cooperative wireless communication for cellular …ck548xg6061/... · 2011. 9. 22. · cho, and...

COOPERATIVE WIRELESS COMMUNICATION

FOR CELLULAR AND MULTI-HOP NETWORKS

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF ELECTRICAL

ENGINEERING

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

HyukJoon Kwon

June 2010

http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/ck548xg6061

© 2010 by HyukJoon Kwon. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

ii



http://purl.stanford.edu/ck548xg6061

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

John Cioffi, Primary Adviser


Fouad Tobagi, Co-Adviser


Madihally Narasimha

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

iii

Abstract

The design of efficient algorithms using cooperation has gained much attention as

an emerging technique for the next-generation wireless system. Such a cooperative

system allows wireless devices to communicate with each other over relaying. With

astute cooperative algorithms, wireless systems are expected to increase sum-rate

performance and to support reliable communication.

In general, wireless systems can be classified into centralized cellular infrastruc-

tures and decentralized ad-hoc multi-hop networks. Cellular networks require high

quality channel information to increase sum-rate performance. However, due to finite-

rate feedback channels, the base station cannot obtain uncorrupted channel informa-

tion from mobile stations (MSs), thereby preventing the improvement in the sum-rate

performance. On the other hand, multi-hop networks also require high level credit

information about neighbor nodes to support reliable communication. Otherwise,

traffic is likely to stop at some selfish nodes while being relayed to the destination.

The first part of this thesis is motivated with the challenging issue: saving the

number of feedback bits while maintaining sum-rate performance. To achieve the

objective, this work exploits the cooperation between MSs, known as conferencing, in

addition to feedback channels. It has been theoretically shown that cooperating en-

coders increase the capacity region in multiple-access channels. Similarly, the increase

of achievable rate region in broadcast channels with cooperating decoders has been

also revealed. In practical systems, the feedback rate is finite as well as cooperation

is imperfect. Therefore, it is essential to exploit both cooperation and feedback effec-

tively. Moreover, when multiple MSs are considered, multi-user diversity can be also

exploited as yet another independent resource. Using these resources, i.e., feedback,

v

cooperation and user-selection, available in broadcast channels, this thesis introduces

the enhancement of the sum-rate performance through rigorous investigation of the

relation among the resources. Moreover, this work derives the requirement for the

number of feedback bits that achieve the multiplexing gain. Simulation results are

presented to evaluate the sum-rate and to verify the derivation.

The second part of this thesis focuses on multi-hop networks where each node op-

erates independently without any centralized base stations. This multi-hop network

can use cooperation among nodes to increase the total throughput with respect to a

single-hop network. However, each node is autonomous and selfish in nature, and thus

spontaneous cooperation among nodes is challenged. To accommodate this otherwise

selfish nature of multi-hop networks, this thesis proposes a cooperative relay strat-

egy under an energy-limited condition with a game-theoretic perspective. The main

focuses are 1) to motivate each node to be cooperative, 2) to decide optimally the

amount of cooperation, 3) to analyze equilibrium for the proposed scheme, and thus

4) to maximize the overall throughput. The proposed scheme formulates a Stackel-

berg game where two nodes sequentially bid their willingness weights to cooperate for

their own benefit. Accordingly, all the nodes are encouraged to be cooperative only

if a sender is cooperative and alternatively to be non-cooperative only if a sender is

non-cooperative. This selective strategy changes the reputations of nodes depending

on the amount of their bidding at each game and motivates them to maintain a good

reputation so that all their respective packets can be treated well by other relays.

Thus, every node forwards other packets with higher probability, thereby achieving a

higher overall payoff.

vi

Acknowledgments

In the first place, I would like to record my gratitude to my principal advisor, Prof.

John M. Cioffi, for his supervision, advice, and guidance throughout my PhD years.

He provided me extraordinary experiences for the fundamentals of advanced digital

communication systems. His remarkable technical insight has been always true guid-

ance to the final stage of my research from the very beginning. Furthermore, his

excellent engineering intuition lifted my spirit and motivated me to keep focusing on

the research with fresh ideas and passions in engineering, which exceptionally inspire

and enrich my growth as a student and a researcher. I am indebted to him more than

he knows.

My special thanks go to my associate adviser, Dr. Madihally (Sim) Narasimha.

I was honored to start my internship at Qualcomm, Inc. with his generous help as

my direct manager. His sincere supervision deeply motivated me consider practical

knowledge on advanced technology, and his involvement with his originality triggered

my intellectual maturity. I am grateful in every possible way for his academic support

as well as engineering guidance.

I gratefully acknowledge my reading committee member, Prof. Fouad A. Tobagi,

for his advice, supervision, and crucial contribution to my research. His exceptional

class on wireless network taught me the fundamentals of ad-hoc systems that became

the research topic of this thesis. I am thankful that in the midst of all his activity, he

accepted to be my reading committee member. I would also like to thank Prof. John

Gill for willingly serving as a chair of my oral exam committee.

I am also deeply grateful to the Samsung Scholarship program for providing the

full scholarship for five years with a financial support.

vii

I was very fortunate to have worked on various projects with such outstanding

individuals at Stanford. I would like to thank HyungJune Lee, Hui Won Je, and

Edward Woongjun Jang for their co-authorship and collaboration on conference or

journal papers. It is a pleasure to convey my gratitude to them all in my humble

acknowledgment.

I would like to thank the former and current members in Prof. Cioffi’s research

group: Rajiv Agarwal, Chiang-yu Chen, Sunghyun Cho, Chan-Soo Hwang, Sumanth

Jagannathan, Edward Woongjun Jang, Ryoulhee Kwak, Wooyul Lee, Vinay Majjigi,

Moshe Malkin, Shu-ping Yeh, Hao Zou, Aakanksha Chowdhery, Ming-Yang Chen,

Haleh Tabrizi, Takki Yu, Seung Hoon Hwang, Hyuk Jun Oh, and Chan-Soo Hwang.

I am proud to record that I had several opportunities to work with an exceptionally

experienced researchers like them. It has been my great honor to be a member of this

distinguished group. Also, my special thanks go to our administrative assistant, Pat

Oshiro, for her outstanding administrative support.

I would like to thank my Korean friends at Stanford: Jongduk Baek, HyungJune

Lee, Younggeun Cho, Jaedon Kim, Taesup Moon, Sangbum Kim, Jaekwang Lee,

Jinsung Kwon, Wonseok Shin, Jungho Ahn, Taejung Yoon, Yenho Thomas Chung,

Chunki Park, and many others, and I would also like to extend my gratitude to friends

who stays in the States: Jeansoo Khim, Yonghak Albert Park, Junwon Jung, Ahryon

Cho, and many others. Thanks to them, my life at Stanford was so memorable and

enjoyable.

Last, but most importantly, I would like to show my heartfelt appreciations to

my family members. I owe my deepest gratitude to my parents, brother, and sister

for their constant encouragement throughout my Stanford life. I would also like to

thank my parents-in-low, sister-in-law, and my niece, Sieon Lee, for their support to

finish this thesis. My deepest gratitude goes in particular to my wife, Sejin Kim, for

her endless love. She is the reason for my blissful life at Stanford. I dedicate this

dissertation to my family.

viii

Contents

Abstract v

Acknowledgments vii

1 Introduction 1

1.1 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Theoretic Background for Cooperative Communication 12

2.1 Point-to-Point Communication . . . . . . . . . . . . . . . . . . . . . . 13

2.2 Multi-Point Communication . . . . . . . . . . . . . . . . . . . . . . . 15

2.3 Cooperative Communication . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.1 MAC with Cooperating Encoders . . . . . . . . . . . . . . . . 17

2.3.2 BC with Cooperating Decoders . . . . . . . . . . . . . . . . . 20

2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3 Multi-User BC using Conferencing and Limited Feedback 24

3.1 System Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.1.1 Broadcasting Models . . . . . . . . . . . . . . . . . . . . . . . 27

3.1.2 Conferencing Models . . . . . . . . . . . . . . . . . . . . . . . 27

3.2 Joint Processing with Filtering Vectors . . . . . . . . . . . . . . . . . 30

3.2.1 Receive-Combining . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2.2 Transmit-Beamforming . . . . . . . . . . . . . . . . . . . . . . 31

3.3 Limited Feedback and Partial Cooperation . . . . . . . . . . . . . . . 33

3.3.1 Throughput Analysis with M = K . . . . . . . . . . . . . . . 33

ix

3.3.2 Throughput Analysis with M < K . . . . . . . . . . . . . . . 36

3.4 Simulation Results and Discussion . . . . . . . . . . . . . . . . . . . . 41

3.4.1 Results with M = K . . . . . . . . . . . . . . . . . . . . . . . 41

3.4.2 Results with M < K . . . . . . . . . . . . . . . . . . . . . . . 46

3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4 Relaying Power Allocation on Conferencing for OFDM Channels 50

4.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.2 Multi-Carrier Channels with Cooperation . . . . . . . . . . . . . . . . 53

4.2.1 Amplify-and-Forward Relaying . . . . . . . . . . . . . . . . . 53

4.2.2 Transmit Beamforming and Receive Combining . . . . . . . . 56

4.3 Relaying Power Allocation on Conferencing . . . . . . . . . . . . . . . 57

4.3.1 M × 1 with M = 2 . . . . . . . . . . . . . . . . . . . . . . . . 60

4.3.2 M × 1 case with M > 2 . . . . . . . . . . . . . . . . . . . . . 61


4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5 Cooperative Strategy for Multi-Hop Networks 69

5.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.2 Cooperative Relay Scheme . . . . . . . . . . . . . . . . . . . . . . . . 74

5.3 Equilibrium Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.3.1 Stackelberg Equilibrium . . . . . . . . . . . . . . . . . . . . . 79

5.3.2 Cournot Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 81

5.4 Relay Protocol and Successive Games . . . . . . . . . . . . . . . . . . 82


5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

6 Conclusion 91

Bibliography 93

x

List of Tables

4.1 Relaying Power-Allocation Algorithm . . . . . . . . . . . . . . . . . . 62

5.1 The Credit Table of Relay . . . . . . . . . . . . . . . . . . . . . . . . 75

5.2 The Credit Table of Sender . . . . . . . . . . . . . . . . . . . . . . . 76

xi

List of Figures

1.1 Both centralized networks and decentralized networks are illustrated. 2

1.2 The amount of CSI decides whether or not achieving the full multi-

plexing gain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 The heterogenous interfaces are exploited simultaneously. . . . . . . . 7

2.1 Point-to-point channels . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 Multiple access channel (MAC) . . . . . . . . . . . . . . . . . . . . . 16

2.3 Broadcast channel (BC) . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 Full cooperation and no cooperation. . . . . . . . . . . . . . . . . . . 17

2.5 MAC with cooperating encoders . . . . . . . . . . . . . . . . . . . . . 18

2.6 BC with cooperating decoders . . . . . . . . . . . . . . . . . . . . . . 21

2.7 Illustration of the achievable rate region for physically degraded BSBC

from [17] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1 The quantized channel information prevents the zero-forcing beam, wi,

from being orthogonal to channel vectors, hj 6=i, of other MSs. . . . . . 25

3.2 The combining vector for MS i is chosen in the null space of Ri so that

it is orthogonal to rj 6=i. . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3 The beamforming vector for MS i is chosen such that it is the closest

to the vector qi from a finite codebook F where |F| = 2B. . . . . . . 32

xii

3.4 The throughput of a MISO broadcast channel with several schemes is

illustrated with fixed feedback bits B = 10 and a finite gain β = 0.2

when K = M = 4. UCZF is evaluated only with user-cooperation,

ZFBF only uses feedback channels, and UCLF uses both feedback

channels and conferencing. . . . . . . . . . . . . . . . . . . . . . . . . 42

3.5 The throughput of a MISO broadcast channel with perfect CSI at the

BS and full cooperation among MSs is illustrated when K = M = 4.

