Cooperative Communication for Multi-User Cognitive Radio Networks
MAKSYM GIRNYK
Licentiate Thesis in Telecommunications Stockholm, Sweden 2012
ISSN 1653-5146
ISBN 978-91-7501-399-2
SE-100 44 Stockholm SWEDEN Akademisk avhandling som med tillst˚and av Kungl Tekniska h¨ogskolan framl¨agges till offentlig granskning f¨or avl¨aggande av teknologie licentiatexamen fredagen den 8 juni 2012 klockan 13.15 i h¨orsal Q2, Kungl Tekniska h¨ogskolan, Osquldas v¨ag 10, Stockholm.
Maksym Girnyk, June 2012c Tryck: Universitetsservice US AB
Abstract
In recent years, the main trend in wireless communications has been shifted from voice transmission to data-centric communication. This shift has caused an increase in the data rate requirements for future wireless communication systems. These requirements result in need for large bandwidth. Being a limited and thus expen- sive resource, wireless spectrum needs to be used efficiently. For higher spectral efficiency, new transmission techniques as well as new dynamic spectrum-allocation policies are needed.
Cognitive radio is a promising approach for increasing spectral efficiency of wireless systems. By exploiting advanced signal processing techniques and sophis- ticated transmission schemes, cognitive radio devices allow to serve new wireless users within the existing crowded spectrum. Typically, a cognitive radio network is installed in parallel to an existing primary network, a legacy owner of the spectrum.
The cognitive radio network adapts to its electro-magnetic environment in order to limit or even avoid the disturbance to the primary network.
This thesis focuses on the underlay cognitive radio paradigm, which assumes that both the primary network and the ad hoc cognitive radio network operate within the same time and frequency band, as well as at the same geographic lo- cation. The cognitive network is able to estimate the interference caused to the primary network by means of channel training and possible feedback. This knowl- edge is then used to adjust the cognitive network’s transmissions in such a way that the disturbance to the primary network is below some acceptable threshold.
In the first part of the thesis, we discuss the multi-hop line cognitive networks, in which the information content before reaching its destination passes through several hops from node to node within the cognitive network. In this way, transmission power at the source terminal may be decreased, thus producing less interference to the primary network. Moreover, the powers at each terminal within the cogni- tive network may be optimally allocated so that the interference constraint at the primary network is satisfied. This power allocation can be realized in both cen- tralized and decentralized ways, depending on the available information about the channel state. We discuss both of these allocations subject to different interference constraints employed at the primary network.
In the second part of the thesis, we discuss the reliability of transmission within the line cognitive ad hoc networks in terms of outage probability and diversity.
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We also illustrate the benefit of network coding for such networks and provide a heuristic algorithm for optimal scheduling.
In the final part of the thesis, we study the uplink relay-assisted cellular cogni- tive radio scenario. Both, the cognitive network and the primary network, contain a set of multi-antenna users that communicate with a corresponding base station.
The users create mutual interference and hence limit each other’s performance.
Using certain mathematical tools originally developed within the field of statistical physics, we are able derive a closed-form expression for the ergodic mutual informa- tion for arbitrary channels inputs, which enables characterization of the achievable rate region of such scenario.
Sammanfattning
Under de senaste ˚aren har den st¨orsta trenden inom tr˚adl¨os kommunikation fly- ttats fr˚an r¨ost˚atergivning till data-centrerad kommunikation. Denna f¨or¨andring har medf¨ort en ¨okning av datahastigheten f¨or framtida tr˚adl¨osa kommunikation- ssystem, vilket resulterar i krav p˚a stor bandbredd. Eftersom tr˚adl¨ost spektrum
¨
ar en begr¨ansad och dyr resurs, beh¨over det anv¨andas effektivt. F¨or h¨ogre spek- traleffektivitet kr¨avs nya s¨andningstekniker samt nya principer f¨or dynamisk spek- trumtilldelning.
Kognitiv radio ¨ar en lovande metod f¨or att ¨oka spektraleffektiviteten hos tr˚adl¨osa system. Genom att utnyttja avancerad signalbehandlingsteknik och sofistikerade s¨andningsmetoder, s˚a m¨ojligg¨or kognitiv radioenheter att nya tr˚adl¨osa anv¨andare kan betj¨anas inom existerande begr¨ansade frekvenser. Typiskt ¨ar ett kognitivt radion¨at installerad parallellt med en befintligt prim¨arn¨at, en legal ¨agare av spek- trumet. Det kognitiva radion¨atet anpassar sig till den elektromagnetiska milj¨on i syfte att begr¨ansa eller undvika st¨orningen till den prim¨ara n¨atverket.
Denna avhandling fokuserar p˚a underlay-paradigmen f¨or kognitiv radio, vilket f¨oruts¨atter att b˚ade prim¨ar-n¨atverket och kognitiva radion¨atet arbetar inom samma tid och frekvensband, och p˚a samma geografiska plats. Det kognitiva radion¨atet kan skatta vilken st¨orning som orsakas till det prim¨ara n¨atverket med hj¨alp av uts¨anda tr¨aningssekvenser och eventuell feedback. Denna kunskap anv¨ands sedan f¨or att anpassa kognitiva radion¨atets s¨andning p˚a ett s˚adant s¨att att de samverkar under en acceptabel gr¨ans. Vi unders¨oker tandem multi-hop kognitiva radion¨at, d¨ar in- formationsinneh˚allet g˚ar flera steg, fr˚an nod till nod, inom kognitiva n¨atverket. P˚a detta s¨att kan s¨andningseffekten vid k¨allterminalen minskas, vilket skapar mindre interferens f¨or det prim¨ara n¨atverket. Dessutom kan s¨andeffekten vid varje ter- minal inom kognitiva radion¨atet anpassas optimalt s˚a att st¨orningsniv˚aerna inom det prim¨ara n¨atverket h˚alls p˚a en acceptabel niv˚a. Denna effektf¨ordelning kan
˚astadkommas b˚ade centraliserat och decentraliserat, beroende p˚a tillg¨anglig in- formation om kanaltillst˚andet. I den f¨orsta delen av avhandlingen diskuterar vi b˚ada dessa principer, f¨or ett antal olika formuleringar av st¨orningsvillkoren f¨or det prim¨ara n¨atet.
I den andra delen av avhandlingen diskuterar vi tillf¨orlitligheten f¨or ¨overf¨oring inom kognitiv radion¨at i termer avbrottssannolikhet och diversitet. Vi illustrerar
¨
aven f¨ordelen av s˚adana n¨at och tillhandah˚aller en heuristisk algoritm f¨or optimal v
schemal¨aggning.
I den sista delen av avhandlingen studerar vi ett uppl¨anksscenario d¨ar rel¨aer anv¨ands f¨or att st¨odja cellul¨ar kognitiv radio. B˚ade det kognitiva n¨atverket och det prim¨ara n¨atverket har ett antal anv¨andare, utrustade med multipla antenner, som kommunicerar med en motsvarande basstation. B˚ada p˚averkar varandra ¨omsesidigt och kan d¨armed begr¨ansa varandras prestanda. Med hj¨alp av matematiska verktyg fr˚an statistisk fysik, h¨arleder vi en slutet uttryck f¨or ergodiska ¨omsesidiga infor- mationen f¨or s˚adana kanaler, vilket g¨or det m¨ojligt att karakt¨arisera omr˚adet av uppn˚aeliga datatakter.
