Mathematical optimization and signal processing techniques for cooperative wireless networks

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This item was submitted to Loughborough University as a PhD thesis by the

author and is made available in the Institutional Repository

(https://dspace.lboro.ac.uk/) under the following Creative Commons Licence

conditions.

For the full text of this licence, please go to:

http://creativecommons.org/licenses/by-nc-nd/2.5/

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Mathematical Optimization

and Signal Processing Techniques for

Cooperative Wireless Networks

by

Georgia Bournaka

A Doctoral Thesis submitted in partial fulﬁlment of the requirements for the award of the degree of Doctor of Philosophy (PhD), at Loughborough University under a Joint PhD Programme with National Center for Scientiﬁc Research “Demokritos”, Greece.

November 2013

Advanced Signal Processing Group,

School of Electronic, Electrical and Systems Engineering, Loughborough University, Loughborough

Leicestershire, UK, LE11 3TU.

c

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CERTIFICATE OF ORIGINALITY

This is to certify that I am responsible for the work submitted in this thesis,

that the original work is my own except as speciﬁed in acknowledgements

or in footnotes, and that neither the thesis nor the original work contained

therein has been submitted to this or any other institution for a degree.

... (Signed)

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Abstract

The rapid growth of mobile users and emergence of high data rate multime-dia and interactive services have resulted in a shortage of the radio spectrum. Novel solutions are therefore required for future generations of wireless net-works to enhance capacity and coverage. This thesis aims at addressing this issue through the design and analysis of signal processing algorithms. In particular various resource allocation and spatial diversity techniques have been proposed within the context of wireless peer-to-peer relays and coordi-nated base station (BS) processing.

In order to enhance coverage while providing improvement in capacity, peer-to-peer relays that share the same frequency band have been consid-ered and various techniques for designing relay coeﬃcients and allocating powers optimally are proposed. Both one-way and two-way amplify and for-ward (AF) relays have been investigated. In order to maintain fairness, a signal-to-interference plus noise ratio (SINR) balancing criterion has been adopted. In order to improve the spectrum utilization further, the relays within the context of cognitive radio network are also considered. In this case, a cognitive peer-to-peer relay network is required to achieve SINR bal-ancing while maintaining the interference leakage to primary receiver below a certain threshold.

As the spatial diversity techniques in the form of multiple-input-multiple-output (MIMO) systems have the potential to enhance capacity signiﬁcantly, the above work has been extended to peer-to-peer MIMO relay networks. Transceiver and relay beamforming design based on minimum mean-square error (MSE) criterion has been proposed. Establishing uplink-downlink MSE duality, an alternating algorithm has been developed.

A scenario where multiple users are served by both the BS and a MIMO relay is considered and a joint beamforming technique for the BS and the MIMO relay is proposed. With the motivation of optimising the transmis-sion power at both the BS and the relay, an interference precoding design is presented that takes into account the knowledge of the interference caused by the relay to the users served by the BS.

Recognizing joint beamformer design for multiple BSs has the ability to reduce interference in the network significantly, cooperative multi-cell beam-forming design is proposed. The aim is to design multi-cell beamformers to maximize the minimum SINR of users subject to individual BS power constraints. In contrast to all works available in the literature that aimed at balancing SINR of all users in all cells to the same level, the SINRs of users in each cell is balanced and maximized at different values. This new technique takes advantage of the fact that BSs may have different available transmission powers and/or channel conditions for their users.

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Statement of Originality

The contributions of this thesis are mainly on the development and analysis

of novel coordinated resource allocation and spatial multiplexing techniques

for wireless networks. The following aspects of this thesis are believed to be

originals:

• Spatial diversity and power allocation techniques for peer-to-peer relay

networks have been proposed in Chapter 3. The novelty of the work

in this chapter is the consideration of user fairness in the form of

signal-to-interference and noise ratio (SINR) balancing for the design

of peer-to-peer relays as supported by [4]-[7]. The algorithms were

ﬁrst proposed for multiple one-way amplify and forward (AF) relays

[4] and then it has been extended for multiple two-way AF relays

[5]. An SINR balancing technique for underlay cognitive peer-to-peer

relay network, where the ratio between the achieved SINR and the

target SINR is balanced for all secondary users while satisfying the

primary users’ interference and total transmit power constrains was

also proposed [6]. The SINR balancing algorithm has been extended

to a two-way relay based cognitive radio (CR) relay network [7].

• A spectrum sharing peer-to-peer relay network has been proposed in

Chapter 4, where multiple source nodes with multiple antennas

com-municate with their desired destination nodes with multiple antennas

through a multiple-input and multiple-output (MIMO) relay. Initially

the duality between uplink and downlink peer-to-peer MIMO

chan-nels with any number of antennas at each node has been established

to demonstrate that the mean square error (MSE) of a downlink

peer-to-peer network can be achieved in a virtual uplink network with the

same total network transmission power. Using this MMSE duality

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Contents vi

iterative algorithm that optimized the source, relay and receiver

pro-cessing matrices. The novelty of this work is supported by [1].