The performance of the proposed scheme is between the capacity of a

point-to-point MIMO channel and the maximum sum throughput of

zero-forcing beamforming in a multi-user MISO channel. . . . . . . . 43

3.6 The throughput of a MISO broadcast channel with scalable feedback

and a finite conferencing gain is illustrated with b = 4 when K = M =

4. As a conferencing channel gain β increase, the required number of

feedback bits B decreases as shown in Fig. 3.7. . . . . . . . . . . . . . 44

3.7 Illustration about the relation between the number of feedback bits

and conferencing gains at each SNR. . . . . . . . . . . . . . . . . . . 45

3.8 Illustration about the relation between the number of feedback bits

and SNR given conferencing gains. . . . . . . . . . . . . . . . . . . . 45

3.9 MISO broadcast channels with fixed feedback bits, B = 6, for ZFBF

and a fixed cooperative gain, β = 1.5, for UCLF are compared with

the sum-capacity in a single MIMO channel. . . . . . . . . . . . . . . 46

3.10 MISO broadcast channels with scalable feedback bits, β = 2.0 and

K = 20 are shown with a upper-bound, UCLF with perfect CSI, and

a lower-bound, M log(1 + ρ △) . . . . . . . . . . . . . . . . . . . . . 47

3.11 The number of feedback bits required for achieving the multiplexing

gain decreases as β or K increases. . . . . . . . . . . . . . . . . . . . 48

3.12 As K increases, the sum-rate for the UCLF increases with respect to

β or B. The curves are plotted at the condition of SNR = 10 dB . . . 49

xiii

4.1 The total throughput of all the RPAUC, EPAUC, and ZFBF is com-

pared under a limited feedback where M = 4, N = 16, B = 3, and

β = 1, 0.1, 0.01. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4.2 The per-MS throughput of both RPAUC and EPAUC is illustrated

with M = 4, N = 16, β = 0.01, and B = ∞, 3. . . . . . . . . . . . . . 64

4.3 The 5 % outage total throughput of all the RPAUC, EPAUC, and

ZFBF is shown with respect to the number of subcarriers, N , where

M = 4, ρ = 25 dB, β = 0.01, and B = 3, 5. . . . . . . . . . . . . . . . 65

4.4 Thd CDFs of the total throughput under both RPAUC and EPAUC

are compared to each othere for N = 16 and 128, respectively. The

parameters M = 4, B = 3, ρ = 25 dB, and β = 0.01 are used. . . . . 66

5.1 P4’s wrong report to P2 could isolate P5 in error. . . . . . . . . . . . . 70

5.2 Additional authority is required to ensure every payment. . . . . . . . 71

5.3 P2, P3 and P4 are competing for being selected as a next hop of P1. . 72

5.4 Illustration of 100 nodes uniformly distributed. . . . . . . . . . . . . . 74

5.5 The proposed two-stage game is established with two phases between

a sender and a relay. The packet is relayed according to the calculated

forwarding probability at the second phase. . . . . . . . . . . . . . . . 83

5.6 Illustration showing how the distribution of nodes’ credit changes under

the proposed scheme as the normalized time goes from 0.00 to 1.00. . 84

5.7 Illustration showing how the distribution of nodes’ credit changes under

the reputation-based model as the normalized time goes from 0.00 to

1.00. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.8 Required time to reach 70 percent cooperative nodes over all the nodes

where α = 1, β = 0.1, and βtot = 100. . . . . . . . . . . . . . . . . . . 86

5.9 The effect of each parameter: cooperation factor α and transmission

cost β, respectively, on the cooperative percentage. . . . . . . . . . . 87

5.10 The forward probability increases as time goes by under the proposed

scheme where α = 1, β = 0.1, and βtot = 100. . . . . . . . . . . . . . 88

xiv

5.11 The total throughput utility under different schemes to decide the will-

ingness wi with α = 1, β = 0.1, and βtot = 100, and a hybrid scheme. 89

xv

Chapter 1

Introduction

In the past decade, wireless devices have rapidly gained wide use in mobile telephony.

Easier access to personal wireless devices has then furthered the demand for wireless

communication and more ubiquitous use as well as higher quality service. Accordingly,

wireless broadband’s improved service attracts attention to the demand for smarter

wireless devices. This positive interaction between the supply-and-demand of wireless

communication increases customer familiarity with wireless device use. As a result,

the wireless industry prepares for further increase of the capacity of wireless networks

and how to guarantee their reliable communication. A consequent key design issue

is satisfaction of the need for higher data rates and reliable traffic. These require the

design of proper algorithms for efficient exploitation of wireless resources in future

wireless networks.

Wireless networks are classified into two distinct networks, centralized networks

and decentralized networks, as shown in Fig. 1.1. The centralized networks oper-

ate with authority stations that control sub-stations and focus on maximizing total

system profit rather than individual stations’ profit. On the other hand, the decen-

tralized networks operate with independent stations that are not controlled by the

authority stations. Thus, each station in the decentralized networks maximizes its

own profit rather than total system profit.

As a typical example of centralized networks, cellular systems have base stations

(BSs) that select the mobile stations (MSs) available at each block period and then

1

2 CHAPTER 1. INTRODUCTION

Cellular Network Multi-hop Network

Centralized Decentralized

Figure 1.1: Both centralized networks and decentralized networks are illustrated.

broadcast to the selected MSs to maximize the total throughput. The broadcasted

messages thus serve multiple MSs. Simultaneously, the broadcasted messages are

possible multi-user interference that may reduce the performance. Thus, it is essential

to mitigate this multi-user interference as well as to increase the sum-capacity of all

MSs served together. On the other hand, multi-hop networks, where each node may

both send and/or relay, are an example of decentralized networks. In multi-hop

networks, distributed algorithms are required to support each node’s private profits.

However, inconsiderate distributed algorithms can be so selfish as to refuse use of any

of its relaying resources for other nodes’ traffic. Even though instantaneous selfish

activities might be beneficial to each node, such selfish behavior dramatically harm

the system’s traffic reliability or eventually halt the system. Therefore, intelligent

distributed algorithms must ensure individual nodes’ performance as well as the whole

system’s performance. This thesis intends to design proper algorithms of the issues

above for both types of networks.

Ref. [52] shows that wireless capacity significantly increases with multiple an-

tenna use. This result stimulates considerable research about multiple-input multiple-

output (MIMO) techniques on point-to-point communication where both the trans-

mitter and receiver have multiple antennas. If antennas spacing is the order of a wave

length, spatial diversity can enhance performance through use of space-time channel

3

coding as in [2,51].Achievement of MIMO channel capacity can apply precoding and

post-processing at the transmitter and receiver, respectively, based on singular value

decomposition (SVD) of channel matrix. As another way to boost the achievable

throughput is through the frequency diversity of orthogonal frequency division mul-

tiplexing (OFDM) techniques. After converting a frequency selective fading channel

into parallel frequency flat fading subchannels, this multi-carrier technique can ob-

tain high spectral efficiency with low complexity for channels with large delay spread,

as in [7, 12]. Even though both MIMO and OFDM techniques are independent,

these techniques share a common principle that the performance can be enhanced

by exploiting new resource-related dimensions such as multiple antennas or multiple

carriers. Recently, this principle has extended further to develop multi-user systems

using multi-user diversity effects in a space.

With the increasing demands to support multiple users concurrently, multi-user

systems have drawn much attention as a promising extension for future wireless net-

works. A BS with multiple antennas can concurrently broadcast multiple signals in

each block period, and then each of multiple MSs can decode its own signal from the

broadcasted messages, respectively. In order to easily decode received signals and

reduce the interference effects on the received signals, a line of recent research has

focused to develop precoding technique at the BS. Theoretically, dirty-paper cod-

ing (DPC) has been revealed as optimal to achieve the sum-capacity of Gaussian

broadcast channels in [57, 66]. DPC pre-subtracts the non-causal multi-user inter-

ferences before broadcasting the messages at the BS. Even though this non-linear

method is optimal, it requires high-complexity to preprocess the broadcast signals.

As a simplified approach, the linear zero-forcing beamforming (ZFBF) method has

been proposed in [64], which instead asymptotically achieves the same throughput

as dirty-paper coding for a large number of MSs. Both schemes assume that the BS

knows the channel state information (CSI) of all the MSs a priori. However, since this

CSI is delivered back to the BS via finite feedback channels practically, the amount of

CSI is correspondingly limited by feedback capacity. Therefore, the quantity of CSI

highly affects the performance of both schemes.


For example, Fig. 1.2 illustrates how the achievable throughput varies depend-

ing on the amount of CSI, where the number of arrows indicates the multiplexing

gain as a performance measure. The multiplexing gain is defined as the ratio of the

total throughput to the logarithm of transmit power as signal-to-noise ratio (SNR)

increases. When the system fully obtains the perfect CSI at the BS, it can achieve

the full multiplexing gain, which is the same as the number of transmit antennas as

shown in Fig. 1.2(a). On the other hand, the BS requires CSI to take advantage of

the multiple BS antennas because the BS does not know which channels are strong

at each block period. Thus, the multiplexing gain would be fixed as one regardless of

the number of transmit antennas as shown in Fig. 1.2(b) in the absence of CSI.

Since the performance of beamforming strategies highly depends on the amount

of CSI supported by finite feedback rates, the investigation into the analytical rela-

tion between the finite amount of feedback and the corresponding performance is an

essential prerequisite for practical broadcast transmission design. Recently, [28] has

shown this relation based on the zero-forcing beamforming (ZFBF) strategy. There,

the number of feedback bits should linearly increase as the SNR increases to prevent

performance degradation and to achieve the multiplexing gain. This ZFBF scheme

operates by decoupling a multi-user channel into single-user sub-channels so that the

beam for each MS becomes orthogonal to beams for other MSs. However, if the

feedback rates are finite, the CSI delivered back to the BS inevitably needs to be

quantized.

CSI quantization errors are the difference between the CSI fed back to the BS

and the real CSI of MSs. This difference reduces orthogonality among the beams of

ZFBF and consequently the performance of ZFBF. When the number of feedback

bits is fixed, the amount of multi-user interference increases as the SNR increases,

because the amount of multi-user interference is proportional to both the SNR and

the quantization errors. Thus, to reduce the interference effects, the quantization er-

rors should correspondingly decrease as the SNR increases. Equivalently, the number

of feedback bits needs to increase, as the SNR increases. A scalable feedback-bits

strategy in ZFBF should not only be simple but also effective to achieve substan-

tial multiplexing gain with finite feedback rates. However, this strategy is only valid

5

BS

MS

MS

MS

MS

(a) Full CSI at the BS

MS

MS

MS

BS

MS

MS

MS

MS

(b) No CSI at the BS

Figure 1.2: The amount of CSI decides whether or not achieving the full multiplexinggain.


when the required number of feedback bits can be increased with higher SNR. Oth-

erwise, the multi-user interference could not be cancelled sufficiently and the total

throughput saturates at high SNR. Many promising wireless systems such as mobile

WiMAX (Worldwide Interoperability for Microwave Access) and 3GPP LTE (The

3rd Generation Partnership Project Long Term Evolution) restrict the availability of

feedback bits because of uplink bandwidth limitations from MSs to the BS. Thus,

it is crucial to consider innovative methods to conserve the number of feedback bits

while maintaining the performance.