Acknowledgments
Foremost, I would like to express my gratitude to my supervisor Prof. Lars K.
Rasmussen for his support and guidance throughout my research. His encourage- ment and positive attitude helped me to overcome difficulties during the research process.
I am thankful to Asst. Prof. Ming Xiao for his help and collaboration. Ming always had many inspiring ideas and valuable comments, whenever I came to him.
I am also grateful to Dr. Mikko Vehkaper¨a. I enjoyed very much working with him on some topics covered by this thesis. In particular I am indebted to Mikko for his guidance through the minefield of statistical physics. I also would like to thank Dr.
Vishwambhar Rathi for many valuable discussions on the related research topics. I gratefully acknowledge the joint work with my colleagues Fr´ed´eric Gabry, Nan Li and Nicolas Schrammar within the QUASAR-ACROPOLIS project cooperation.
In addition, my appreciation goes to Prof. Mikael Skoglund for giving me the opportunity to join the Communication Theory lab and to experience its great scientific atmosphere.
I am grateful to Mikko, Dr. Chao Wang, Hamed Farhadi, Iqbal Hussain, Dennis Sundman and Ali Zaidi for proofreading some parts of this thesis. I also thank Prof.
Mats Bengtsson for the quality review and valuable comments.
I would like to express my thanks to Dr. Fredrik Rusek for taking time to act as opponent for this thesis.
It was a privilege to share the office with Amirpasha Shirazinia all these years.
I am also thankful to all my current and former colleagues at “plan 4” for a cre- ative and friendly working environment. Special thanks goes to Annika Augusts- son, Tetiana Viekhova, Ir´ene Kindblom and Raine Tiivel for taking care of the administrative issues. L˚angholmen Football Club is acknowledged for giving me the possibility to maintain my physical shape during these years.
I am thankful to my family and friends for supporting and encouraging me.
Finally, more than anyone else, I would like to thank Karina for her love and care, for all the happiness she brings to my life. This thesis is dedicated to her.
Maksym Girnyk Stockholm, May 2012
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Contents
Abstract iii
Sammanfattning v
Acknowledgments vii
Contents ix
List of Acronyms xiii
Notation xv
List of Figures xxi
1 Introduction 1
1.1 Evolution of Wireless Communication Systems . . . 1
1.2 Cooperative Communication . . . 3
1.3 Network Coding . . . 5
1.4 Cognitive Radio . . . 6
1.5 Contribution and Related Work . . . 7
1.5.1 Optimal Resource Allocation in Multi-Hop CRNs . . . 7
1.5.2 Network-Coded Cooperation in Multi-User Multi-Hop CRNs 8 1.5.3 Asymptotic Sum-Rate of Relay-Assisted Cellular MIMO CRNs 9 1.6 Outline of the Thesis . . . 10
1.7 Contributions Outside the Scope of the Thesis . . . 12
2 Fundamentals 13 2.1 Elements of a Digital Communication System . . . 13
2.2 Entropy and Mutual Information . . . 14
2.3 The AWGN Channel Model . . . 16
2.4 The Wireless Channel . . . 18
2.4.1 Slow Fading Scenario . . . 19
2.4.2 Fast Fading Scenario . . . 20 ix
2.5 The Relay Channel . . . 21
2.6 Basics of Network Coding . . . 22
2.7 Cognitive Radio Scenario . . . 24
2.8 Multi-Antenna Transmission . . . 27
2.9 Statistical Physics and The Replica Method . . . 29
2.9.1 Replica Trick . . . 30
2.9.2 Replica Symmetry . . . 31
2.10 Convexity and Convex Optimization . . . 31
2.10.1 Lagrange Duality . . . 32
2.10.2 The KKT Conditions . . . 34
3 Optimal Power Allocation 35 3.1 System Model . . . 35
3.2 Aggregate-SI-Constrained Throughput Maximization . . . 38
3.2.1 Power Allocation in the Absence of Intra-CRN Interference . 39 3.2.2 Power Allocation in the Presence of Intra-CRN Interference . 42 3.2.3 High- and Low-SNR Approximate Power Solutions . . . 46
3.2.4 Distributed Power Allocation . . . 47
3.2.5 Limited-Feedback Solution . . . 47
3.3 Individual-SI-Constrained Throughput Maximization . . . 48
3.3.1 Centralized Solution . . . 48
3.3.2 Distributed and Limited-Feedback Solutions . . . 52
3.4 Numerical Illustration . . . 52
3.4.1 Aggregate SI Constraint . . . 53
3.4.2 Individual SI Constraints . . . 56
3.5 Summary . . . 59
4 Diversity Network-Coded Cooperation 61 4.1 System Model . . . 61
4.2 Evaluation of Transmission Strategies . . . 63
4.2.1 Conventional Regenerative TDD Transmission . . . 63
4.2.2 Binary Network-Coded Transmission . . . 65
4.2.3 Diversity Network-Coded Transmission . . . 66
4.3 Three-User Network Example . . . 69
4.3.1 Conventional TDD Transmission . . . 69
4.3.2 BNC-Based Transmission . . . 71
4.3.3 DNC-Based Transmission . . . 73
4.3.4 Simulation Results . . . 74
4.4 Optimal Scheduling . . . 75
4.5 Summary . . . 81
5 Asymptotic Sum-Rate Analysis 83 5.1 System Description . . . 83
5.2 Asymptotic Sum-Rate . . . 86
xi
5.3 Proof of Theorem 5.1 . . . 89
5.4 Applications . . . 102
5.4.1 Gaussian Channel Inputs . . . 102
5.4.2 Quadrature Phase-Shift Keying Channel Inputs . . . 103
5.5 Numerical Illustration . . . 103
5.5.1 Amplify-and-Forward Relay Channel . . . 104
5.5.2 Communication in the Presence of Interference . . . 105
5.5.3 Relay-Assisted Interference MIMO channel . . . 107
5.6 Summary . . . 109
6 Conclusions and Future Work 111 6.1 Conclusions . . . 111
6.2 Future Work . . . 112
A Omitted Steps from the Proof of Theorem 5.1 115 A.1 Derivation of Covariance Matrices Q0, Q1j and Q2 . . . 115
A.2 Evaluation of G(u)(Q0,Q2) . . . 118
A.3 Evaluation of G(u)1 (Q1j) . . . 119
A.4 Derivation of the Third Term of (5.41) . . . 119
A.5 Derivation of the Eighth Term of (5.41) . . . 121
A.6 Saddle-Point Conditions . . . 123
A.7 Evaluation of the Free Energy . . . 131
A.8 Evaluation of Second Term of the Mutual Information . . . 134
Bibliography 141
List of Acronyms
1G First generation cellular mobile communication system.
2G Second generation cellular mobile communication system.
3G Third generation cellular mobile communication system.
4G Fourth generation cellular mobile communication system.
AF Amplify-and-forward.