• A new precoder design technique for a BS serving a number of users

directly and another set of users through a MIMO wireless relay has

been proposed in Chapter 5. The novelty of the work is the

exploita-tion of the knowledge of the interference caused by the relay to the

users served by the BS to perform more eﬃcient interference

mitiga-tion which results into a lower overall network power consumpmitiga-tion.

The novelty is supported by [2].

• A coordinated multi-cell beamforming technique has been proposed

for SINR balancing under multiple BS power constraints in Chapter

6. Instead of balancing SINR of all users in all cells to the same level

as considered in the literature, a novel approach to balance SINR of

users in various cells to diﬀerent maximum possible values has been

proposed. This has the ability to allow users in cells with relatively

more transmit power or better channel condition to achieve a higher

balanced SINR than that achieved by users in the worst case cells. This

multi-level SINR balancing problem was solved using SINR constraints

based SINR balancing criterion and subgradient method. The novelty

of this work is supported by [3].

Journal Papers

1. G. Bournaka, K. Cumanan, S. Lambotharan and F. Lazarakis,

“Trans-mitter receiver and relay optimisation for spectrum sharing

multiple-input and multiple-output peer-to-peer users”, IET Signal Processing,

vol. 7, no. 5, pp. 411-419, July 2013

2. G. Bournaka, J. Tang, S. Lambotharan and F. Lazarakis, “A

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Contents vii

at the Base Station”, IEEE Communication Letters, vol. 17, no. 6,

pp. 1176-1179, June 2013.

3. G. Bournaka, Y. Rahulamathavan, K. Cumanan, S. Lambotharan and

F. Lazarakis, “Cooperative Multicell Beamforming with Per

Basesta-tion SINR Balancing”, submitted to IEEE TransacBasesta-tions on Wireless

Communications.

Conference Papers

4. G. Bournaka, K. Cumanan, S. Lambotharan, J. A. Chambers and F.

Lazarakis “An SINR balancing based multiuser relaying scheme”, in

Proc. IEEE International Conference on Communication Technology

(ICCS), Singapore, pp. 274-278, 17-19 November 2010.

5. G. Bournaka, K. Cumanan, S. Lambotharan and F. Lazarakis, “An

Iterative Semideﬁnite and Geometric Programming Technique for the

SINR Balancing in Two-Way Relay Network”, IEEE Global

Commu-nications Conference (Globecomm 2011), pp. 1-5, Houston, TX, 5-9

December 2011.

6. G. Bournaka, K. Cumanan, S. Lambotharan and F. Lazarakis, “SINR

balancing techniques for a cognitive radio relay network with multiple

peer-to-peer users”, IEEE International Conference on

Communica-tion, Networks and Satellite (ComNetSat), pp. 108-112, Bali,

Indone-sia, July 2012.

7. G. Bournaka, K. Cumanan, S. Lambotharan and F. Lazarakis, “An

SINR Balancing Technique for a Cognitive Two-Way Relay Network”,

IEEE Vehicular Technology Conference (VTC Fall), pp. 1-5, Quebec

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Acknowledgements

I wish to thank my supervisors Professor Sangarapillai Lambotharan and

Professor Jonathon Chambers at Loughborough University and Dr. Fotis

Lazarakis at Demokritos for their support and supervision during my PhD

study. In particular, I am very grateful for Professor Lambotharan for his

excellent supervision, valuable insight and guidance. His knowledge and

intuition has opened my way to a new ﬁeld.

I would like to thank Loughborough University and Demokritos for

pro-viding me with the training and facilities to perform this research. I am very

grateful to the Scholarship provided by these two institutions.

I would like to express my appreciations to many members from

Ad-vanced Signal Processing Group, who have generously helped me to develop

my knowledge through wide-ranging discussions. I would like to extend my

appreciations to my friends, in particular, Foteini, Vivi, George and

Anas-tasia, for making my stay at Loughborough pleasant.

I wish to take this opportunity to thank my parents Dimitra and Vassilio

Bournaka to whom I dedicate this thesis as well as my sister Soﬁa for their

moral support throughout my studies.