As an alternative technology, relaying has been extensively researched to extract

another diversity effect, cooperation, for future wireless networks. Along with spatial,

frequency and multi-user diversities, cooperative diversity has been also regarded

as a strong resource that can enhance performance. In [38], relaying technology

is integrated to MSs in wireless cellular networks and used with the following two

methods: The first uses in-band relaying, where inactive MSs in a cell play a role of

relay stations (RSs) to serve active MSs. The second uses out-of-band relaying where

MSs equipped with multiple radio interfaces communicate with other MSs for joint

signal processing. The in-band relaying scheme is relatively simple. Its performance

depends highly on the scheduling intervals between the role of MS and of RS. On the

other hand, the out-of-band relaying is essentially the same as conferencing, which

is the theoretical strategy of simultaneous message exchanges over orthogonal links

between nodes as proposed in [59]. It has been already shown that the conferencing

can expand achievable rate regions of multiple access channels in [59] and of broadcast

channels in [17]. Fig. 1.3 illustrates that current MSs operate on multiple interfaces

as well as communicate with one-hop relaying. In future wireless networks, both

functions are expected to converge to implement cellular networks conferencing.

The first part of this thesis is entirely motivated by the potential of cooperative

diversity to save the number of feedback bits without sacrificing the performance.

Thus, this thesis comprehensively addresses the scenario where MSs can cooperate

with nearby MSs via orthogonal relaying to broadcast channels. The focus is on the

trade-off relation between system resources such as the number of feedback bits, the

amount of cooperation over relaying, and the number of MSs. Furthermore, optimal

7

Smart Relaying

WiFiCellular

Cellular

Bluetooth

Figure 1.3: The heterogenous interfaces are exploited simultaneously.

allocation of relay power across multiple subcarriers can enhance the cooperative

effectiveness so as to maintain the reliable cooperation. The main objectives of the

first part summarize as.

• Verify the advantages of MS cooperation in cellular channels.

• Investigate the trade-off relation between system resources and identify the

smallest number of feedback bits to achieve the multiplexing gain in broadcast

channels.

• Develop a relaying-power optimization algorithm for effective cooperation be-

tween MSs based on OFDM modulation.

Multi-hop relay networks can significantly increase total throughput. Ref. [31]

shows that the total throughput can be larger in multi-hop networks than in single-

hop networks. When packets can be delivered to the next hop, it is possible that each

node transmits packets toward the destination that may be far from the source. Thus,

the system becomes more active and the total throughput increases correspondingly.

However, these gains assume that all the nodes are spontaneously willing to cooperate

with each other and that the requested packets are always relayed to the next hop.


Since every node independently operates without central authority, each node mainly

considers its own profit, and it may be consequently difficult to expect unconditional

cooperation from the neighbor nodes. Even though every node might be designed to

cooperate inherently, distributed networks could be vulnerable to any nodes’ private

activities or faults. For example, a node could take advantages of other node’s help,

so then some nodes would only take beneficial actions to themselves and refuse to help

others. Once every node becomes suspicious of neighbors’ behaviors, then it would

not spontaneously cooperate any more and become selfish for all further activities

and thereby degrade the performance. Therefore, it is essential to develop intelligent

distributed algorithms to motivate each node to be cooperative as well as to be

beneficial to their own performance.

Recently, game theory has attracted an attention as a powerful tool designed for

distributed algorithms. In game theory, every player is selfish and pursues only their

own profit. When competing with opponents, every player decides his best action

or his best response based on game parameters in terms of their profit. Under the

assumption that other players also behave reasonably, the best responses of all the

participants could converge to an equilibrium, where each can improve no further.

This point is called a ”Nash Equilibrium”, and the game becomes stable at this Nash

Equilibrium. Among many proposed game-theory models, this thesis investigates

”Cournot competition” and ”Stackelberg competition” for distributed algorithms in

multi-hop networks. In Cournot competition, both players decide their responses

simultaneously; in Stackelberg competition, both players take actions sequentially.

In multi-hop networks, a sender initiates the game by requesting to relay packets

and then the next hop responds based on given game parameters. Therefore, this

sequential procedure is a better fit to the Stackelberg model.

The second part of this thesis describes simultaneous cooperation between inde-

pendent nodes under limited energy. The energy constraint drives each node toward

careful decision on whether or not to cooperate. Using game theory, this thesis de-

signs a proper algorithm that can be beneficial to both individual nodes and to the

network itself. As a result, the new presented results can increase the reliability of

relayed traffic in multi-hop networks. The key objectives for this second part are

1.1. THESIS OVERVIEW 9

summarized as follows:

• Corroborate the advantage of cooperation with a game-theoretic perspective in

multi-hop networks.

• Develop the distributed algorithm where even selfish nodes can contribute to

the network instead of being isolated.

1.1 Thesis Overview

This thesis consists of six chapters. This section summarizes each chapter with its

key contents and describes each chapter’s link to other chapters.

Chapter 2 introduces the fundamental results of communication with an informational-

theoretical view of capacity as the supremum of all achievable rates. Prior to consid-

ering the capacity of cooperative communication, the basics of point-to-point commu-

nication and multi-point communication are first presented, and then their relation

to cooperative communication is addressed. In fact, point-to-point communication

using multiple dimensional resources such as multiple antennas can be considered as

fully cooperative communication because a single user exploits all the information

across multiple antennas coherently. On the other hand, the multi-point communi-

cation using a single dimension such as a single antenna can be considered as non

cooperative communication because a single antenna limits each user to use of only

its own information. Accordingly, partial-cooperative communication is also then in-

troduced and modelled. As a result, the cooperation between nodes using orthogonal

bit-pipes with finite capacities, called conferencing, has been proposed theoretically

and is introduced to derive the capacity in this chapter.

Chapter 3 applies the background listed in Chapter 1 and 2 into multi-user broad-

cast channels (BCs) for cellular systems. Each mobile station (MS) will be equipped

with multiple interfaces such as cellular, Wi-Fi and bluetooth, and only one such

interface is used today according to its respective requirements. This chapter focuses

on the potential advantages of using multiple interfaces simultaneously to implement


conferencing between MSs. Furthermore, cooperation through the conferencing be-

tween MSs inevitably involves use of feedback channels from MSs to the base station

(BS). In multi-user cellular channels, the total throughput performance depends on

the quality of channel state information (CSI) of each MS at the BS. The CSI at

the BS are then positively related to the amount of feedback information as well as

the amount of cooperation. Since both types of resources, cooperation between MSs

and feedback from MS to BS, contribute to increased throughput, the amount of

feedback information from MSs is inversely related to the strength of cooperation be-

tween MSs. Thus, this chapter analyzes this trade-off relation in order to achieve the

constant level of throughput, and the results are extended into the case with multiple

MSs. Finally, the relation among these system parameters such as the number of

feedback bits, the amount of cooperative gain, and the number of MSs are revealed

so that the proposed scheme can reduce the required number of feedback bits while

maintaing the sum-rate performance. Part of the work in Chapter 3 is presented

in [32,33,35].

In Chapter 3, the focus is on what resources can be exploited to enhance the sum-

rate performance of multi-user cellular channels through MS cooperation. On the

other hand, Chapter 4 investigates efficient exploitation of the resources to enhance

the sum-rate performance. Thus, Chapter 4 formulates the optimal power-allocation

problem across multi-carrier subchannels on relaying channels used in conferencing.

Since the quality of each subchannel on relaying channels between MSs is differ-

ent, proper power-allocation across multiple subchannels based on their strength can

mitigate the inevitable noise enhancement in amplify-and-forward relaying. As a

result, the sum-rate performance over signal-to-interference-and-noise ratio (SINR)

is improved, and the conferencing between MSs becomes more stable. The original

relaying power-allocation problem is shown to be non-concave so that it is difficult

to solve with general convex strategies. Instead, this chapter transforms the original

non-convex optimization power-allocation problem into a series of standard convex

optimization sub-problems so that an interior-point method can be used for solution.

Part of the work in Chapter 4 is presented in [34].

Chapter 5 addresses a cooperative algorithm for relay nodes from a game-theoretic

1.1. THESIS OVERVIEW 11

perspective. In multi-hop networks, every node must operate independently without

any central authority under energy constraints. Therefore, unconditional cooperation

between nodes is not encouraged because each node preserves its own energy by not

relaying other nodes’ packets. Using a Stackelberg competition from game theory,

the conditional cooperation between nodes can adjust the amount of limited energy

to allocate some to cooperative activities. Thus, the relaying of packets is negotiated

between a sender and a relay. This negotiation between nodes encourages each node

to be cooperative by accumulating conditional cooperative histories. As a result, the

total network throughput increases, and the system becomes more reliable. Chapter 5

also derives equilibrium analysis for the proposed scheme to show the stable operation

under energy constraints. Part of the work in Chapter 5 is presented in [36].

Finally, Chapter 6 summarizes this thesis with the key points of each chapter, and

concludes with the benefit of cooperative communication for both centralized and de-

centralized networks. Cooperative communication is viewed as a positive activity that

improves through use of new resources such as conferencing between MSs in multi-

user cellular channels or relaying between nodes in multi-hop networks. Therefore, it

is essential to compute the gain of the resource use. This thesis thus answers some

important questions about cooperative communication for future wireless networks.

Chapter 2

Theoretic Background for

Cooperative Communication

This chapter introduces theoretical backgrounds of the evolution of wireless commu-

nication from point-to-point systems to multi-point systems, and the relationship of

cooperative communication to them. The capacity of wireless communication can be

increased by evolving point-to-point communication to multi-point communication.

Thus, tracking of this evolution facilitates understanding the pros and cons of each of

these systems. Moreover, it explains the need for cooperative communication as an

alternative method to improve the capacity for future systems. Information theory

is a suitable tool that can describe the transition in wireless communication by pro-

viding mathematically precise proofs and also system insights. This chapter surveys

previous information theoretic achievable rates to demonstrate the advantage of co-

operative communication, and provides theoretical backgrounds from the survey for

understanding the cooperative schemes in the next chapters.

The rest of this chapter is organized as follows: Sec. 2.1 models point-to-point

communication system, and introduces some important results to derive the channel

capacity. Sec. 2.2 explains multi-point communication with multiple access chan-

nels and broadcast channels. Sec. 2.3 shows how cooperative communication relates

to both point-to-point communication and multi-point communication, and Sec. 2.3

introduces conferencing as a tool of cooperation. Finally, Sec. 2.4 summarizes this

12

2.1. POINT-TO-POINT COMMUNICATION 13

chapter.