AMPS Advanced mobile phone system.
AWGN Additive white Gaussian noise.
BNC Binary network coding.
BPSK Binary phase-shift keying.
bpcu bits per channel use.
CF Compress-and-forward.
CR Cognitive radio.
CRN Cognitive radio network.
CSI Channel side information.
CDMA Code division multiple access.
DF Decode-and-forward.
DMT Diversity-multiplexing trade-off.
DNC Diversity network coding.
DSA Dynamic spectrum allocation.
FCC Federal communication commission of the U.S.
FDMA Frequency division multiple access.
GEV Global encoding vector.
GSM Global system for mobile communication.
i.i.d. Independent and identically distributed.
KKT Karush-Kuhn-Tucker.
LF Limited feedback.
LICQ Linearly independence constraint qualification.
LSL Large system limit.
LTE Long-term evolution.
MGF Moment-generating function.
MIMO Multiple-input and multiple-output.
MMSE Minimum mean square error.
xiii
MSE Mean square error.
NMT Nordic mobile telephony.
OFDM Orthogonal frequency-division multiplexing.
Ofcom Office of communications in the U.K.
pdf Probability density function.
pmf Probability mass function.
PTS Swedish post and telecom authority.
PU Primary user.
QAM Quadrature amplitude modulation.
QoS Quality of service.
QPSK Quadrature phase-shift keying.
RT Relay terminal.
r.v. Random variable.
SF Store-and-forward.
SI Secondary interference.
SU Secondary user.
SNR Signal-to-noise ratio.
TDD Time division duplex.
TDMA Time division multiple access.
UMTS Universal mobile communication system.
UWB Ultra-wideband.
WLAN Wireless local area network.
XOR Exclusive or.
ZMCSCG Zero mean circular symmetric complex Gaussian.
Notation
CN×M The set of complex-valued N× M matrices.
RN×M The set of real-valued N× M matrices.
ai= [a]i ith entry of a vector a.
aij = [A]i ith entry of a matrix A.
AT The transpose of a matrix A.
AH Hermitian transpose of a matrix A.
a∗ The complex conjugate of a scalar a.
a Optimal solution of an optimization problem.
A−1 Inverse of a square matrix A.
Re{a} Real part of a complex scalar a.
Im{a} Imaginary part of a complex scalar a.
j The imaginary unit,√
|a| absolute value of a scalar a.−1.
a L2 norm of a vector a.
diag(a1, . . . , aN) The diagonal matrix with a1, . . . , aN on the main diagonal.
tr{A} The trace of a square matrix A.
IN The N× N identity matrix.
0N×m The N× M matrix of zeros.
1N The N -vector of ones.
E{X} Expectation of a random variable X.
|A| Cardinality of a setA.
A \ B Set-theoretic difference ofA and B.
A ∪ B Union ofA and B.
A ∩ B Intersection ofA and B.
CN (m, C) The circular symmetric complex Gaussian distribution with mean vector m and covariance matrix C.
O(·) Order of a function / computational complexity.
arg{·} Argument / phase of a complex variable.
s.t. Means “subject to”.
∀ The universal quantifier.
∇ The gradient operator.
δ (x) The Dirac function.
GF(q) The Galois field of size q.
xv
⊕ Exclusive or operation, i.e., addition in binary field GF(2).
α The pathloss exponent.
√A Diagonal element of the channel matrix of a fixed MIMO channel z =√
AIx + w.
β The inverse temperature.
Ci Network codeword for user i.
C Capacity of a point-to-point channel.
Cε Outage capacity of a point-to-point channel.
ci ith constraint of an optimization problem.
D The domain of a function.
Dc Matrix of gradients for all constraints ciof an optimization problem.
Di Diversity order for user i.
DiC Diversity order for user i using conventional TDD trans- mission.
DiB Diversity order for user i using conventional BNC trans- mission.
DDi Diversity order for user i using conventional DNC trans- mission.
dij Distance between nodes i and j in a network.
Em The error event for a message m.
E(·) Energy.
F The (normalized) free energy.
Fj Forwarding matrix of jth relay terminal.
Fc(·) Complementary cumulative density function of|h|2. γ Interference threshold.
G Outage threshold.
Gi Global encoding vector of user i.
g(·) The dual function.
gij Channel power gain of the link between nodes i and j.
˜
gij Channel power gain of the link between secondary node i and primary node j.
H Instantaneous channel side information at the receiver.
H MIMO channel matrix.
Hp Effective MIMO channel matrix consisting of scaled chan- nel matrices of MIMO links from all primary users to the primary base station through the direct path and through the relay terminals.
Hs Effective MIMO channel matrix consisting of scaled chan- nel matrices of MIMO links from all secondary users to the primary base station through the direct path and through the relay terminals.
Notation xvii Hˆ Effective MIMO channel matrix consisting of scaled chan-
nel matrices of MIMO links from all relay to the primary base station.
Hp01k Channel matrix of the MIMO link between primary user k and the primary base station.
Hp1jk Channel matrix of the MIMO link between primary user k and relay terminal j.
H21j Channel matrix of the MIMO link between relay terminal j and the primary base station.
Hs01k Channel matrix of the MIMO link between secondary user k and the primary base station.
Hs1jk Channel matrix of the MIMO link between secondary user k and relay terminal j.
H Hamiltonian.
H(X) The entropy of a discrete random variable X.
h Channel gain.
hij Channel gain of the link between nodes i and j.
h(X) The differential entropy of a continuous random variable X.
h(X, Y ) The joint differential entropy of continuous random vari- ables X and Y .
h(Y|X) The conditional differential entropy of a continuous ran- dom variable Y given the knowledge about the random variable X.
Ii Information packet of user i.
I(·) The rate function.
I(Y ; X) The mutual information between random variables Y and X.
I(Y ; X|Z) The mutual information between random variables Y and X, given the knowledge about the random variable Z.
λ Dual variable.
Lij Link between nodes i and j.
L(·) The Lagrangian.
M· Moment generating function.
μ(·) Probability measure.
n AWGN vector of a MIMO channel.
n01 AWGN vector added at the primary base station during direct transmission from primary and secondary users.
n1j AWGN vector added at relay terminal j during transmis- sion from primary and secondary users.
n21 AWGN vector added at the primary base station during transmission from relay terminals.
n AWGN in a channel.
ω Dual variable.
Oij Outage event for linkLij. Pmax Power constraint.
Pi Transmit power at user i’s terminal.
P Vector of powers of all users in a network.
p Diagonal element of a symmetric matrix Q.
p(n)max Maximal probability of error for a transmission.
pm Conditional probability of error for a transmitted message m.
po Link outage probability.
po(Ii) Outage probability for a packet Ii.
p(x) Probability mass/density function1 of a dis- crete/continuous random variable X.
˜
p Diagonal element of a symmetric matrix ˜Q.
Q Covariance matrix of a vector V.
Q˜ Auxiliary matrix of the same size as Q.
Q Set of all Q’s.
Q˜ Set of all ˜Q’s.
q Off-diagonal element of a symmetric matrix Q.
˜
q Off-diagonal element of a symmetric matrix ˜Q.