Georgia Bournaka November, 2013

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Abbreviations

AF Amplify and Forward

BER Bit Error Rate

BS Base Station

CDMA Code Division Multiple Access

CR Cognitive Radio

CSI Channel State Information

dB Decibel

DF Decode and Forward

GP Geometric Programming

ICI Inter-cell Interference

ISI Inter Symbol Interference

KKT KarushKuhnTucker

MIMO Multiple Input Multiple Output

ML Maximum Likelihood

MMSE Minimum Mean Square Error

MSE Mean Square Error

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Abbreviations x

PU Primary User

QoS Quality of Service

SDP Semi Deﬁnite Programming

SINR Signal to Interference plus Noise Ratio

SNR Signal to Noise Ratio

SOCP Second Order Cone Programming

SU Secondary User

TDD Time Division Duplex

Tr Trace

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List of Symbols

Scalar variables are denoted by plain lower-case letters, (i.e., a), vectors by

bold-face lower-case letters, (i.e., a), and matrices by upper-case bold-face

letters, (i.e., A). Some frequently used notations are as follows:

E{·} Statistical expectation (·)T Transpose (·)H Hermitian transpose |.| Euclidean norm ||.||F Frobenius norm (.)−1 Matrix inverse 1M M × 1 vector of ones 0M M × 1 vector of zeros