2.1 Point-to-Point Communication

This section explains how a point-to-point communication has been developed in

information theory. In [46, 47], Shannon initially established a complete theory for

point-to-point communication, and provided many principal theorems of communi-

cation. For instance, his source-coding theorem introduced the concept of entropy

to quantify an uncertain event by a number of bits. Moreover, he has also found

a noisy-channel maximum capacity that limits the reliable communication over a

noisy channel. These principles have been developed to more complex cases, such as

channels with multiple dimensions or multiple antennas.

Research on a simple single-path channel has extended to multi-path channels,

based on scattering effects. A wireless signal is often transmitted over a line-of-sight

channel. However, the signal could also be reflected and refracted by the obstacles

near the channel. As a result, the received signal may experience fading when signals

on different paths arrive 180 degrees out of phase. Ref. [19] considers the capacity

of wireless channels in such fading environments. In particular, [19] shows that the

channel capacity can be significantly enhanced with multiple antennas to transmit

several symbols simultaneously. Ref. [52] extends this observation to any systems

using multi-dimensional resources in Gaussian channels. Fig. 2.1 shows various types

of point-to-point communication systems that differ in the number of antennas. The

most basic point-to-point communication system is single-input single-output (SISO)

over which only scalar symbols can be transmitted sequentially as in Fig. 2.1(a). By

increasing the number of antennas either at the transmitter or at the receiver as in

Fig. 2.1(b), a vector form of signals can be transmitted over the channel so that

the channel capacity increases correspondingly. If both sides use multiple antennas

simultaneously as in Fig. 2.1(c), a vector form of the signal is delivered through a

matrix form of the channel in a multiple-input multiple-output (MIMO) system so as

to increase the channel capacity.

With such multi-dimensional resources, the channel extends from a scalar form

14CHAPTER 2. THEORETIC BACKGROUND FOR COOPERATIVE COMMUNICATION

ChannelEnc. Dec.M

X YM

(a) SISO

ChannelEnc. Dec.M M

YX

ChannelEnc. Dec.M

Y

M

X

(b) MISO, SIMO

ChannelEnc. Dec.M M

YX

(c) MIMO

Figure 2.1: Point-to-point channels

2.2. MULTI-POINT COMMUNICATION 15

to a vector and matrix form. The channel capacity can be further increased by

adding more nodes at the transmitter side or at the receiver side. Thus, multi-point

communication extends point-to-point communication, and will be explained in the

next section.

2.2 Multi-Point Communication

Classically, multi-point communication divides into a multiple access channel (MAC)

and a broadcast channel (BC). The MAC has multiple encoders transmit their mes-

sages to a single receiver that decodes all the messages together. The BC has a single

encoder broadcasting the signals generated by multiple decoders. The MAC and BC

are thus duals to each other.

Fig. 2.2 shows a MAC consisting of two encoders and a decoder. Since both

encoders have a message set to send, the maximum achievable rate extends to the

concept of a rate region. Ref. [1,39] defines the MAC’s capacity region as the closure

of the set of all achievable rate pairs, and mathematically it is expressed as those rate

pairs (R1, R2) satisfying

R1 ≤ I(X1;Y |X2, Q),

R2 ≤ I(X2;Y |X1, Q),

R1 +R2 ≤ I(X1, X2;Y |Q) (2.1)

where Q is an auxiliary variable with cardinality |Q| ≤ 2. When MAC follows a

Gaussian distribution, the achievable rate region is specified rigorously in [15, 61].

Similarly, Fig. 2.3 shows a BC consisting of a encoder and two decoders. However,

it is not as easy to characterize the BC rate region in practice because one encoder

should decide coding schemes for two separated decoders a priori before sending the

messages. To find a solution for this challenge, an idea based on superposition cod-

ing has been used in the degraded BC, as in [14]. The message sets are generated

independently, and then one set plays a role in encoding the second set. By using


Enc. 1

Enc. 2

MAC Dec.

X1

X2

M1

M2

(M 1,M 2)

Figure 2.2: Multiple access channel (MAC)

Enc. BC

Dec. 1

Dec. 2

(M1,M2)X

Y1

Y2

M1

M2

Figure 2.3: Broadcast channel (BC)

superposition coding, the maximum achievable rate region for the BC can be success-

fully achieved.

2.3 Cooperative Communication

This section introduces cooperative communication, and describes how it has evolved

from classical point-to-point and multi-point communications. For instance, Fig. 2.4

compares point-to-point communication where a decoder uses two antennas with

multi-point communication where both decoders use a single antenna. In the first

case, the decoder simultaneously receives two streams such that it can coherently

share the signals received at both antennas to achieve the capacity. However, each

decoder in the second case receives only one signal from which to decode its own

2.3. COOPERATIVE COMMUNICATION 17

ChannelEnc. Dec.

Channel

Dec.

Enc.

Dec.

Figure 2.4: Full cooperation and no cooperation.

information where any interference is treated as a noise. This thesis considers the

first as a fully cooperative communication system, i.e., a decoder with two antennas

is equivalently considered as two decoders with a single antenna which can cooperate

with each other. On the other hand, the second is a non-cooperative communication

system.

Then, this thesis defines partial-cooperative communication. Initially, [59] ad-

dressed the same definition and proposed a new communication situation where two

users are connected by a cooperative link. The following subsections investigate this

partial-situation known as a ”conferencing”.

2.3.1 MAC with Cooperating Encoders

The classical MAC scenario has two encoders that transmit independent messages

to a single decoder as shown in Fig. 2.2. If the encoders are at the same location

and are able to unrestrictedly communicate with each other, the capacity for this

MAC would be the same as that of the point-to-point communication where the

encoder is equipped with two antennas. However, if both encoders are at different

locations and connected with finite-capacity links, the capacity of this partial coop-

erating MAC would be less than that of full cooperating MAC. [59] proposed this


Enc. 1

Enc. 2

MAC Dec.

X1

X2

M1

M2

(M 1,M 2)C12C21

Conferencing

Figure 2.5: MAC with cooperating encoders

partial-cooperation scenario and derived its capacity region for a discrete memory-

less MAC with cooperating encoders. Briefly, this section summarizes the result of

cooperating MAC in [59].

Fig. 2.5 shows two encoders that use conferencing, i.e., the simultaneous mes-

sage exchange through finite-capacity bit-pipes. In the scenario of [59], the discrete

memoryless MAC is denoted by the triplet (X1 × X2, p(y|x1, x2),Y) and the mes-

sages sent from both encoders are the random integers as W1 ∈ {1, 2, . . .M1} and

W2 ∈ {1, 2, . . .M2}. At each block period, each pair (w1, w2) is randomly selected

with equal probability and is transmitted to the receiver over the channel. Then, the

ith encoder maps both the original message W1 (or W2) and the conferencing message

into a codeword Xn1 (or Xn

2 ), where the superscript n is the length of the codeword

vector, by using the encoding function fi.

The conference between both encoders results in K subsequent pairs of commu-

nications on the conferencing links. Let hik denote the mapping function for the

ith encoder and the kth conferencing message from previously received conferencing

messages (vj1, vj2, . . . , vjk−1)j 6=i△= V k−1

2 . Then, this process is summarized as follows:

v1k = h1k(W1, Vk−12 ), (2.2)

v2k = h2k(W2, Vk−11 ), (2.3)

XN1 = f1(W1, V

k2 ), (2.4)

XN2 = f2(W2, V

k1 ) (2.5)


where k = 1 . . . K. The cardinalities of v1k and v2k are represented by V1k and V2k,

respectively.

Since the conferencing is the partial cooperating-based process, the amount of

information exchanged on the conferencing links are limited by their finite capacities,

C12 and C21, where C12 stands for the capacity of the link from encoder 1 to encoder

2, and vice versa. Thus, a conference is called (C12, C21)-permissible only if the

cardinalities of vik satisfies

1

N

∑

k

log(|V1k|) ≤ C12, (2.6)

1

N

∑

k

log(|V2k|) ≤ C21. (2.7)

Then, the decoder produces the estimates of a pair of the message, (W1, W2), from

the received output sequences Y n. The rate pair (R1, R2) is said to be achievable

when the probability, p((W1,W2) 6= (W1, W2)), goes to zero as N increases.

As a result of a single exchange between conferencing messages, the capacity

region for the discrete memoryless MAC with conferencing encoders is derived in [59,

Theorem 8.1] as follows:

R1 ≤ I(X1;Y |X2, U) + C12,

R2 ≤ I(X2;Y |X1, U) + C21,

R1 +R2 ≤ min{I(X1, X2;Y |U) + C12 + C21, I(X1, X2;Y )} (2.8)

for p(u, x1, x2, y) = p(u)p(x1|u)p(x2|u)p(y|x1, x2) and U ≥ min{|X1||X |2+2, |Y|+3}.When the conferencing links deliver no messages, i.e., C12 = C21 = 0, the rate region in

(2.8) becomes identical to the capacity region of a classical MAC where two encoders

transmit messages to a decoder without cooperation.

The conferencing at a MAC has been developed into a variety of distinct models.

In [41], the discrete memoryless compound MAC with conferencing encoders has

been considered where two encoders transmit messages to two decoders and two

independent messages are decoded at both decoders. In addition, [10] extends the


result into the Gaussian MACs with conferencing encoders under power constraints,

and simplifies the analysis on the conferencing. Also, [48] and [58] have increased

the number of users in a MAC and investigated a three-user Gaussian MAC with

conferencing encoders. Recently, it is generalized in [24] that fading channels have

been considered in a Gaussian MAC with conferencing encoders under the constraint

of partial channel information at the encoders.

2.3.2 BC with Cooperating Decoders

This subsection describes a BC with cooperating decoders, which is the dual of a

MAC with cooperating encoders. In the classical BC scenario, each decoder only

decodes its own messages while treating interference as a noise. Thus, the maximum

achievable sum-rate of the BC cannot be larger than the capacity of a single point-to-

point channel having the same number of antennas as the number of users in the BC.

The bridge between the classical BC and the point-to-point channel is that the BC

uses cooperation between decoders as the MAC uses cooperation between encoders.

Initially, [17] proposed a BC with direct cooperation between decoders as depicted

in Fig. 2.6, which is the dual of Fig. 2.5. In this scenario, a single encoder transmits

two independent messages encoded into a single codeword Xn with the length n to

two decoders over the BC. Then, each decoder receives the noisy codeword Y n1 and

Y n2 , respectively. The received signals are exchanged through conferencing links of

finite capacities, C12 and C21, between decoders, and each decoder then decodes its

own messages from both Y n1 (or Y n

2 ) using previously received conferencing messages.

As explained in [17], the scenario for a BC with cooperating decoders combines

broadcasting with the relaying so as to consider a hybrid version of both broadcast

and relay systems. Ref. [13]’s enumeration of relaying technologies lead to extensions

of the single-relay results, [63] and [31]. Also, [56] characterizes relay channels with

multiple antennas. This subsection considers a BC with conferencing decoders that

use relaying channels that are in addition to, and orthogonal to, those of the BC.

