the previous eNB. Even though the users equipment connection with the network core tends to be established through HeNBs devices that have seen their coverage area extended, the existing eNBs are still able to accommodate users, since their signal quality remains intact. All the gain is on the HeNB side, which allows eNBs to maintain their services, and if it is the case still accommodate users, for example, on an overload of the HeNBs capacity. Fig.10 shows a clear improvement of the network system coverage using the presented SON system over a traditional random configuration of HeNBs. 15

Using two carriers the system presents approximately 14.7% more coverage when the SON system is applied. Whereas in the five carrier scenario the improvement is lower (approximately 13.6), but still noticeable. As expected, the results on the increased coverage area, for a five carrier scenario, are lower since an higher number of carriers actually minimises itself the probability of inter-cell interference. Thus, when the carriers reuse factor increases, the probability of two cells in the close vicinity of each other being using the same carrier decreases. Furthermore, an increase of the number of cells in the scenario would counteract this effect, and increment the inter-cell interference problems.

6

Summary

After the simulations that the SON system presented in this paper was subjected to, it is visible the effect of planning the configuration parameters of a HeNB against an approach which doesn’t gives any attention to that detail. The cells coverage comes with an area increase of about 15%, for the test scenarios. The HeNB coverage area visibly increases in both cases (two and five dedicated carriers), being this the area where this cells act as primary access points to the network. Thus, this represents an 2.2% of total coverage area that is routed through HeNBs instead of the operators eNBs, for these specifics scenarios. Off-course this value is highly dependent on the number of HeNBs used, but considering the free areas where more HeNBs could be deployed it is highly expectable to see this value raise, off-loading even more the eNBs’ network.

Acknowledgement The research work presented on this technical report was carried out under the scope of the FP7 project ICT-248894 Wireless Hybrid Enhanced Mobile Radio Estimators (WHERE2) which is partially funded by the European Union.

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References [1] Femto Forum. Lte network monitor mode specification. Femto Forum Technical Paper, 1.01, 2010. [2] COGEU FP7 ICT-2009.1.1. Dynamic radio resource management algorithms for an efficient use of tvws. Deliverable, 6.1:72–74, 2010. [3] I.P. Freely. A small paper. The journal of small papers, -1, 1997. to appear.

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