Diag(·) Diagonal matrix with the arguments as the diagonal elements

Tr{·} Trace operator

⊙ Schur-Hadamard product

I Identity matrix

A ≽ 0 Positive semideﬁnite matrix

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List of Symbols xii

⊗ Kronecker product

Vec(.) Forms a vector by stacking the columns of a matrix

[A]ij (i, j)th element of A

[a]i ith element of a

x∼ N(µ, σ2) Random variable x is drawn from a Gaussian

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List of Figures

1.1 A visual representation of the congestion in radio spectrum

allocation in the United States of America [3] 2

1.2 Mobile Video Will Generate Over 66 Percent of Mobile Data

Traﬃc by 2017. Source: Cisco Mobile Forecast 2013 [1] 3

1.3 Cisco Forecasts 11.2 Exabytes per Month of Mobile Data

Traf-ﬁc by 2017. Source: Cisco Mobile Forecast 2013 [1] 4

2.1 An example of delay proﬁle 15

2.2 An example of typical fading proﬁle 16

2.3 A receiver beamformer design. 19

2.4 A transmitter beamformer design. 24

2.5 A MIMO system with Mt transmit antennas and Mr receive

antennas. 28

2.6 Transmit precoding and receiver shaping. 29

2.7 Parallel decomposition of the MIMO channel. 30

2.8 Water ﬁlling power allocation 31

2.9 Relay network 33

2.10 A two-hop MIMO AF relay network 36

2.11 A two-hop MIMO AF relay network 38

2.12 (a) Four-time slot two-way relaying scheme. (b) Three-time

slot TDBC scheme 42

2.13 Two-time slot MABC approach 42

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LIST OF FIGURES xiv

2.14 Joint Transmission 46

2.15 Coordinated Beamforming 48

3.1 A relay network of d pairs of nodes and R relay nodes. 55

3.2 SINR histogram. SINR is shown in linear scale 63

3.3 The mean SINR versus the maximum allowable transmit power

Pmax(Watts) at the relays for a network with 3 relays without

controlling the power usage for each user. 63

3.4 The mean balanced SINR versus the maximum allowable

trans-mit power Pmax at the relays for a network with 3 relays. 64

3.5 The mean SINR versus diﬀerent number of relays for a

net-work with maximum allowable transmit power Pmax=2 Watts. 64

3.6 A relay network of d pairs of nodes and r relay nodes, all

single-antenna units. 66

3.7 The mean SINR versus the maximum allowable relay transmit

power Pmax at the relays for a network with 5 relays. 75

net-work with maximum allowable transmit power Pmax=5 75

3.9 The two-way multi-antenna relay channel with multiple users 77

power PRmaxat the relays for a network with 2 users on both

sides, 4 relays, equipped with 2 antennas each and PImax=0.2W. 86

net-work with maximum allowable transmit power PRmax=5W

and PImax=0.2W. 86

3.12 The two-way multi-antenna relay channel with multiple users 87

power P2at the relays for a network with 2 users on both sides,

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LIST OF FIGURES xv

3.14 The mean SINR versus diﬀerent number of users for a network

with 2 relays, each with two antennas and maximum allowable

transmit power P2=10W and I1R=7W. 96

net-work with maximum allowable transmit power P2=5W and

I₁R=7W. 96

4.1 A MIMO relay with multiple peer-to-peer MIMO users 100

4.2 Multiple peer-to-peer MIMO users and downlink channel. The

combined eﬀect of the original channels and the relay transceiver

matrix is shown with an equivalent set of channels Hlk. 103

4.3 Multiple peer-to-peer MIMO users and the equivalent virtual

uplink channel 104

4.4 The sum MMSE against number of antennas at the relay for a

network with 2 users on both sides equipped with 2 antennas

each. PT=1W, PRmax=10W 117

4.5 The histogram of the ﬁnal sum MMSE due to diﬀerent random

initializations of the relay matrix. The results are shown for

two diﬀerent noise variances 0.01W and 0.001W. 118

4.6 The sum MMSE against SNR of the relay-user terminal link,

averaged over 10 set of random channels. The results are

shown for sum MMSE of both users and sum MMSE of user

1 and user 2. SNR of transmitter-relay link was set to 30dB. 119

5.1 Block diagram of a cellular relay system consisting of one BS,

one MIMO Relay and a number of users served by either BS

or relay. 122

5.2 The total transmission power against various target data rates.129

5.3 The total transmission power against various interference

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LIST OF FIGURES xvi

5.4 The total transmission power against various target data rates

for BS users, averaged over 300 random channel realizations. 132

6.1 Multicell wireless network 136

6.2 Evolution of auxiliary variables a1 and a2 against adaptation

number. 152

6.3 Achieved SINR (dB) of the users in the 1st and 2nd cell versus

the transmit power constraint of the 2nd cell. 157

6.4 Achieved SINR (dB) of the users in the 2nd cell for decreasing

values of target SINRs (dB) for the users in the 1st cell with

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List of Tables

3.1 Algorithmic solution of the SINR balancing problem 62

3.3 The probability of non-one rank solution for various numbers

of users 74

3.5 Optimization of the relays’ beamforming vectors and sources’

power 94

6.1 Algorithmic solution of the SINR Balancing Problem (6.2.1) 141

6.2 Algorithmic solution of the mixed SINR balancing based

beam-forming design (6.3.2) 149

6.3 Complexity of the 1st stage of the algorithm 150

6.4 Complexity of the 2nd stage of the algorithm 151

6.5 Power allocations and the achieved SINRs using the proposed

method. 155

6.6 Target SINRs and the user power consumptions using the

SDP-Based Method. 156

6.7 The achieved balanced SINRs using the extended work of [2]

and our proposed method 161

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Chapter 1 INTRODUCTION

Traditionally, diﬀerent parts of the radio spectrum are licensed exclusively

for diﬀerent applications and services. For example, ultra-low frequencies

in the range of 300-3000 Hz are used for submarine communications and

super high frequencies in the range of 3-30 GHz are used for satellite

com-munications. The current radio frequency (RF) spectrum allocation in the

United States of America is presented in Figure 1.1. As seen in Figure 1.1,

the spectrum is very crowded and there is not much radio spectrum

avail-able for new applications and services. Generally, cellular networks use the

ultra high frequencies in the range of 300 MHz to 3 GHz. This range of

frequency spectrum is very valuable and called a “sweet spot”as it has many

advantages in terms of good transmission capabilities compared to other

parts of the radio spectrum. This is because at lower frequencies, the signals

will experience very good propagation characteristics, however the available

bandwidth is very limited, but at high frequencies, considerably high

band-width is available, but the signals would experience very poor propagation

characteristics. The frequencies in the range of 300 MHz to 3 GHz provide

a good balance between propagation characteristics and bandwidth.

When multiple wireless devices operate in the same frequency band,

they often interfere with each other. Spectrum management is essential for

mitigating interference among various wireless devices. The spectrum

man-agement process is called frequency or spectrum allocation. The current

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atuer EACSP.ER-SATINT-EMOBILEDFIX

RES . E A R T H EXPL . SAT SPAC E R ES EARC H SPA CERES .. This c hart is a g raphic s ingle -point-in-tim e portra yal of the T able o f Frequency A llocations used b y t he FCC and N TIA . As such, it d oes n ot complete

ly reflect all aspects,

i.e., footn otes a nd recent changes m ade to t he T able o f Fre quency A llo cations. There fore , for com plete info rm ation, users should consult the Table to d eterm in

e the current sta

tus of

U.S. allo

cations.

Figure 1.1. A visual representation of the congestion in radio

spec-trum allocation in the United States of America [3]

spectrum management regime is known as “command and control” [4]. In

this approach, the spectrum is licensed by frequency regulators to various

operators or service providers for predeﬁned services for a longer period with

strict rules on the physical layer technologies employed. However, this ﬁxed

spectrum assignment policy is a bottleneck for achieving eﬃcient spectrum

utilization. This has motivated the development of communication

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3

way.

The ﬁrst breakthrough technology that enhanced signiﬁcantly the

utiliza-tion of the radio spectrum can be attributed to cellular architecture, as it

oﬀered high capacity without requiring any major technological changes [5].

This technique exploits the exponential propagation loss and reuse of the

same frequency at spatially separated locations. More speciﬁcally, in this

traditional cellular architecture, the coverage area is divided into smaller

ar-eas called cells and each cell typically consists of a base station (BS), often

located at the center of the cell, providing coverage to mobile stations. This

basic design of the cellular network has not changed considerably in the last

30 years. At the same time the growing adoption of rich multimedia services

and smart phones has led to unprecedented demand for wireless data

capac-ity as seen in Figure 1.2.