Similar to a MAC with conferencing encoders, a discrete memoryless BC with


Enc. BC

Dec. 1

Dec. 2

(M1,M2)X

Y1

Y2

M1

M2

C12

C21

Figure 2.6: BC with cooperating decoders

conferencing decoders is denoted by the triplet (X , p(y1, y2|x),Y1 × Y2). The confer-

ence rate pair (R12, R21) is said to be admissible when both conditions, R12 ≤ C12

and R21 ≤ C21, are satisfied where the Rij stands for a conference rate from a decoder

i to a decoder j. When (R12, R21) are admissible, the conference message sets are

defined as W12 = {1, 2, . . . , 2nR12} and W21 = {1, 2, . . . , 2nR21} to represent the mes-

sages relayed through conferencing links. These conferencing messages are mapped

with the received symbols from one decoder to the other decoder by using mapping

functions, h12 and h21, as

h12 : Yn1 ×W21 7→ W12,

h21 : Yn2 ×W12 7→ W21 (2.9)

where a single exchange of the conferencing messages between decoders is considered.

In this BC with conferencing decoders, an encoding function f maps two message

sets for two decoders into a codeword X n as

f : W1 ×W2 7→ X n, (2.10)

where Wi = {1, 2, . . . , Ri} is the integer set for the decoder i and Ri is the correspond-

ing rate for the BC. Then, the combined symbols from the BC and the conferencing


links are decoded by using two decoding functions as follows:

g1 : W21 × Y1 7→ W1,

g2 : W12 × Y2 7→ W2. (2.11)

Under this scenario, Theorem 2 of [17] derives the achievable rate region of a BC

with conferencing decoders as any rate pair (R1, R2) satisfying

R1 ≤ R(U),

R2 ≤ R(V ),

R1 +R2 ≤ R(U) +R(V )− I(U ;V ), (2.12)

subject to,

C21 ≥ I(U ;Y2)− I(U ;Y1),

C12 ≥ I(V ;Y1)− I(V ;Y2),

where

R(U) = I(U ;Y1, U),

R(V ) = I(V ;Y2, V ),

for some joint distribution p(u, v, x, y1, y2, u, v) = p(u, v, x)p(y1, y2|x)p(u|y2)p(v|y1)with u ∈ U , v ∈ V , u ∈ U , v ∈ V , ‖U‖ ≤ ‖Y2‖ + 1 and ‖V‖ ≤ ‖Y1‖ + 1 is

achievable. It becomes clear in (2.12) that the achievable rate region for the BC

with conferencing decoders is increased by the capacities of the conferencing links.

To illustrate the conferencing effect in a BC, the capacity region for the physically

degraded binary symmetric BC is depicted in Fig. 2.7 from [17] and shows how much

this rate region can be increased compared to the non-cooperative case.

Recently, the discrete memoryless BC is extended into the Gaussian BC supported

by various types of cooperation between decoders. Ref. [37] considers a single common

message transmitted over the Gaussian BC with cooperating decoders for several

2.4. SUMMARY 23

1I(X;Y )

2I(X;Y )

2I(X;Y )+C

1I(X;Y )

R2

R1

C12

12

Figure 2.7: Illustration of the achievable rate region for physically degraded BSBCfrom [17]

coding schemes such as estimate-and-forward or decode-and-forward. In addition, [5]

studies the Gaussian BC with bidirectional cooperation channels, and [16] studies BC

with cooperation as well as feedback for a finite-state model.

2.4 Summary

This chapter reviews information theoretic results for several types of communication:

point-to-point communication, multi-point communication, and cooperative commu-

nication. The capacity region of cooperative communication exceeds that of a multi-

point communication by the amount of conferencing links’ capacities. This advantage

of cooperation motivates application of cooperation in cellular networks, as well as in

multi-hop networks. The following chapters propose cooperation and analyze results

with simulations.

Chapter 3

Multi-User BC using Conferencing

and Limited Feedback

Multiple-input multiple-output (MIMO) techniques in broadcast channels enhance

the performance of multi-user cellular systems. However, a challenge is simultane-

ous service of several mobile stations (MSs) with multi-user interference, for which

many transmission techniques have been extensively studied. The dirty-paper cod-

ing technique is the optimal scheme for maximization of the Gaussian BC sum-

capacity [57]. Lower-complexity linear precoding techniques such as zero-forcing

beamforming (ZFBF) [64] and per-user unitary rate control (PU2RC) [26] also can

be effective. Both these schemes achieve the same asymptotic sum-capacity as dirty-

paper coding as the number of MSs becomes large. All these methods require perfect

knowledge of each MS’s channel state information (CSI) at the base station (BS).

The BS obtains the CSI of each MS by using feedback channels. Such feedback-

channel rates are finite and thus limit the performance of multi-user MIMO schemes.

For example, an insufficient number of feedback bits in ZFBF significantly degrades

multi-user channel performance [28]. Fig. 3.1 illustrates MS channel vectors and the

ZFBF’s corresponding antenna beams. If the BS perfectly knows the CSI, then each

channel vector such as h1 and h2 for MS 1 and MS 2 must be fed back without

errors. With such perfect feedback, the beam w3 for MS 3 becomes orthogonal to the

channel vectors h1 and h2. However, finite feedback prevents the BS from obtaining

24

25

h2

h1

w3

R1

R2

h1

h2

w3

h3

Figure 3.1: The quantized channel information prevents the zero-forcing beam, wi,from being orthogonal to channel vectors, hj 6=i, of other MSs.

the exact channel vectors so that h1 is fed back to the BS instead of h1. Therefore,

the corresponding beam becomes w3 instead of w3, which is not orthogonal to h1

or h2. To reduce this degradation, the number of feedback bits can be increased as

signal-to-noise ratio (SNR) increases [65]. However, especially at high SNR, a large

number of feedback bits limits the improvement of multi-user MIMO schemes.

Another approach to increase the achievable rate uses cooperation between MSs.

Ref. [59] initially proposed a multiple-access channel (MAC) with cooperating en-

coders using conferencing, i.e., the simultaneous communication between nodes on

finite-capacity additional links. Ref. [10] extends this scheme to Gaussian MACs.

The dual of the Gaussian MAC’s conferencing is a broadcast channel with cooperat-

ing decoders [17], and [16] shows the benefits of both feedback and cooperation. In

addition to these theoretical approaches, [60] applies cooperation to cellular networks

that are integrated with ad-hoc relaying systems. [38] classifies integrated relaying

into two methods: in-band relaying and out-of-band relaying. The first method uses

inactive MSs as RSs, and the second method uses MSs equipped with multiple radio

26CHAPTER 3. MULTI-USER BC USING CONFERENCING AND LIMITED FEEDBACK

interfaces operating on the additional out-of-band spectrum for relaying. The latter

method is compatible with theoretical conferencing because cellular networks use dif-

ferent spectrum compared with ad-hoc relaying networks. This motivates the design

of cooperating MSs with effective precoding and postcoding techniques to reduce the

feedback load.

This chapter combines conferencing between MSs in a broadcast channel with

limited feedback. With MS cooperation, the proposed scheme can achieve full mul-

tiplexing gain, even though the number of feedback bits decreases. This result is

meaningful because the feedback channel in cellular networks is expensive, while the

amount of out-of-band resources between nearby MSs may be less costly. Thereby,

use of out-of-band relaying substantially improves the sum-rate gain in broadcast

channels.

The investigated scenario consists of a two-stage feedback procedure as in [30,49].

First, each MS reports the set of nearby cooperating MSs in an effort to maximize the

sum-rate after receiving training sequences. Once the BS selects the best set of MSs,

the selected MSs inform the BS of their preferred beamforming indices. Under this

scenario, the proposed scheme satisfies a derived relation among the SNR, the number

of feedback bits, cooperative gains, and the number of MSs to achieve full multiplexing

gain. Simulation results permit evaluation of the sum-rate and verification of the

derived relation. As the number of MSs or cooperative gain increases, the minimum

number of feedback bits decreases accordingly. In other words, the proposed scheme

enhances the performance while saving feedback resources.

The rest of this chapter is organized as follows: Sec. 3.1 describes multi-user

broadcast channels with conferencing. Sec. 3.2 explains the receive combining and

transmit beamforming strategies. Sec. 3.3 discusses the number of feedback bits with

respect to cooperation and the number of MSs. After evaluating the simulation results

for the proposed scheme in Sec. 3.4, Sec. 3.5 summarizes this chapter.

3.1. SYSTEM MODELS 27

3.1 System Models

This section considers a multi-user broadcast channel in a single cell where the BS is

equipped with M transmit-antennas and K ≥ M MSs, each having a single receive-

antenna. Each MS has both cellular and ad-hoc interfaces. Thus, each MS can for-

ward the received signals on the cellular interface into nearby MSs over the secondary

interface, enabling conferencing.

3.1.1 Broadcasting Models

The received signal at MS i from a broadcast channel is represented as

yi = h†ix+ ni, i = 1, 2, · · · , K (3.1)

where hi ∈ CM×1 is a channel vector of MS i with zero mean unit variance i.i.d.

complex Gaussian entries. The channel is quasi-static, i.e., it is invariant over each

block period. The noise ni follows an independent complex Gaussian distribution

with variance N0. The signal x ∈ CM×1 consists of data symbols sm and beamforming

vectors bm for MS m as follows:

x =M∑

m=1

bmsm. (3.2)

The input x satisfies an average power constraint E[‖x‖2] = Pt, and the total power

is equally distributed to all the symbols. Using reference signals, each MS has perfect

knowledge of its own channel vector as well as nearby MSs’ channel vectors that are

forwarded on relay channels.

3.1.2 Conferencing Models

To cooperate with nearby MSs, each MS uses an amplify-and-forward relaying. This

relatively simple strategy reduces the delay to remodulate the received signals. Before


being forwarded, the received signal is normalized as

yi =yi

√

E [‖yi‖2]=

yi√

Pt

Mh†i

(

∑M

m=1 bmb†m

)

hi +N0

, (3.3)

and is amplified with the mobile power Pr. Then, the relayed signal from MS i to MS

j is described as

yij =√

αijPryi + nij

=√giyi + nij , (3.4)

where αij is a relay channel gain and nij is the additive noise with unit variance at the

relay channel. This work assumes that cooperation occurs for MSs that are closely

located. Thus, the multi-path effect on relay channels and the distance difference

between MSs is negligible so that the relay channel gain is considered constant, αij :=

α, for all i and j. In (3.4), the relayed signal from MS i is simplified with a relay

gain,

gi = αPr/E[

‖yi‖2]

=αPr

Pt

Mh†i

(

∑M

m=1 bmb†m

)

hi +N0

(3.5)

↔ 1

gi=

h†i

(

∑M

m=1 bmb†m

)

hi

Mβ+

1

βρ(3.6)

where the inverse of the relay gain is equivalently expressed in (3.6). The cooperative

gain β is defined as αγ where the variable γ is the ratio of mobile power at a MS

to transmit power at a BS, i.e., γ = Pr

Pt. In addition, ρ represents the SNR Pt

N0. To

coordinate the received signals from relay channels, each MS aggregates all the signals

3.1. SYSTEM MODELS 29

after dividing them by the corresponding relay gains. These signals are given by

¯yij = yi +1√ginij

=

{

h†ix+ ni +

1√ginij ∀ i 6= j

h†ix+ ni ∀ i = j,

(3.7)

where, as a result, noise signals are amplified through relaying. The aggregated signals

at MS j can be equivalently expressed as a vector form,

yj =

¯y1j¯y2j...