ρ Signal-to-noise ratio.
ρp01k Signal-to-noise ratio of the direct MIMO link between pri- mary user k and the primary base station.
ρp1jk Signal-to-noise ratio of the MIMO link between primary user k and relay terminal j.
ρ21j Signal-to-noise ratio of the MIMO link between relay ter- minal j and the primary base station.
ρs01k Signal-to-noise ratio of the direct MIMO link between sec- ondary user k and the primary base station.
ρs1jk Signal-to-noise ratio of the MIMO link between secondary user k and relay terminal j.
R Rate.
σ2 Noise variance.
Sx Support set for x.
Tcoh Coherence time interval.
T Total number of time instances/slots.
t Time instant.
ti Number of time-slots allocated to user i.
tCi Number of time-slots allocated to user i using conventional TDD transmission.
tBi Number of time-slots allocated to user i using conventional BNC transmission.
1For notational convenience, we do not distinguish between the random variables and their realizations.
Notation xix
tDi Number of time-slots allocated to user i using conventional DNC transmission.
w AWGN vector of a fixed MIMO channel z =√
AIx + w.
X Set of all possible discrete channel inputs.
x Channel input.
x Input vector to a MIMO channel.
xpk Signal vector transmitted by primary user k.
xsk Signal vector transmitted by secondary user k.
x The MMSE estimate of x.
Y Set of all possible discrete channel outputs.
y Output vector of a MIMO channel.
y01 Noisy signal vector received at the primary base station directly from all primary and secondary users.
y1j Noisy signal vector received at the relay terminal from all primary and secondary users.
y21 Noisy signal vector received at the primary base station all relay terminals.
Y Support set for the channel outputs.
y Channel output.
yj Signal received at user kth terminal.
Z(·) The partition function.
z Output vector of a fixed MIMO channel z =√
AIx + w.
List of Figures
2.1 Typical digital communication system. . . 14
2.2 The relay channel. . . 21
2.3 Store-and-forward relaying on the butterfly network. . . 23
2.4 Network Coding on the butterfly network. . . 24
2.5 Network Coding in the uplink cooperative relay scenario. . . 25
2.6 Interference channel. . . 25
3.1 Multi-hop cognitive radio network. . . 36
3.2 Multi-hop transmission with overhearing upstream and downstream. . . 37
3.3 Example of a two-hop CRN. . . 42
3.4 Optimal power allocation for a two-hop CRN. . . 43
3.5 Thee-hop transmission with overhearing upstream and downstream. . . 52
3.6 End-to-end throughput as function of the aggregate SI threshold of the primary network for different power allocation strategies. . . 56
3.7 End-to-end throughput as a function of the SI threshold of PU 1 for different power allocation strategies. . . 58
4.1 Multi-user multi-hop CRN. . . 62
4.2 Schedule for the conventional TDD regenerative transmission. . . 64
4.3 Schedule for the BNC transmission. . . 65
4.4 Schedule for the DNC transmission. . . 67
4.5 Three-user CRN. . . 69
4.6 Conventional TDD transmission. . . 70
4.7 BNC transmission. . . 71
4.8 DNC transmission. . . 73
4.9 Outage probability of SU 3 when using conventional TDD DF, BNC and DNC strategies. . . 75
4.10 Outage probability of SU 2 when using conventional TDD DF, BNC and DNC strategies. . . 76
4.11 Outage probability of SU 1 when using conventional TDD DF, BNC and DNC strategies. . . 77
xxi
4.12 Outage probability for different users the DNC transmission according to the equal time-slot assignment. . . 79 4.13 Outage probability for different users the DNC transmission according
to the optimized schedule. . . 80 5.1 Uplink of a cellular non-regenerative relay-assisted cognitive MIMO net-
work. . . 84 5.2 AF relay MIMO channel. . . 104 5.3 Average mutual information per dimension versus SNR of the first-hop
link ρ1. . . 105 5.4 Communication in the presence of interference. . . 106 5.5 Average mutual information per dimension versus SNRs ρp1 and ρs1. . . . 106 5.6 Average mutual information per transmit antenna versus SNRs ρp1 and
ρs1for different combinations of PU’s and SU’s signalings. . . 107 5.7 Relay-assisted interference MIMO channel. . . 108 5.8 Average mutual information per dimension versus SNRs ρp1 and ρs1. . . . 108 5.9 Mobile-relay-assisted interference MIMO channel with shadowing. . . . 109 5.10 Achievable rate region for the mobile-relay-assisted multi-access inter-
ference MIMO channel. . . 110
Chapter 1
Introduction
In this chapter we start with a brief review the history of communication systems, and then in Sections 1.2, 1.3 and 1.4, we give a short introduction to cooperative communications, as well as cognitive radio. Furthermore, we go through the pre- vious work related to the topic in Section 1.5, and provide an outline of the thesis in Section 1.6. The final section of this chapter informs the reader about the work that is not covered by the present thesis.
1.1 Evolution of Wireless Communication Systems
Wireless communication is a century old field of industry, which remains one of the most successful and fast growing fields at present. Being one of the fundamental needs of a human, social interaction through communication stimulates continuous development for connecting people all over the world. Recent progress in technology enables production of tiny devices able to realize very complex signal processing tasks consuming limited power that allows implementation of more and more so- phisticated communication devices.
In recent years, we have witnessed a great success of cellular mobile telephony, which has become an important part of people’s everyday life in all developed countries. As a consequence, the demand of new audio, video and data services has significantly increased over the past decade and continues growing from year to year. In this perspective, new techniques and tools for fast, efficient and reliable communication over the wireless channel are needed.
The first digital communication system (telegraph network), developed by Samuel Morse, was demonstrated to the public in 1838. Later on, after the discovery of electro-magnetic waves by James Maxwell in 1864, and the series of experiments by Heinrich Hertz in 1887, during which the radio waves were physically transmitted in the free space, Alexandr Popov demonstrated to the public the world’s first short- range transmission of continuous radio signal in 1895. Already in 1901, Guglielmo Marconi established the first Trans-Atlantic reception. Since then, radio transmis-
1
sion methods and services advanced rapidly enabling more reliable transmission, using smaller and cheaper devices, and thereby leading to appearance of new ap- plications, such as radio and TV broadcast, mobile communication, navigation, remote control, etc.
The first generation (1G) cellular mobile systems appeared in 1980s when the advances in technology allowed to implement the ideas of mobile communication.
Although these systems were not the first mobile radio networks, they were the first to consider the cellular structure of coverage. This approach allowed to signifi- cantly increase the capacity of the network and provided support for mobility. One of the first 1G systems implemented in Europe was Scandinavian NMT (Nordisk Mobiltelefoni). The system was designed for wireless speech service; it used analog signaling and was based on frequency division multiple access (FDMA). Two years later, Advanced Mobile Phone Service (AMPS) was launched in the U.S. [Mol11].
The development of integrated circuits together with new digital signal process- ing algorithms led to the replacement of the analog 1G systems by new digital sec- ond generation (2G) cellular mobile systems. In 1992, the first such system – Global System for Mobile Communication (GSM) – was implemented in Europe. Allowing better speech quality and increased capacity, GSM made an important contribution to the development of the wireless communication systems. Namely, it provided users with new services, such as roaming, handover and SMS-messaging [Red98].