The global mobile data traﬃc grew 70 percent in 2012 and it is

ex-Figure 1.2. Mobile Video Will Generate Over 66 Percent of Mobile

Data Traﬃc by 2017. Source: Cisco Mobile Forecast 2013 [1]

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4

Figure 1.3. Cisco Forecasts 11.2 Exabytes per Month of Mobile Data

Traﬃc by 2017. Source: Cisco Mobile Forecast 2013 [1]

increase (Figure 1.3 [1]). This rapid increase of the traﬃc volume and the

subscriber number, has led to the need for more eﬃcient way of utilizing the

radio spectrum.

The possible ways of achieving this includes use of even smaller cells for

delivering suﬃcient capacity. The gains from employing smaller cells come

from higher area spectral eﬃciency [6]. Nonetheless, this approach leads

to degradation of performance, in particular to the users at the cell edge

who suﬀer from both high signal attenuation and severe inter-cell

interfer-ence (ICI). One of the promising approaches to mitigate interferinterfer-ence is array

processing. The use of antenna arrays was an active area of research during

World War II in radar systems [7]. Since 1970, more wider and sophisticated

applications have emerged due to advances in digital signal processors.

One of the antenna array processing techniques that oﬀers high diversity

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5

employed at the transmitter as well as at the receiver. At the receiver side,

the beamformer is designed in such a way to steer beam towards the

direc-tion of the interest and to attenuate signals arriving from other direcdirec-tions.

Beamformer designs can be classiﬁed into diﬀerent categories depending on

various requirements and optimization criteria. The design based on the

lin-early constrained minimum variance beamformer (LCMV) [9], aims to put

a constraint on the response of the beamformer so that signal from the

di-rection of interest is passed with a speciﬁc gain and phase while interfering

signals are attenuated. The weights of the beamformer are chosen to

mini-mize output variance subject to the response constraint. This has the eﬀect

of preserving the desired signal, while minimizing the contributions to the

output due to interfering signals arriving from directions other than the

di-rection of interest. To determine this beamformer, the estimate of the angle

of arrival is required. For uncorrelated sources, algorithms such as

mini-mum variance distortionless response (MVDR) (also known as Capon) and

MUSIC can be used. However, all of these methods i.e. LCMV, MVDR,

MUSIC, require calibration of the array of antennas. In communication

networks, generally pilot signals are available for the estimation of the

chan-nels or to design appropriate receivers directly. Hence, beamformers based

on minimum-mean-square error (MMSE) can be designed with the aim of

minimizing the diﬀerence between a desired response and the actual ﬁlter

output. The optimum set of weights of the beamformer depends on the cross

covariance between the beamformer input signal vector and the training

sig-nal [10]. This category of beamformer is distinguished from the LCMV from

the fact that the direction of the desired signal is not required to be known.

If the requirement is to maximize the signal to noise ratio (SNR), then for

the design of the beamformer, the knowledge of both the desired and noise

covariance matrices is required [11].

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6

receiver but also at the transmitter. The main motivation for the design of

the beamformers at the transmitter is that the deployment of antenna arrays

at the mobiles maybe impractical. In addition, BS’s higher processing power

capability enables easier deployment of the beamformers. The beam-pattern

of each antenna array can be adjusted to maximize the signal in the

direc-tion of interest and minimize the induced interference to other receivers. For

determining appropriate transmit beamformer, either a feedback channel is

required to obtain the channel state information (CSI) from the receiver or

the receiver needs to calculate the transmitter beamforming coeﬃcients and

inform to the BS [12]. In either way, the bandwidth required for

transmis-sion of information back to the BS is considerably high and for this reason,

quantized information is required, for example Grassmannian Beamforming

techniques can be used [13, 14]. The transmit and receive diversity have

been widely adopted in third-generation (3G) code division multiple access

(CDMA) cellular systems [15] as well as in 802.16 worldwide interpretability

for microwave access (WiMaX).

In wireless networks, when a BS aims to transmit signals simultaneously

to multiple users in the same frequency band, directional antennas has to be

employed at the transmitter. This innovative means of using the available

spectrum eﬃciently is called spatial multiplexing and it requires multiple

antennas at the transmitter to steer multiple beams to multiple users. In

this case, it is crucial that the BS allocates power optimally to each user.

Joint power control and beamforming techniques have been proposed in the

literature to satisfy diﬀerent Quality of Services (QoS) criteria. There are

numerous diﬀerent optimizations that are of interest. Some examples

in-clude maximizing total throughput given a constraint on total transmission

power, or minimizing transmission power subject to a set of QoS constraints.