¯yMj

= H†x+ [ IM Dj ]

[

n

nj

]

= H†x+Gjnj, (3.8)

where H is a broadcast channel matrix whose ith column is hi, and nj ∈ C2K×1 is

the total noise vector consisting of n and nj. In addition, IM is an identity matrix

with a size of M , and Dj is a diagonal matrix whose ith element is 1√gi

if i 6= j or

zero if i = j. Thus, the matrix Gj ∈ CK×2K is represented by the concatenation of

IM and Dj. Finally, the aggregated signal vector is filtered with receive combining

vector wj ∈ CM×1 at MS j so that the processed signal for MS j reduces to

zj = w†jyj

= w†jH

†bjsj +∑

m 6=j

w†jH

†bmsm +w†jGjnj, (3.9)

which consists of the decoded signal, the multi-user interference caused by imperfect

CSIT at the BS, and the enhanced noise caused by partial cooperation among MSs,

respectively.


3.2 Joint Processing with Filtering Vectors

This section explains how receive-combining vectors are chosen and how beamforming-

vectors are selected. Then, the corresponding throughput is jointly processed to

reduce multi-user interference so as to increase the SINR at each MS.

3.2.1 Receive-Combining

A receive combining vector wi is designed to employ only the channel information for

MS i. To extract such user-specific information, the channel matrix is factored with

QR decomposition (QRD) as

H = QR† (3.10)

where Q is an orthonormal matrix and R is a lower triangular matrix. The vector

qi and ri are the ith column vector of Q and R, respectively. The inner-product

of combining vector with the aggregated signal vector causes unintended multi-user

interference. To avoid the effect of interference, MS i determines the combining vector

in the null space of Ri, which is a matrix, to exclude only ri from R as

Ri = [ r1 . . . ri−1 ri+1 . . . rK ] ∈ CM×(K−1), (3.11)

and the corresponding combining vector is represented by

wi ∈ N (Ri). (3.12)

Then, the vector wi is orthogonal to the space spanned by Ri as shown in Fig. 3.2.

The inner-product with R results in

w†iR = [ 0 . . . w†

iri . . . 0 ] ∈ C1×M (3.13)

where all the elements except the ith are canceled.

3.2. JOINT PROCESSING WITH FILTERING VECTORS 31

ri+1

rk

ri-1

wi

ri

Figure 3.2: The combining vector for MS i is chosen in the null space of Ri so that itis orthogonal to rj 6=i.

3.2.2 Transmit-Beamforming

To eliminate multi-user interference, the beamforming vector bi should be chosen to

align with a vector qi and simultaneously be orthogonal to the remaining column

vectors in the matrix Q. However, finite-rate feedback prevents the BS from using

the beamforming vector that satisfies the condition above. Instead, the BS selects the

best beamforming vector from a finite codebook F = {fi}2B

i=1 where B is the number

of available feedback bits, and fi is the ith codeword, isotropically and independently

distributed in CM×1. Random vector quantization (RVQ) is sub-optimal to create

such a codebook, but it is very simple and can be well analyzed. In addition, the

RVQ penalty of sub-optimality is very small when B is high enough [3]. Using RVQ,

the beamforming vector is determined as

bi = argmaxf∈F

|q†i f|2 (3.14)

and is shown in Fig. 3.3. The index of bi is fed back to the BS. Let the random

variable Z denote the quantization error corresponding to the selected beamforming


qi bi

qj

qk

bj

bk

Figure 3.3: The beamforming vector for MS i is chosen such that it is the closest tothe vector qi from a finite codebook F where |F| = 2B.

vector as

Z = 1− |q†ibi|2. (3.15)

If the perfect CSI at the BS is available, Z would always be zero. However, finite rate

feedback causes imperfect CSI, which leads to quantization errors. The cumulative

distribution function (CDF) of Z is given by [28] and expressed as

FZ(z) =

{

2BzM−1 0 ≤ z ≤ δ

1, x ≥ δ(3.16)

where δ = 2−B

M−1 . This quantization error distribution is used to analyze the required

number of feedback bits and conferencing channel gain to achieve the multiplexing

gain as the transmit power goes to infinity.

3.3. LIMITED FEEDBACK AND PARTIAL COOPERATION 33

3.3 Limited Feedback and Partial Cooperation

This section analyzes the system performance achieved by the proposed user-cooperation

with limited feedback scheme. Using the combining vectors and beamforming vectors

in (3.12) and (3.14), the signal-to-interference-plus-noise ratio (SINR) of MS i is given

by

SINRs,i =Pt

M|w†

iri|2|q†ibi|2

∑

j 6=iPt

M|w†

iri|2|q†ibj|2 +N0‖w†

iGi‖2(3.17)

where the subscript s indicates a set of MSs. This section considers two cases in the

following subsections. The first is that the number of transmit antennas is equal to

the number of MSs, i.e., M = K, and the second is that the number of transmit

antennas is less than the number of MSs, i.e., M < K so that a user-selection step is

required a priori.

3.3.1 Throughput Analysis with M = K

Under the condition, M = K, the SINR of MS i in (3.17) is only a function of both

B and β. Depending on B and β, the SINR varies to

SINRi

(a)=

Pt

M|w†

iri|2N0‖w†

iGi‖2(b)=

Pt

MN0

|w†iri|2 (3.18)

where (a) corresponds to the case when B goes to infinity so that no quantization

errors occur. In conjunction with (a), (b) uses infinite β, which corresponds to full

cooperation among MSs and makes ‖w†iGi‖2 = 1. This SINR is achieved only with

the ideal conditions of both parameters.

However, with a finite feedback rate and a limited cooperative gain, the through-

put performance is degraded accordingly. Under this constraint, the beamforming


vector bi can be decomposed by using a unit vector ti as

bi = qi cos θi + ti sin θi (3.19)

where the θi is the angle between two vectors, bi and qi, as shown in Fig. 3.3. Since

qi ⊥ ti and qi ⊥ qj, the inner-products with the beamforming vectors are

|q†ibi|2 = cos2 θi

|q†ibj|2 = |q†

itj|2 sin2 θj = β(1,M − 2) sin2 θj, (3.20)

where a beta-distributed random variable with parameters, 1 and M − 2, is used

to describe the relation where both unit vectors are isotropically distributed in the

M − 1 dimensional hyperplane orthogonal to qj, as in [28]. Since the beamforming

vector is chosen from independent 2B codewords, the expected quantization error is

correspondingly given by

Eb

[

|q†ibi|2

]

= Eb[cos2 θi] ≥ 1− 2−

BM−1 (3.21)

where the inequality follows Lemma 1 in [28]. Likewise, the expected quantization

error caused by interfered beamforming vectors is represented as

Eb

[

|q†ibj|2

]

=1

M − 1Eb[sin

2 θj] ≤1

M − 12−

BM−1 . (3.22)

Then, the enhanced noise via relay channels with finite gains is derived as

Eb

[

‖w†iGi‖2

]

= 1 + Eb

[

w†iD

2iwi

]

≤ 1 + Eb

(

1

mini=1...M gi

)

= 1 +1

β

(

maxi

h†iEb

[

M∑

m=1

bmb†m

]

hi

)

+M

βρ

= 1 +maxi=1...M‖hi‖2

β+

M

βρ= Zi. (3.23)


Using these properties, the performance loss can be measured by the rate gap

per MS which is the difference between two rates for MS i: one is with perfect CSI

at the BS and full cooperation, and the other is with limited feedback and partial

user-cooperation. The rate gap is defined by using (3.17) and (3.18), and is given by

∆R(B, β) = E

[

log2

(

1 +Pt

MN0

|w†iri|2

)

− log2

(

1 +Pt

M|w†

iri|2|q†ibi|2

∑

j 6=iPt

M|w†

iri|2|q†ibj|2 +N0‖w†

iGi‖2

)]

= E

[

log2

(

1 +Pt

M|w†

iri|2)

− log2

(

Pt

M|w†

iri|2M∑

j=1

|q†ibj|2 + ‖w†

iGi‖2)

+ log2

(

Pt

M|w†

iri|2∑

j 6=i

|q†ibj|2 + ‖w†

iGi‖2)]

(a)

≤ E

[

log2

(

Pt

M|w†

iri|2∑

j 6=i

|q†ibj|2 + 1 +w

†iD

2iwi

)]

(b)

≤ log2

(

1 +Pt

ME[

|w†iri|2

]

∑

j 6=i

E[

|q†ibj|2

]

+ E[

w†iD

2iwi

]

)

(c)

≤ log2

(

1 +Pt

MXi2

− BM−1 +

maxj h†i

(∑

bmb†m

)

hi

βM+

1

βPt

)

(d)≈ log2

(

1 +Pt

MXi2

− BM−1 +

1

βMF−1χ2(K)

(

K

K + 1

))

(3.24)

where N0 = 1 is assumed without loss of generality. In the above derivation, (a)

uses the facts that the expectation of the sum of quantization error |q†ibi|2 and M−1

random variables |q†ibj|2 is equal to 1 [28, Lemma 3], and ‖w†

iGi‖2 = 1+w†iD

2iwi ≥ 1.

Since log is a monotonically increasing function, the sum of first two expectations is

always non-positive. (b) follows from Jensen’s inequality applied to a log function.

(c) is obtained by using (3.22) where the sum of quantization errors is bounded by

2−B

M−1 . (c) also uses the fact that wi is a unit norm vector and the expectation of

w†iD

2iwi is bounded by 1/mini gi in (3.23). Xi is defined as the expectation of |w†

iri|2.Since ri is obtained from QR factorization, Xi is in the range of (0,M) and will be

analyzed in a detail in Sec. 3.3.2. When ri is projected to all the subspaces in CM ,

Xi approaches M . When ri is excluded from the subspaces spanned by other rj 6=i,


then Xi is close to 0. According to [18], it is known that for large K, the expectation

of the maximum of a random variable ‖hi‖2 is approximated by the inverse of CDF

of chi-square distribution with K degrees of freedom at KK+1

. Using the assumption

that∑

m b†ibi is close to an identity matrix, which is valid when a large number of

feedback bits is supported, (d) is justified at high SNR.

To keep a constant rate offset, this rate gap should be upper bounded by

∆R(B, β) ≤ log2 b, (3.25)

which requires the condition for B and β as follows.

B ≥ (M − 1) log2

Pt

MXi

b− 1− 1βM

F−1χ2(K)

(

KK+1

)

. (3.26)

As the number of feedback bits, the conferencing channel gain, or the mobile power

increases, the condition for maintaining a rate offset is relieved as desired. Thus, (3.26)

shows that both B and β are inversely proportional to each other. One resource can

be exploited more or less according to the amount of the other resource.

3.3.2 Throughput Analysis with M < K

Under the condition, M < K, the BS needs to select a group of M MSs out of K

MSs such that they easily cooperate as well as maximize the sum-rate. During a

training period, the BS broadcast pilot training sequence is known a priori by the

MSs. Then, each MS forwards these sequences to nearby MSs to get the knowledge of

the channel information, and decides a group of MSs who can cooperate together. The

following subsection considers a user-selection process and analyzes the inter-related

parameters, B, β and K, for the proposed scheme, and then derives the minimally

required condition for B to achieve the full multiplexing gain.