The latter shifted the emphasis of the communication system design from voice calls to data transmission. This shift established a new era in wireless communi- cations, the era of data-centric services, such as web-browsing, file downloading, video streaming, gaming, on-line banking, etc.
All these applications increased the data rate demands on the networks. Even though being already a successful mobile communication system, GSM was not able to provide high enough data rates to satisfy these demands. Thus, current – third generation (3G) – systems appeared to be designed indeed to meet these high rate demands. European Universal Mobile Telecommunication System (UMTS) is based on a wideband code division multiple access (CDMA) standard enabling high data rates up to 2 Mbps [HT04]. Further evolution follows by the forth generation (4G) communications systems, which is currently being under investigation by the 3GPP, a group of telecommunication associations responsible for the finalization of the standard. Long-Term Evolution (LTE) Advanced standard, which is finalized as one of the candidates, includes the target of supporting 1 Gbps data rates, advanced MIMO options, coordinated multiple point transmission and reception, relaying and autonomous component carrier selection for uncoordinated femto-cell deployment [MK09].
At the same time, another class of wireless communication systems – wireless local area networks (WLANs) – developed into a large field of short-range com- munication systems. WLANs are destined for communication at high data rates within a small region between objects that are stationary or moving at pedestrian speeds. The systems operate within unlicensed bands, and in order to mitigate interference from one WLAN to others, the constraint on the transmit power is
1.2. Cooperative Communication 3
imposed to all user terminals within the given area and the given band. Often used protocols for WLANs are IEEE 802.11 family in the U.S. and HIPERLAN/2 in Europe [DAB+02]. There are also small-scale WLAN standards, such as Blue- tooth [Haa00], and ultra-wideband (UWB) [IOH04] standards used for substitution of cabling. WLANs typically use either centralized or ad hoc topology [CCL03].
While for centralized WLANs there is a central node (access point) which manages the connections within its range, in ad hoc WLANs the central node is absent and the network organizes itself into a set of links between pairs of nodes using relaying of information and routing algorithms.
Further development of the communication systems has to deal with growing number of applications and services that demand higher quality of service (QoS) for users, in terms of data rates, reliability, security, fairness, etc. In addition, the fact that communication becomes more data-centric puts new constraints on latency. New services may exploit all range of latency requirements, from bursty applications to on-line streaming.
1.2 Cooperative Communication
One of the main challenges in the design of a communication system is the time- varying nature of the wireless channel due to multi-path radio wave propagation, distance attenuation and possible shadowing by obstacles. This phenomenon, also known as fading, may cause poor performance of a system even when high transmit powers are used. The reason of this poor performance is that the aforementioned fading effects significantly increase the probability for the channel to be in deep fade. When the channel is in deep fade, the signal experiences severe degradation while the noise power remains the same. Hence, the communication system will most likely suffer from errors.
A natural approach to combat fading is to incorporate diversity, i.e., to ensure that multiple signal copies pass through different paths experiencing statistically independent changes. The probability that all the paths turn to deep fade decreases dramatically, and reliable communication is possible as long as at least one path is strong enough to carry the signal. The diversity may be obtained via different diversity techniques:
• Temporal diversity may be obtained by repetition of a signal over time.
• Frequency diversity is achieved when the signal is sent over several sub-carriers of the orthogonal frequency division multiplexing (OFDM) system.
• Spatial diversity is acquired by using multiple antennas at the transmitter and/or the receiver.
The easiest way of obtaining diversity is the so-called repetition coding, i.e., the very same signal is transmitted over several paths separated in time, frequency or space. Although repetition coding achieves full diversity available in the channel, it
is not optimal in the sense of the degrees of freedom available in the channel [TV05].
In other words, repetition coding does not use all the potential of the channel. For instance, more sophisticated coding schemes, additionally to diversity gain, may provide coding gain, which is also useful for increasing reliability of transmission.
As an example, interleaving of coded symbols in time, used in GSM [Red98], may illustrate an efficient diversity acquisition technique.
Another way of obtaining diversity gains is to use of multiple-input multiple- output (MIMO) transmission [FG98], [Tel99]. In this scenario, both the transmit- ter and the receiver are equipped with multiple properly spaced transmit/receive antennas. In this way, the transmitter may send the same signal from each of its antennas, so that the receiver obtains several copies of the signal. On the other hand, when transmitting different signals from different antennas the transmitter may produce several data streams, which may be received at the receiver simulta- neously, thereby increasing the data rate. The latter advantage of MIMO is often referred to as multiplexing gain. These two gains of MIMO are shown to form the diversity-multiplexing trade-off (DMT) which is the fundamental trade-off for any communication system [ZT03].
The advantages described above are coupled with the availability of multiple antennas at the terminals. In practice, antennas have to be separated in space, which may be a problem for the mobile phones. Fortunately, single-antenna termi- nals may obtain some of the benefits of MIMO systems by implementing cooperative communication techniques. In this way, a virtual MIMO system may be created from a set of mobiles sharing their antennas for the transmission. The terminals may assist each other by transmitting the partner’s signal. Hence, the signals arriv- ing at the receiver traverse several independent paths allowing for diversity gains.
Another important benefit of cooperative communication is coverage extension. If the direct communication between the transmitter and the receiver is not possible (e.g., due to the far geographical location or some obstacles on the way), the partner terminal may still deliver the signal to the destination through multi-hop link.
The benefits of the cooperative communication come at cost of sharing the terminal’s transmission power and computation resources with others. However, this loss of own power may be counteracted when helping terminal sends its own signal, which can be then relayed by others. Thus, although the benefits depend of users’ willingness to cooperate, the cooperation may potentially lead to significant resource savings for the whole network.
The fundamental block of the cooperative communication, the so-called relay channel, was firstly introduced by van der Meulen in 1968 [vdM71]. Further, Cover and El Gamal analyzed the relay channel from the information theoretic point of view and developed several fundamental relaying strategies [EC79]. The main idea of the relay channel is that a relay terminal can overhear the signal from the transmitter and retransmit it towards the receiver. In this way, the relay channel then can be regarded as superposition of a broadcast channel [Cov72], [KM77] and a multiple access channel [Ahl71], [CES80] well investigated before. Cover and El Gamal provoked high interest to the cooperative communication, which remains a
1.3. Network Coding 5
hot topic within the area of communication theory. Interested reader is referred to [KMY06] for an excellent overview of the topic.
There are many relaying strategies proposed in the literature. We may roughly divide those into two classes: non-regenerative and regenerative. A typical repre- sentative of non-regenerative strategies is the so-called amplify-and-forward (AF) strategy. The basic underlying principle of the strategy is the amplification of the noisy received signal at the relay terminal and its retransmission towards the desti- nation. This is quite an old technique used by radio engineers to increase the cov- erage of the microwave transmission almost sixty years ago, e.g., [RSF51], [PT58].