An overview of the problem of minimizing transmission power under a set of

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7

be found in [16]. Another interesting problem that was studied in [17] is the

user fairness based beamformer design. The aim is to maximize the SINR of

the worst case receiver in a multiple user scenario subject to a total power

constraint. This leads every user achieving the same SINR, namely SINR

balancing.

Spectral eﬃciency, coverage and quality of wireless links can be improved

further by employing multiple antennas at both the transmitter and the

re-ceiver [18]. This scheme is known as multiple-input-multiple-output (MIMO)

system. The large spectral eﬃciencies associated with the MIMO systems

is based on the assumption that a rich scattering environment provides

in-dependent paths from each transmit antenna to each receive antenna. The

gain obtained is called spatial diversity gain. Space-time coding to exploit

spatial diversity gain in a point-to-point MIMO channel has been studied

in [19, 20].

Diﬀerent assumptions can be made about the CSI at the transmitter

and the receiver. Consider a MIMO channel with M transmit and N

re-ceiver antennas and assume that the channel side information is not known

at the transmitter. This yields a system of N equations with M unknowns.

The most simple way of estimating the transmitted signal at the receiver,

is to process the received signal through the inverse of the MIMO channel

matrix. Assuming the channel matrix is of full rank and has independent

entries based on the assumption of a rich scattering environment, the

ca-pacity of this scheme scales linearly with min(M, N ) compared to a system

with one antenna at the transmitter and the receiver [21]. The capacity can

be increased further if the channel is known at the transmitter. If the CSI is

known to the transmitter via feedback from the receiver or due to the

reci-procity of channels as in a time division duplex (TDD) system, the MIMO

channel can be decomposed into parallel independent spatial sub-channels.

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wa-8

ter ﬁlling techniques. MIMO is being widely considered for next-generation

cellular systems such as IEEE 802.16/WiMAX and Third Generation

Part-nership Project (3GPP) Long Term Evolution (LTE).

For applications such as cellular telephony, MIMO systems can be

de-ployed in an environment where a single BS must communicate with many

users simultaneously. Multi-user systems with multiple antennas both at the

BS and the users have the advantage to combine the high capacity achievable

with MIMO processing, with the beneﬁts of space-division-multiple access

(SDMA). Adding multiple antennas at each user facilitates the transmission

of multiple parallel data streams to multiple users . The CSI at the

trans-mitter is very useful not only for achieving a high SNR at the receiver but

also to reducing the interference introduced to various users.

For multiuser MIMO systems, two problems can be considered. The

downlink, where the BS attempts to transmit signals to multiple users and

the uplink where a group of users transmits data to the BS. In the uplink

no coordination between users is assumed and for this reason the downlink

problem diﬀers from the uplink problem. In the uplink, the challenge is

for the BS to separate the signals transmitted by diﬀerent users using

ar-ray processing, multi-user detection or other methods. In the downlink, the

main challenge is the multiple access interference caused by the BS due to

simultaneous transmissions of signals. The inter-user interference can be

mitigated by intelligent beamforming techniques or by dirty paper coding

techniques [22].

So far the uplink and downlink transmissions within the context of single

cell based processing have been described. Due to characteristics of

wire-less propagation, signals transmitted from the BS do not conﬁne within the

corresponding cell only. Users will experience interference from other BSs

as well. In the 3rd generation partnership project (3GPP) LTE systems,

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9

managing time or frequency or power resources available for each cell in a

coordinated way [23]. Such approaches provide improvement in the SINR

ratio.

Coordinated Multipoint Transmission (CoMP) is the ﬁrst cooperative

MIMO scheme proposed for cellular networks. The BSs have the ability to

communicate to each other through high-speed reliable connection,

possi-bly consisting of optical ﬁber links that is capable of having very high data

rates. This enables them to cooperate and process diﬀerent users’ signals.

These multi-BS MIMO cooperation is expected to play an important role in

terms of interference mitigation. Coordinated multi-cell beamforming

tech-niques can improve substantially the received signal quality and decrease the

received spatial interference. Relays also form an important part of

coordi-nated processing.

Instead of cooperating through backhaul links, a separate relay node

that assists the direct communication within each cell has similar beneﬁts

to multi-cell MIMO network because it can strengthen the eﬀective direct

channel gain between the BS and the remote users and helps with ICI

miti-gation. Relays are also beneﬁcial to reduce infrastructure deployment costs.

This is essential under the demand for high data rates envisioned for fourth

generation (4G) wireless systems.

Transmission power for relays are generally less than that is required by

BSs, as relays are expected to cover a region smaller than that of a BS. The

wireless relays receive the data from the BS and forward them to the users.