User-Selection

Using training sequences, each MS estimates the best sum-rate that it can achieve

from cooperation with nearby MSs and reports the rate to the BS. Once the BS

receives these estimated sum-rates from MSs, it selects a set of MSs to maximize the

sum-rate. Then, the selected MSs feed the indices of beamforming vectors back to

the BS. During this period, each MS receives the channel information of neighbors

via relay channels. The corresponding sum-rate is given by

Rsum = E

[

maxs⊂{1...K}

M∑

i=1

log (1 + SINRs,i)

]

. (3.27)

Thus, the sum-rate depends on both how strong the selected channels are and how

much they are correlated. The properties of the selected channels will be discussed

in the next subsections.

Multiplexing Gain

For a given set of the selected MSs, the expected SINR over beamforming vectors

{bi}Mi=1 is lower bounded by a function of B and relay gains using Jensen’s inequality,

Eb(SINRs,i) ≥Eb

[

Pt

M|w†

iri|2|q†ibi|2

]

Eb

[

∑

j 6=iPt

M|w†

iri|2|q†ibj|2

]

+ Eb

[

N0‖w†iGi‖2

]

≥ρXi

(

1− 2−B

M−1

)

ρXi2− B

M−1 + Zi

= γs,i (3.28)

where the variables ρ, Xi and Zi represent Pt

MN0, |w†

iri|2, and the enhanced noise

described in (3.23). The SINR lower bound in (3.28) depends on both parameters, B

and β, and is maximized to select best channels for Xi. Also, the inequality becomes

tight as B and β increases. For ease of analysis, γs,i will be used as the approximation

of SINRs,i.


The sum-rate is said to achieve the full multiplexing gain if

limρ→∞

Rsum(ρ)

log2 ρ= M, (3.29)

which has been considered as a performance measure [53]. Let s∗ denotes a set of MSs

that maximizes the sum-rate of the proposed scheme. Under the SNR degradation △

from some practical issues, the sum-rate for a selected set s∗ should be lower bounded

by∑M

i=1 log(1 + ρ △) in order to achieve the full multiplexing gain as follows:

M∑

i=1

log(1 + ρ △) ≤ Rsum

≈ E

[

M∑

i=1

log(1 + γs∗,i)

]

= E

[

M∑

i=1

log

(

1 +ρXiEb[cos

2 θi]

ρXiEb[sin2 θi] + Zi

)

]

= E

[

M∑

i=1

log(1 + ρf(Xi))

]

(a)

≤M∑

i=1

log(1 + ρf(E[Xi])) (3.30)

where f(x) is used to simplify the derivation. Moreover, (a) follows from Jensen’s

inequality because g(x) = log(

ax+bcx+b

)

subject to a > c > 0 and b > 0 is concave and

Rsum is the expected sum of g(x). Thus, the relation among parameters is given by

△ ≤ E[Xi](

1− Eb[sin2 θi])

ρE[Xi]Eb[sin2 θi] + E[Zi]

. (3.31)

Accordingly, E[Xi] is a function of channel-selection, E[Zi] is a function of β, and

Eb[sin2 θi] is a function of B. The corresponding condition for the number of feedback

bits is

B ≥ −(M − 1) log2

(

1

ρ △ +1

(

1− E[Zi]

E[Xi]△

))

, (3.32)


which mainly depends on the ratio of E[Zi] to E[Xi].

Channel Decomposition

The sum-rate in (3.27) can be rewritten as

Rsum = E

[

maxs

∑

i

log g(Xs,i)

]

(3.33)

where g(Xs,i) is redefined as ρXi+Zi

ρXiEb[sin2 θi]+Zi

and is non-decreasing over Xi. Since the

logarithmic function is also non-decreaseing, the set s∗ should be chosen to maximize

the following,

s∗ = argmaxs

∏

i

g(Xs,i). (3.34)

From a concatenated channel matrix H of M MSs, the product of Xs,i over i is

maximized when both conditions are satisfied: ‖hi‖ is as large as possible, and the hi

are as orthogonal to each other as possible. Let h∗i be the ith selected channel vector

of the set s∗. Then, QR decomposition is developed for H such that the elements of

ri are described with hi using Gram-Schmidt process [22],

ri =

ri1...

riM

where rij =

0 if j < i

‖ui‖ if j = i

< ei,h∗j > otherwise

(3.35)

where ui = h∗i −

∑

j<i ∠ejh∗i , ei =

ui

‖ui‖ , and ∠ejh∗i is the projected unit vector of h∗

i

to ej. Also, <,> denotes the inner-product of two vectors. To calculate Xs,i, the

direction of h∗i , i.e., h

∗i =

h∗

i

‖h∗

i ‖, is decomposed into two orthogonal vectors as

h∗i = ei cosϕi +mi sinϕi. (3.36)

where ϕi is the angle between ei and h∗i with ϕ1 = 0. By selecting MSs nearly

orthogonal to each other, ϕi approaches zero, and R becomes a diagonal matrix.


Under a set of the selected semi-orthogonal MSs with a small ϕi, the inner-product

of ei with h∗j is

< ei,h∗j >= ‖h∗

j‖|e†imj| sinϕj, (3.37)

and accordingly Xi is upper bounded by

Xi = ‖w†iri‖2 ≤ ‖h∗

i −∑

j<i

‖h∗i ‖|e†jmi|(sinϕi)ej‖2

= ‖h∗i ‖2 −

∑

j<i

‖h∗i ‖2|e†jmi|2 sin2 ϕi, (3.38)

wherewi is obtained from the null space of Ri in (3.12) such that it is slightly deviated

from the direction of the ith base vector depending on the semi-orthogonality of ri. In

(3.38), ‖h∗i ‖2 is less than max‖hi‖2 and |e†jmi|2 can be described as a beta-distributed

random variable with parameters 1 andM−2 as in (3.20). Since the ith channel semi-

orthogonal to ej is chosen from K independent isotropic channel vectors, it should be

closest to ei 6=j, which is orthogonal to ej. Thus, ϕi is the minimum of K independent

beta-distributed random variables with parameters (M − 1, 1) as in [28], and its sin2

expectation is computed in a closed form [3] as

E[

‖h∗i ‖2]

≤ E[ maxi=1...K

‖hi‖2] = E[max1...K

χ22M ]/2,

E[

|e†jmi|2]

= E [β(1,M − 2)] =1

M − 1,

E[sin2 ϕi] = Kβ

(

K,M

M − 1

)

≤ K− 1M−1 . (3.39)

These correspond to E[Xi] and E[Zi] as follows:

E[Xi] ≤(

1− K− 1M−1 (i− 1)

M − 1

)

E[max1...K

χ22M ]/2

E[Zi] = 1 +1

β

(

E[max1...M

χ22M ]/2 +

M

ρ

)

. (3.40)

3.4. SIMULATION RESULTS AND DISCUSSION 41

Then, both expectations can be applied to (3.32) to derive the amount of feedback

bits which should be scaled with ρ for achieving the full multiplexing gain of M .

3.4 Simulation Results and Discussion

This section presents numerical results for evaluating the performance of the pro-

posed scheme. MATLAB generates the channel environments of MSs. Although the

simulation simply provides fast-fading channel models, it empirically verifies the cor-

rectness of the analysis. The number of BS antennas is M = 4, and the number

of MSs in a cell varies from K = 4 to 100. For comparison, alternative transmis-

sion techniques are plotted together such as multi-user ZFBF with limited feedback

and singular value decomposition with full CSI for evaluating the sum-capacity on a

point-to-point MIMO channel.

3.4.1 Results with M = K

Fig. 3.4 shows the throughput of MISO broadcast channels with several schemes.

Fig. 3.4 to 3.8 hold the number of MSs equal to the number of transmit antennas. The

proposed scheme that exploits both user-cooperation and limited feedback (UCLF)

is compared to the user-cooperating scheme with zero-forcing decoder (UCZF) [32]

and to the zero-forcing beamforming scheme with limited feedback (ZFBF) [28], each

using the same parameters. Thanks to the conferencing among MSs, the throughput

of UCLF is always higher than that of ZFBF. As SNR increases, the forwarded

messages among MSs are less corrupted by channel noise so that the the throughput

of UCLF is more improved versus ZFBF. In addition, the throughput curves of UCLF

and UCZF cross at about 22 dB. UCZF only depends on user-cooperation, which

makes the performance of UCZF highly sensitive to a conferencing channel gain. At

β = 0.2 in Fig. 3.4, the quality of a conferencing channel is not fully guaranteed

so that the throughput of UCZF degrades especially at low SNR. However, UCLF

still maintains the performance at the same gain because of the feedback. As SNR

increases, the interference caused by the fixed rate feedback also increases, which


0 5 10 15 20 25 300

5

10

15

20

25

30

35

SNR (dB)

Spe

ctra

l Effi

cien

cy (

bps/

Hz)

CapacityUCZFUCLFZFBF

Figure 3.4: The throughput of a MISO broadcast channel with several schemes isillustrated with fixed feedback bits B = 10 and a finite gain β = 0.2 whenK = M = 4.UCZF is evaluated only with user-cooperation, ZFBF only uses feedback channels,and UCLF uses both feedback channels and conferencing.

allows the performance of UCZF to outperform UCLF. Hence, the feedback rate is

needed to increase according to (3.26).

Fig. 3.5 compares the performance of the proposed scheme with full cooperation

and infinite feedback (UCIF) to ZFBF with perfect CSI at the BS. Both ideal schemes

achieve the multiplexing gain as SNR increases. Since the conferencing among MSs is

an additional benefit of the throughput, UCIF more closely approaches the capacity

of a point-to-point MIMO system. However, UCIF’s throughput is not completely

matched with the capacity because full coherent cooperation among MSs is not pro-

vided and only the amplify-and-forward relaying scheme is used to cooperate.

Fig. 3.6 shows the effect of limited feedback and finite cooperation on the through-

put of the proposed scheme. All the throughput of UCLF in the figure is maintained


0 5 10 15 20 25 300

5

10

15

20

25

30

SNR (dB)

Spe

ctra

l Effi

cien

cy (

bps/

Hz)

Sum−CapacityUCLFZFBF

Figure 3.5: The throughput of a MISO broadcast channel with perfect CSI at the BSand full cooperation among MSs is illustrated when K = M = 4. The performanceof the proposed scheme is between the capacity of a point-to-point MIMO channeland the maximum sum throughput of zero-forcing beamforming in a multi-user MISOchannel.


0 5 10 15 20 25 300

5

10

15

20

25

30

SNR (dB)

Spe

ctra

l Effi

cien

cy (

bps/

Hz)

UCIFUCLF β = 0.9UCLF β = 1.5UCLF β = 3.0

Figure 3.6: The throughput of a MISO broadcast channel with scalable feedback and afinite conferencing gain is illustrated with b = 4 when K = M = 4. As a conferencingchannel gain β increase, the required number of feedback bits B decreases as shownin Fig. 3.7.

within a rate offset per MS log2(4), which corresponds to a 6 dB power offset [28].

Even though the throughput of each case is almost the same, the required number of

feedback bits that achieve multiplexing gain decreases as conferencing gain increases.

The relation between two parameters appears in Fig. 3.7.

Fig. 3.7 demonstrates the relation of B and β to maintain the throughput of

Fig. 3.6 at each SNR. As derived in (3.26), these two parameters are inversely re-

lated to each other. Thus, cooperation with a MS in a better position mitigates the

condition of feedback load, while maintaining the performance of the system.