Within the context of cooperative communication, the AF strategy was firstly in- troduced and investigated by Lanemann et al. in [LTW04]. The most frequently used regenerative relaying strategy is decode-and-forward (DF), originally suggested in [EC79]. The key idea of the DF strategy is that the received signal is first de- coded at the relay, then re-encoded and retransmitted to the destination. Another representative of the class of regenerative strategies is compress-and-forward (CF), also initially suggested in [EC79]. The idea here is that the relay quantizes the received signal and encodes the samples into a new message which is forwarded to the destination serving as additional redundancy for the signal received directly from the source.
1.3 Network Coding
The regenerative relaying strategies discussed above are implemented on the packet level, so that an information message (or packet) received at the relay terminal is processed, stored and retransmitted towards the destination. For instance, when two packets are received by a relay node at the same time, and assuming that the capacity of the relay-destination link is one packet per channel use, only one of these two packets may be transmitted at a time. The other packet has to be stored and transmitted afterwards. Therefore, this class of strategies is referred to as store- and-forward (SF). This approach is shown to be sub-optimal in terms of network throughput for networks with one information source and many information sinks, i.e., so-called multicast scenario. Instead, a new ground-breaking technique, named network coding is proposed by Ahlswede et al. in [ACLY00]. With network coding, each intermediate node in the network is allowed to mix the incoming packets in a certain way, which may provide the highest possible throughput for multicast networks.
A large amount of literature has appeared after the discovery of network cod- ing. In [LYC03], it was shown that linear network coding suffices for achieving the min-cut capacity for multicast sessions. In other words, all the intermedi- ate nodes combine the incoming packets via linear combinations with coefficients picked from a finite field and assigned to each node. In this way, each sink knows which coefficients are used by which node. In [HMK+06], a practical suggestion was proposed to choose the coefficients randomly and then send the information
about the coefficients en route with a packet as an overhead. Knowing all the ran- dom coefficients, a sink can easily recover the packets. This approach is referred to as random network coding. In turn, K¨otter and M´edard, in [KM03], proposed to track the network coding process via transfer matrices, thereby establishing a convenient algebraic framework for design and analysis of network codes. For in- stance, the problem of finding the feasible coding scheme is turned into a search for a set of non-singular transfer matrices corresponding to all source-destination pairs.
For more details on the topic the reader is referred to the textbooks on network coding [Yeu08], [FS06], [FS07] and [HL08].
1.4 Cognitive Radio
The development of new wireless applications and services requires increased data rates which is coupled with higher demands for wireless spectrum. The electro- magnetic spectrum is a limited natural resource, access to which is regulated by governmental agencies. For example, in the U.S., the usage of spectrum is regu- lated by the Federal Communications Commision (FCC), in the U.K., it is done by the Office of Communications (Ofcom), or in Sweden, by Post- och Telestyrelsen (PTS). Spectrum is assigned to network operators within some geographic re- gions on a long-term basis. This policy is proved inefficient by recent measure- ments [RHLM06, VMB+10] since large parts of spectrum remain unutilized or par- tially utilized during certain periods of time, whereas the other frequency bands may be heavily exploited.
Furthermore, wireless spectrum is a very expensive resource, and therefore it must be utilized efficiently, so that the resource is allocated only as long as it is needed. Hence, there is a clear need for new techniques for increasing the effectiveness of the present spectrum policies. A promising approach of the dy- namic spectrum allocation (DSA) allows to overcome this problem by exploiting advanced digital communication and signal processing techniques at the commu- nication terminals. The DSA policy is based on the technology of cognitive radio (CR), firstly introduced by Mitola and Maguire [MM99] and expanded further in Mitola’s Ph.D. thesis presented at KTH - Royal Institute of Technology, Sweden, in May 2000 [Mit00]. The CR is defined as an intelligent wireless communication system that is aware of its environment and is able to change its transmitter param- eters based on interactions with its environment with objectives of highly reliable communication and efficient spectrum utilization [FCC02]. For some good survey material on the topic the reader is referred to [Hay05], [ALVM08] and [ALVM06].
CR technology allows for coexistence of an adaptive cognitive radio network (CRN), also called a secondary network, together with a primary network, the legacy owner of the spectrum. The CRN is capable to sense and analyze its sur- rounding environment as well as reconfigure its operation in accordance with this radio environment. In this way, based on the available channel side information (CSI), the CRN may dynamically access the spectrum of the primary network
1.5. Contribution and Related Work 7
whenever it does not harm the latter. Examples of potential secondary networks may include the aforementioned WLANs working under IEEE 802.11, Bluetooth or WiMAX standards and exploiting unlicensed bands.
CR systems can be classified into three groups according to their operation principle [GJMS09]:
• Underlay: CRs are allowed to operate in parallel to the primary network under the constraint that the secondary interference (SI) from the CRN to- wards the primary users (PUs) does not degrade performance of the primary network.
• Overlay: CRs are allowed to operate simultaneously with the primary net- work provided that they enhance its performance by having access to PUs’
codebooks and applying advanced precoding and interference cancelation techniques.
• Interweave: CRs are allowed to opportunistically access the underutilized parts of the spectrum without interfering the primary network.
In this thesis we focus on the underlay CR paradigm. Apart from cellular CRNs, we also discuss cognitive ad hoc networks [ABZ09], [ALC09], which use the unlicensed spectrum for peer-to-peer content delivery. By transmitting the infor- mation in multi-hop fashion the CRN can extend its coverage without increasing the amount of power used. Vice versa, by reducing transmit power driven by split- ting the direct path into multiple links, the CRN may decrease the SI towards the primary network while keeping the same coverage.
1.5 Contribution and Related Work
In this thesis we look at different aspects of a multi-hop CR system. Firstly, we consider the problem of throughput optimization of multi-hop underlay CRNs under the constraint on the SI towards the primary network. Secondly, we take a look at the problem of reliable network-coded cooperative communication in multi-user multi-hop CRNs. Finally, we touch upon the primary network in cellular setting by looking at the relay-assisted interference MIMO channel. In the present section we provide the references directly related to the topics of the thesis.
1.5.1 Optimal Resource Allocation in Multi-Hop CRNs
Multi-hop CRNs allow the same infrastructure to be reconfigured in different ways in order to deliver the information from source to destination. For example, as already mentioned, by splitting the whole distance between the source and the destination into set of smaller links, the CRN may reduce the power used at each node, thus reducing the interference to the primary network. On the other hand, there can be blind zones due to shadowing from surrounding buildings or in tunnels.
The presence of wireless nodes around such zones can help in relaying information in a multi-hop fashion and avoid deep fades.
The interference to a primary receiver created by the CRN is determined by the aggregate power of secondary transmitters weighted with the channel gains of the paths to the primary receiver. In the corresponding chapter we address the issue of optimal power allocation in a multi-hop CRN such that the end-to-end data throughput is maximized under a constraint on the secondary interference power at a set of nearest primary receivers.
Optimal power allocation for multi-hop relayed transmission over Rayleigh fad- ing channels, within a non-CR network, is considered in [HA04]. Outage probability of the weakest link is used as the optimization criterion. The optimization problem is shown to be convex and is efficiently solved via Lagrangian duality.