The costs for provisioning the wired backhaul connection is not required for

the wireless relays [24]. With the deployment of relays, the distance

be-tween the transmitter and receiver decreases, hence the propagation loss is

smaller than if only the BS is employed. This becomes more important as

fu-ture generation wireless networks are likely to use very high radio frequency

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in-10

creased bandwidth. Relays will form an important part of the network.

Capacity can be increased further by exploiting spatial diversity and

en-abling simultaneous transmissions by both the BS and the relays. Regardless

of the beneﬁts, it should be understood that there are certain disadvantages

as the relays may introduce additional delays and increase interference due

to frequency reuse at the relays.

Even though relays and multi-cell processing have the ability to enhance

capacity and coverage, the ever increasing demand for spectrum requires

more advancement in terms of spectrum usage. As stated earlier,

wire-less technologies and users’ demands are growing rapidly and the

conven-tional ﬁxed spectrum allocation approach is ineﬃcient to meet this

increas-ing demand. Cognitive radio (CR) is a promisincreas-ing technology that aims to

mitigate the spectrum scarcity problem by allowing secondary (unlicensed)

users (SUs) to access licensed frequency bands under the condition of

pro-tecting primary (licensed) users (PUs) from harmful interference. Various

approaches have been developed regarding the way the SUs can access the

licensed spectrum [25]. The ﬁrst one is through opportunistic spectrum

ac-cess, by using a frequency band only when it is detected to be idle. This is

called an interweave approach, through which the utilization of the spectrum

is improved by opportunistic reuse of temporary frequency voids, which are

called spectrum holes. The second approach is through spectrum sharing,

when the SUs coexist with the primary users by keeping the interference in

the primary users below a certain acceptable threshold. This is also called

underlay approach and allows only short-range communication for the SUs

due to interference power constrains.

In summary, use of multiple antennas, exploitation of spatial diversity,

intelligent resource allocation techniques, together with eﬃcient interference

management and coordinated multi-cell and relay processing techniques are

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11

wireless networks. All these approaches have been exploited to propose

var-ious novel algorithms in this thesis.

Thesis Outline

Spectrum scarcity is one of the most important challenges that wireless

communications need to address, especially due to increasing demand for

wireless services and ever increasing number of users. The work in this

the-sis is focused on techniques that improve spectral eﬃciency, coverage and

quality of wireless links. New resource allocation and spatial multiplexing

techniques have been proposed for cooperative communication networks

in-cluding peer-to-peer, relay and multi-cell networks.

In Chapter 2, a detailed literature survey is provided together with the

necessary theoretical background. The chapter includes characterization of

wireless channels followed by a detailed discussion on spatial diversity

tech-niques, such as transmit and receive beamforming. Existing wireless relay

techniques have also been summarized. Non-regenerative, regenerative and

two-way relay techniques are introduced and the advantages and the

disad-vantages are discussed. Finally, a discussion on cooperative diversity schemes

is provided.

In Chapter 3, spatial diversity and power allocation techniques for

peer-to-peer relay networks, where the source and the destination nodes are

equipped with single antenna have been investigated. An SINR balancing

based relay signal forwarding scheme is proposed. The beamforming

prob-lem is formulated using a semideﬁnite programming (SDP) framework and

the power allocation problem is solved using geometric programming (GP).

Initially, this resource allocation problem is considered for multiple one-way

amplify and forward relays and then it is extended for multiple two-way

am-plify and forward relays. SINR balancing technique for an underlay cognitive

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12

all secondary users while satisfying the primary users’ interference threshold

and total transmit power constrains.

In Chapter 4, the work in Chapter 3 on peer-to-peer relay networks

are extended for multiple antennas at the source and the destination nodes

as well as the relay. The uplink-downlink duality for this problem is

es-tablished. The MMSE of a downlink peer-to-peer network is shown to be

achieved by a virtual uplink network with the same total network

trans-mission power. Based on this result, an iterative algorithm is proposed to

determine the source, relay and receiver processing matrices, such that the

sum mean square error (MSE) of the retrieved signal at the receivers is

min-imized.

Chapter 5 investigates coordinated beamforming design in a network

with one BS and a relay. Most of the works in the literature considered

optimal beamformer design at the BS and the relays but they have not

ex-plicitly considered the backhaul overheads required to transmit the signal

from the BS to the relay. The knowledge of the interference caused by the

relay to the users served by the BS is exploited to enhance the overall

net-work performance. The optimization problem is solved using second order

cone programming (SOCP) and GP. The proposed method is shown to

re-duce signiﬁcantly the transmission power by using interference precoding at

the transmitter for various sets of data rates requirement.

In Chapter 6, a coordinated multi-cell beamforming technique is

pro-posed for SINR balancing under multiple BS power constraints. Instead of

balancing SINR of all users in all cells to the same level, a new approach is

proposed to balance SINR of users in various cells to diﬀerent maximum

pos-sible values. This has the ability to allow users in cells with relatively more

transmit power or better channel condition to achieve a higher balanced

SINR than that achieved by users in the worst case cells. This multi-level

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bal-13

ancing criterion and subgradient method.

Conclusions are drawn in Chapter 7. Possible future research directions

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Chapter 2 SPATIAL DIVERSITY AND

WIRELESS RELAY

NETWORKS

2.1 Introduction

In this chapter a literature review and the underlying technical background

required for the contributing chapters are provided. Starting with the

de-scription of various communication channel models, various techniques that

are important to maximize spectrum eﬃciency are provided. In particular,

the focus is on spatial diversity techniques, such as beamforming, multiuser

spatial diversity, MIMO technologies, wireless relay technologies including

one-way and two-way relays and cooperative communication networks.

Par-ticular emphasis is placed on cooperative relay networks and coordinated

multi-cell processing.

2.2 Characterization of the channel

Due to non-ideal transmission media that could also vary over time and

fre-quency, the transmitted signal gets distorted. For example, when a pulse is

transmitted, the received signal may appear as a pulse train due to

multi-paths. For this case, a typical impulse response may appear as depicted in

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Section 2.2. Characterization of the channel 15

Figure 2.1. An example of delay proﬁle

Figure 2.1. In addition, the nature of multipath could vary over time. This

variation happens because either the transmitter or the receiver moves and

also possibly as a result of variations of the location of the reﬂectors in the

transmission path. In this case, the received signal strength could change as

depicted in Figure 2.2. Generally, the time-variant channel response h(τ, t)

can be modeled as a complex-valued Gaussian random process in time

vari-able t and delay τ . The envelope|h(τ, t)| at any instant t is generally char-acterized by Rayleigh or Ricean distribution. If the real and complex parts

of the channel impulse response are modeled by a zero-mean Gaussian

ran-dom process, then this channel is said to be Rayleigh fading. In addition if

there is a strong line of sight (LOS) path, then the channel will obey Ricean

fading [26]. However, throughout this thesis, the channel is assumed to be

Rayleigh fading.

The channel impulse response is generally assumed to be wide-sense

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Section 2.2. Characterization of the channel 16 0 50 100 150 200 250 300 10−3 10−2 10−1 100 101 102 time channel gain

Figure 2.2. An example of typical fading proﬁle

response associated with a given multipath delay and t represents the time

variation. The autocorrelation is given by

Φhh(τ, t) = E{h(τ; t)h∗(τ ; t + ∆t)} (2.2.1)

when ∆t = 0, Φhh(τ, 0) = Φhh(τ ) is called multipath intensity proﬁle or

power delay proﬁle when ∆t = 0. The range of values of τ for which Φhh(τ )

is non zero is called the multipath spread of the channel, denoted by Tm.

The time-varying multipath channel can be characterized in the

fre-quency domain by taking the Fourier transform of h(τ, t) with respect to

τ , denoted by H(f, t). The autocorrelation in the frequency domain is given

by:

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Section 2.2. Characterization of the channel 17

and it is called the spaced-frequency, spaced-time correlation function of the

channel [26].

If ∆t = 0 is set to 0 in (2.2.2) the autocorrelation function in the

fre-quency variable φhh(∆f ) can be obtained, which provides a measure of the

frequency coherence of the channel i.e. the correlation between two

frequen-cies. The bandwidth of this function (∆f )h is called coherence bandwidth

of the channel and it is the reciprocal of the multipath spread as described

by the equation:

(∆f )h ≈

1

Tm

(2.2.3)

If the bandwidth of the transmitted signal is greater than (∆f )h, the

channel is called frequency-selective and the channel amplitude values for

frequencies separated by more than the coherence bandwidth are

indepen-dent. On the other hand, if the bandwidth of the signal is narrower than the

coherence bandwidth (∆f )h, then the fading across the entire bandwidth is

highly correlated and referred as ﬂat fading.

The frequency selective channel can be also interpreted in terms of inter

symbol interference (ISI). If the period of a transmitted symbol T is assumed

to be smaller than Tm, then the received signal will consist of a number of

past symbols introducing ICI.

The time variations of the channel is characterized by another statistical

property, namely the coherence time (∆t)h, which is a measure of the

corre-lation of the channel impulse response at times separated by (∆t).

Mathe-matically, it is the range of ∆t values over which φhh(∆f, ∆t) is non zero. If

Fourier transform is performed on φhh(∆f, ∆t) with respect to the variable

∆t and ∆f = 0 is set, the function S(λ) is called the Doppler power

spec-trum of the channel. The range of values λ over which S(λ) is nonzero is