In [DGA04], bandwidth and power allocation for ergodic end-to-end throughput maximization was studied for multi-hop FDMA-based systems with line topology.
The logarithmic link capacity expression was approximated by the square root of its argument, which allowed to simplify the non-linear problem, thereby obtaining a closed-form solution. Upon this result, the authors of [SZQY05] proposed three sub-optimal power and bandwidth allocation strategies for multi-hop OFDMA- based line networks.
The question of fundamental power allocation for cooperative relay networks is investigated in [KC09]. A multi-hop OFDM-based network is generalized to arbitrary number of hops and different paths towards destinations. The objective is to minimize network throughput subject to a power constraint. The optimal power allocation is shown to be unique and found by the famous water-filling solution.
Moreover the optimal water-levels are shown to be the same for all paths.
Finally, the problem of transmit power allocation in dual-hop CRNs is solved in [ML09]. The optimization problem considered here is the minimization of the sum transmit power of the relays subject to a set of constraints: constraint on the output SNR of the maximum ratio combiners at the destination, constraint on the SI towards the primary network and the set of individual power constraints of each relay node. The problem is shown to be a linear optimization problem, and hence an efficient centralized solution is established. Moreover, fully and partially decentralized solutions are provided as well.
Yet, none of the preceding references considered interference within the net- work. Therefore, in our work we study the optimal power allocation for a multi- hop CRN of line topology, in which the nodes operate within the same frequency band and hence interfere with each other. The optimization criterion is the end-to- end throughput of the line network. We constrain the interference from the CRN towards the primary network in two different ways; namely, via the aggregate SI constraint at the primary network or via the individual SI constraint at each re- ceiver. Furthermore, we provide fully decentralized power allocation as well as the limited-feedback (LF) solution.
1.5. Contribution and Related Work 9
1.5.2 Network-Coded Cooperation in Multi-User Multi-Hop CRNs
In linear network-coded systems, relays perform a linear combination of the incom- ing packets over a finite field. For example, in [XFKC07] the authors proposed a two-user scheme where each user linearly combines its own message with that of the other user over a binary field GF(2). The scheme is referred to as binary network coding (BNC) and provides substantial coding gains.
Meanwhile, the BNC scheme is shown to be suboptimal for multi-user multi- relay networks in terms of achievable diversity [XS09b]. For such networks, the authors propose a special kind of linear network codes that allow to achieve full diversity, and hence protection against channel fading. The authors also show the existence of such codes. We refer to this coding strategy as diversity network coding (DNC). In the parallel paper [XS09a], the authors show that full diversity in the network is achieved when a network code has linearly independent global encoding vectors for all possible source-relay channel outage situations. Both contributions are summarized and extended in [XS10]. Some simplified network code construc- tions are provided as well.
In [RUFLV12], the aforementioned results are further generalized. The design of the network codes maximizing diversity order is stated as equivalent to the design of linear block codes over a non-binary finite field GF(q) under the Hamming metric. The authors show that the generalized network codes achieve better trade- off between rate and diversity than the result of their precedents. Finally, in [WX11]
the DMT analysis of network-coded wireless relay networks is carried out and a new cluster-based transmission protocol for optimizing the diversity order of the transmission is proposed.
In the corresponding chapter of this thesis we apply the aforementioned idea of the DNC to multi-user ad hoc CRNs with line topology. We show that the DNC strategy with linearly independent global encoding vectors outperforms the BNC strategy and the benchmark TDD-based strategy in terms of diversity gain.
The analysis of the diversity order of the proposed scheme is carried out through outage probabilities.In addition, we explore the problem of optimal transmission scheduling within a given number of available time-slots and derive an effective heuristic algorithm maximizing the minimum diversity.
1.5.3 Asymptotic Sum-Rate of Relay-Assisted Cellular MIMO CRNs
In the last part of the thesis, we look at the topology of the cellular relay-assisted CR scenario. In addition to the CRN, in this case a set of relay terminal (RTs) is present in the field, assisting both networks in communication to their corre- sponding receivers. For instance, these relays can be shared or belong to the CRN offering diversity and/or multiplexing gains to the primary network, thus being able to compensate the loss in performance due to the SI of the CRN.
A suitable model for the analysis of the discussed topology is the so-called relay- assisted interference channel [SVJS08], [MDG09], [SSE09]. Within this model, two source-destination pairs transmit simultaneously, thereby creating interference to each other. An (infrastructure) RT assists both transmissions by performing different relaying and/or coding techniques. Despite of recent attention to this scheme, the capacity of such scenario is still an open problem.
Within the MIMO setting, a relevant scenario was addressed in [SRS10]. The relay-assisted cognitive interference multi-access channels were analyzed in terms achievable rates and outage probability under the assumption of the DF relaying in combination with precoding/precancelation techniques. In this thesis we focus on the multi-user cooperative MIMO relay transmission within the CR scenario aiming at analyzing the achievable ergodic rates of such scheme. In our model, the set of relays have no access to the messages and each relay terminal, employing only the AF strategy. This scenario has not yet been discussed in the literature, in spite of being simple for implementation and hence of practical importance. Due to symmetry of the scenario, we, mainly, study the asymptotic sum-rate of the primary network in the presence of secondary interference. The sum-rate of the secondary network may be found in the same way.
The key technique for our analysis is the so called replica method, invented by Edwards and Anderson [EA75] within the field of statistical physics. It is used for the analysis of the macroscopic behavior of the system consisting of the large number of microscopic bodies. The method per se is not rigorous, since it takes a sequence of steps that have not been proven correct yet. For instance, rigorous justification of such assumptions as replica symmetry, replica continuity and self- averaging is the weak point of the replica method, and it is still an open problem in mathematical physics. However, the method works as it is, providing good approximations for many cases where systematic approaches fail, e.g., computing mutual information for the MIMO systems with discrete signal constellations.
Tanaka was the first one to introduce this approach to the field of communica- tion theory (vide [Tan01], [Tan02]); he derived the asymptotic mutual information of a CDMA system with antipodal inputs. His study was generalized to arbitrary inputs by the authors of [GV05]. Later, in [Mul03] and [MS03], the replica method was applied to evaluation of the capacity of a MIMO system. Finally, in [WRW08]
and [WW10], the method was applied to cooperative communications. The au- thors of both references, by means of the replica method, analyzed the asymptotic achievable ergodic rates of the AF MIMO relay channels.
1.6 Outline of the Thesis
Apart from increasing the efficiency of the spectral usage, a CRN should provide high QoS for secondary users (SUs) in terms of data rate and reliability of com- munication, while keeping the QoS of the PUs high. In this thesis we consider
1.6. Outline of the Thesis 11
multi-hop CRNs, and analyze those from the point of view of achievable network throughput and reliability. The remainder of the thesis is organized as follows.
• Chapter 2 introduces a few fundamentals needed to proceed into the topic, describes the methods and concepts used in the thesis.
• Chapter 3 considers the problem of optimal power allocation within a multi- hop regenerative CRNs under different SI constraints towards the primary network. We derive and compare both centralized and distributed power allocations, as well as high- and low-SNR approximations.
The chapter is based on the paper
[GXR11] M. A. Girnyk, M. Xiao, and L. K. Rasmussen, “Optimal power allocation in multi-hop cognitive radio networks,” in Proceedings of International Symposium on Personal, Indoor and Mobile Com- munications (PIMRC), Toronto, Canada, 2011, pp. 472–476.
• Chapter 4 addresses the problem of reliability of network-coded transmission within the multi-user multi-hop regenerative CRNs. We discuss several relay- ing strategies and analyze those in terms of diversity and outage probability.
A heuristic algorithm for finding the optimal scheduling is derived as well.
The chapter is based on the paper
[GXR12] M. A. Girnyk, M. Xiao, and L. K. Rasmussen, “Cooperative com- munication in multi-source line networks,” in Proceedings of Wire- less Communication and Networking Conference (WCNC), Paris, France, 2012, pp. 2406–2410.
• Chapter 5 turns the reader’s attention to the primary network. Here we an- alyze the achievable sum-rate of the relay-assisted non-regenerative cognitive interference MIMO channel. We derive the closed-form expression of the mu- tual information for the primary multi-access channel under the assumption that the signals from the SUs are treated as noise.
The chapter is based on the papers
[GVR12a] M. A. Girnyk, M. Vehkaper¨a, and L. K. Rasmussen, “On the asymptotic sum-rate of the relay-assisted amplify-and-forward cog- nitive mimo channel,” in Proceedings of International Symposium on Personal, Indoor and Mobile Communications (PIMRC), Syd- ney, Australia, 2012, submitted.
[GVR12b] M. A. Girnyk, M. Vehkaper¨a, and L. K. Rasmussen, “On the asymptotic sum-rate of uplink MIMO cellular systems in the pres- ence of non-gaussian inter-cell interference,” in Proceedings of IEEE GLOBECOM, Anaheim, U.S.A., 2012, submitted.
• Chapter 6 provides the reader with the conclusions and possible directions of the future work. Technical details of some proofs are left to appendices.
1.7 Contributions Outside the Scope of the Thesis
Some results obtained during the studies were not included in the present thesis, mainly because lack of coherence with the topic covered here. The corresponding papers are listed below in order of appearance.
[GR11] M. A. Girnyk and L. K. Rasmussen, “Myopic multi-hop trans- mission strategies in layered wireless networks,” in Proceedings of IEEE International Symposium on Personal, Indoor and Mo- bile Communications (PIMRC), Toronto, Canada, 2011, pp. 1773–
1777.
[GLS+12] F. Gabry, N. Li, N. Schrammar, M. Girnyk, E. Karipidis, R. Thob- aben, L. K. Rasmussen, E. G. Larsson, and M. Skoglund, “Se- cure broadcasting in cooperative cognitive radio networks,” in Pro- ceedings of Future Networking and MobileSummit (FNMS), Berlin, Germany, 2012, to appear.
[GSG+12] F. Gabry, N. Schrammar, M. Girnyk, N. Li, R. Thobaben, and L. K. Rasmussen, “Cooperation for secure broadcasting in cogni- tive radio networks,” in IEEE International Conference on Com- munications (ICC), Ottawa, Canada, 2012, to appear.
In [GR11], a general framework was developed for the analysis of a layered multi- hop network with overhearing. In particular, the network is analyzed in terms of bit
1.7. Contributions Outside the Scope of the Thesis 13
error probability for zero-forcing and linear minimum mean square error detectors at the destination. The scheme is also analyzed in terms of available diversity, coming from possible overhearing between layers.
The collaboration with fellow doctoral students resulted in two following pa- pers. In [GLS+12], we considered the CR scenario, where the CRN is a potential eavesdropper of the message of primary transmitter. Hence, there is a trade-off be- tween cooperation and secrecy in the CR system. We have derived the achievable rate regions from an information theoretic prospective. The scenario was further generalized to multiple secondary receivers. In [GSG+12], the precedent study was twisted to the cases, where the CRN is aware and unaware of the primary message.
The achievable rate regions for both cases are investigated and compared. Finally, cooperation was shown to be beneficial in spite of the secrecy constraint of the primary system.
Chapter 2
Fundamentals
In this chapter we introduce a few fundamentals necessary for understanding the material in the following chapters. We begin with the discussion of the mathemat- ical model of a general communication system. Further, we introduce entropy and mutual information as information measures and define the notion of the capacity for the Gaussian channel. In Section 2.4 we discuss the wireless channel and its inherent features, followed by Section 2.5, where the relay channel is discussed.
In Section 2.6 we describe the minimal basics of network coding required for un- derstanding the material from Chapter 4. Section 2.7 is devoted to the cognitive radio scenario. Section 2.8 briefly discusses the multi-antenna transmission. In particular, we motivate studies of systems with large antenna arrays. The discus- sion is followed by a brief description of some basic concepts of statistical physics necessary for the analysis of very large systems. Finally, in Section 2.10 we cover some necessary parts of convex optimization theory. The chapter is targeted the general audience, and hence, the following should note be considered as a general introduction to the topics. More detailed and comprehensive information can be found in the references within each section of the present chapter.
2.1 Elements of a Digital Communication System
We begin with a description of a general digital communication system and its elements. The goal of any communication system is to transfer information from a source to an information consumer. Figure 2.1 illustrates the block-scheme of a typical digital communication system. An information source produces an output (analog or digital) which is converted into a sequence of bits by the source encoder.
At this stage, the data is aimed to be compressed to as few bits as possible in order to remove the inherent redundancy and increase the speed of communication, taking into account the end user’s requirements. Then, the channel encoder introduces some controlled redundancy to the sequence of bits in order to increase the reliability of the transmission against distortions introduced to the signal on its way.
15
Source Source encoder
Channel
encoder Modulator
Channel
Consumer Source
decoder
Channel
decoder Demodulator Figure 2.1: Typical digital communication system.
The encoded binary sequence then reaches the modulator, which translates the discrete symbols into electrical signals (waveforms) which can be transmitted over a physical medium, such as wires, air, water, etc. This medium is referred to as a communication channel, and is used to deliver the signal from the transmitter to the receiver. The physical characteristics of the channel may vary widely, which makes mathematical channel models essential for the design of efficient communication systems. Communication channels typically can distort the signal in a random manner, due to different mechanisms, e.g., thermal noise, interference created by other systems, etc.
After traversing the channel, the physical signal reaches the receiving end, where the demodulator translates it into a binary sequence representing the estimates of the transmitted symbols. This sequence is then fed to the channel decoder that attempts to reconstruct the sequence of compressed data, which was the input of the channel encoder at the transmitting end. The harmful effects of the channel are removed with help of the controlled redundancy injected at the transmitter.
Finally, the source decoder converts the compressed data sequence into a format suitable for the information consumer.
2.2 Entropy and Mutual Information
In order to mathematically describe the process of information transmission, we first introduce two basic information measures, viz., entropy and mutual information.
The entropy represents a measure of uncertainty about a random variable (r.v.) and hence characterizes its information content. Mutual information, in turn, measures the amount of information, which one r.v. contains about another. This section closely follows Chapters 2 and 8 of [CT91] and Chapter 10 of [Yeu08].