Fig. 3.8 verifies that the approximation used in (3.24) to analyze the proposed

scheme’s throughput is valid especially at high SNR. Given a fixed conferencing gain,

the number of feedback bits needed to achieve the same level of throughput in Fig. 3.6


0 1 2 3 4 52

3

4

5

6

7

Cooperative Gain

Fee

dbac

k B

its

(a) SNR = 10 dB

0 1 2 3 4 512

13

14

15

16

17

Cooperative Gain

Fee

dbac

k B

its

(b) SNR = 20 dB

Figure 3.7: Illustration about the relation between the number of feedback bits andconferencing gains at each SNR.

0 5 10 15 20 25 300

5

10

15

20

25

30

SNR (dB)

Fee

dbac

k B

its

AnalyticSimulated

(a) β = 0.9

0 5 10 15 20 25 300

5

10

15

20

25

30

SNR (dB)

Fee

dbac

k B

its

AnalyticSimulated

(b) β = 2.0

Figure 3.8: Illustration about the relation between the number of feedback bits andSNR given conferencing gains.

is investigated by using computer simulations. Then, Fig. 3.8(a) and Fig. 3.8(b)

show that the two graphs of feedback bits, calculated by the analysis in (3.26) or by

computer simulations, approach each other as SNR increases. This is because the

noise enhancement caused by an amplify-and-forward relaying scheme becomes less

at high SNR.


0 5 10 15 20 25 300

5

10

15

20

25

30

SNR (dB)

Spe

ctra

l Effi

cien

cy (

bps/

Hz)

Sum−CapacityUCLF (K=10)UCLF (K=4)ZFBF (K=10)ZFBF (K=4)

Figure 3.9: MISO broadcast channels with fixed feedback bits, B = 6, for ZFBF anda fixed cooperative gain, β = 1.5, for UCLF are compared with the sum-capacity ina single MIMO channel.

3.4.2 Results with M < K

Fig. 3.9 compares the sum-rates of the ZFBF and the proposed scheme, user-conferencing

with limited feedback (UCLF). For the UCLF, the cooperative gain between MSs is

set at 1.5. On the other hand, the SINR feedback model described in [65] is used for

the ZFBF with the same number of MSs and feedback bits as the UCLF. The result

demonstrates that the UCLF outperforms the ZFBF. This implies that conferencing

between MSs has a practical advantage to increase the sum-rate in a single cell net-

work, confirming that the achievable rate region increases theoretically in [10,17,59].

However, a performance gap to the sum-capacity still exists, and more feedback bits

are required to exceed the bound as the SNR increases.

Fig. 3.10 presents the sum-rate of the UCLF with the increasing feedback bits


0 5 10 15 20 25 300

5

10

15

20

25

30

SNR (dB)

Spe

ctra

l Effi

cien

cy (

bps/

Hz)

UCLF (CSI)Sum−CapacityUCLF (scalable)Lower Bound

Figure 3.10: MISO broadcast channels with scalable feedback bits, β = 2.0 andK = 20 are shown with a upper-bound, UCLF with perfect CSI, and a lower-bound,M log(1 + ρ △)

over the SNR. It is observed that the sum-rate of the UCLF is lower-bounded by

M log(1 + ρ △) while being upper-bounded by the user-conferencing scheme with

perfect CSI. This reveals that the UCLF, even with non-perfect CSI, also achieves the

multiplexing gain of M as the feedback rate correspondingly increases. Moreover, this

curve validates the approximation used to derive (3.32). According to the strength of

conferencing, the UCLF has another advantage over the ZFBF that is to reduce the

number of feedback bits required for achieving the multiplexing gain.

Fig. 3.11 shows the relation between the two parameters, B and β, with respect to

K. As β increases, it is possible for MSs to reliably communicate through conferencing

and thereby mitigate the noise enhancement caused by relaying. This effect also

equivalently compensates for reducing the number of feedback bits. Further, as K


1 2 3 4

4

6

8

10

12

Cooperative gain (β)

The

num

ber

of F

eedb

ack

Bits

(B

)

K = 10K = 20K = 100

(a) SNR = 10 dB

1 2 3 411

12

13

14

15

16

17

Cooperative gain (β)

The

num

ber

of F

eedb

ack

Bits

(B

)

K = 10K = 20K = 100

(b) SNR = 20 dB

Figure 3.11: The number of feedback bits required for achieving the multiplexing gaindecreases as β or K increases.

increases, it is more feasible to select cooperating MSs with near-orthogonal channel

vectors and thus to reduce feedback load. Comparing with Fig. 3.11(b), B falls off

sharply in Fig. 3.11(a). This implies that the conferencing is more effective to reduce

the multi-user interference at the moderate SNR.

Fig. 3.12 shows the sum-rate of the UCLF over the number of MSs with respect to

β and B, respectively. The sum-rate curves rise steeply at a small K. This is consis-

tent with the fact that the marginal effect of multi-user diversity is significant when

the number of MSs is small. As B increases linearly, the codebook size 2B increases

exponentially. Thus, the sum-rate is improved significantly even with a single addi-

tional feedback bit. On the other hand, since the enhanced noise power on relaying

channels is inversely proportional to β, it is seen that the sum-rate improvement is

saturated at a large enough β.

3.5 Summary

This chapter investigated a MISO broadcast channel where conferencing occurs over

relay channels between MSs and finite feedback rates are supported from MSs. This

work showed the relationship of the number of feedback bits, cooperative gains, and

3.5. SUMMARY 49

0 20 40 60 80 1005

6

7

8

9

10

11

The number of MSs

Spe

ctra

l Effi

cien

cy (

bps/

Hz)

β = 2.00β = 0.80β = 0.20

(a) B = 10

0 20 40 60 80 1005

6

7

8

9

10

11

The number of MSs

Spe

ctra

l Effi

cien

cy (

bps/

Hz)

B = 10B = 8B = 6

(b) β = 2

Figure 3.12: As K increases, the sum-rate for the UCLF increases with respect to βor B. The curves are plotted at the condition of SNR = 10 dB

the number of MSs in achieving full multiplexing gain. In particular, more MSs

allow selection of a set of MSs that can cooperate effectively to reduce feedback load.

Thus, the number of feedback bits can be adapted in proportional to the increase

of cooperative strength and multi-user diversity gain. For future research, different

forms of conferencing could be considered to extend this work.

Chapter 4

Relaying Power Allocation on

Conferencing for OFDM Channels

In response to the growing demand for next-generation cellular networks, many wire-

less techniques have been developed to support high-rate data communication and

reliable quality-of-service (QoS). Among these, multiple-antenna and multicarrier sys-

tems are promising techniques that provide high performance over wireless channels.

Ref. [52] shows that multiple-input multiple-output (MIMO) systems can significantly

increase the channel capacity over single antenna systems. Additionally, [7] has gen-

erated great interest for multicarrier modulation. Among many multicarrier systems,

orthogonal frequency division multiplexing (OFDM) [12] has been regarded as a vi-

able technology because of its robustness to multipath fading, and thus was selected

for recent 4th-Generation standards such as WiMAX and LTE.

Dirty-paper coding is an optimal algorithm that achieves the sum capacity of a

Gaussian broadcast channel [57]. However, this nonlinear technique is complex and

requires the complete channel state information (CSI) of all mobile stations (MSs) at

the base station (BS). Instead, [64] proposes a zero-forcing beamforming technology.

For a large number of MSs, this linear method asymptotically achieves the same sum

capacity as dirty-paper coding with lower complexity. However, this method still

assumes that the full CSI of all MSs is known at the BS. Recently, [28] has analyzed

the performance of zero-forcing beamforming with limited feedback, and showed that

50

51

the number of feedback bits should linearly increase with the signal-to-noise ratio

(SNR). Otherwise, the total throughput saturates as the SNR increases.

Ref. [60] proposes relaying as another potential technology to enhance the per-

formance of cellular networks. This relaying scheme pre-installs relay stations (RSs)

to balance the load among cells. Relaying has been integrated with MSs for cellular

networks in the following two methods [38]: In-band relaying uses MSs at a standstill

to serve as RSs. In-band relaying does not modify MSs, but its performance depends

strongly on the scheduling intervals of MSs as RSs. Alternatively, out-of-band relay-

ing uses MSs equipped with multiple radio interfaces such as cellular, IEEE 802.11

(WiFi), and bluetooth. Using an ad-hoc interface in out-of-band channels, both [67]

and [6] show outage probability improvements and multicast throughput increases,

respectively. Theoretically, orthogonal relaying among MSs has already been pro-

posed as ”conferencing” in [59]. Recently, theoretic research on conferencing shows

that conferencing can increase BC’s achievable rate [17]. Moreover, [33] analyzes the

trade-off between the amount of limited feedback and the amount of MS cooperation.

This chapter addresses the broadcast channel model with conferencing through

out-of-band relaying. Based on the results of [33], this chapter presents a power allo-

cation scheme for the out-of-band relaying channels that maximizes OFDM through-

put. The proposed scheme works as follows: During a training period, pilot sequences

known a priori to the MSs are broadcast and then conveyed to nearby MSs through

relay channels. After estimating the broadcast channels, each MS selects the best

beamforming vector and calculates the optimal relaying power allocation among sub-

carriers. Next, during a data transmission period, each MS uses the calculated power

distribution for subcarriers when it relays the data to nearby MSs. As a result, the

proposed scheme enhances the average throughput over equal power allocation on

relay channels. The result also shows improved performance with respect to the re-

lay channels’ efficiency over a zero-forcing beamforming scheme. Another advantage

of the proposed scheme is better outage throughput. The following summarizes the

main contributions of this work:

• A novel power-allocation for the direct cooperation among MSs without any

RSs in multi-user OFDM systems is proposed.

52CHAPTER 4. RELAYING POWERALLOCATIONON CONFERENCING FOROFDMCHANNELS

• The original relaying power allocation scheme is simplified into a series of stan-

dard convex sub-problems that are solved easily.

• The enhanced throughput is evaluated from both average and outage perspec-

tives.

The rest of this chapter is organized as follows: Sec. 4.1 describes a multi-user

broadcast channel model. Sec. 4.2 explains the cooperation scheme among MSs as

well as beamforming and combining vectors. Then, Sec. 4.3 formulates the proposed

problem, and presents solutions to the optimization problem. Simulation results in

Sec. 4.4 evaluate the proposed scheme, and finally Sec. 4.5 concludes this chapter.

4.1 System Model

This chapter considers an OFDM-based multi-user broadcast channel. The BS is

equipped with M transmit antennas, and K MSs, each having a single antenna, are

supported in a cell. In the BS, the serial symbols for each MS are fed into N subcar-

riers in the frequency domain and are transformed into the time domain samples by

an inverse fast Fourier transform (IFFT). These samples are added with the cyclic

prefix on a guard period. After removing the cyclic prefix, each MS demodulates

the received signals by using a fast Fourier transform (FFT). As a result, each MS’s

channels are orthogonally decomposed into parallel N subchannels as

yi,n = h†i,nxn + ni,n, (4.1)

where yi,n, hi,n ∈ CM×1, and ni,n are the received signal, the channel frequency

response, and the zero-mean complex-Gaussian noise with variance N0/N on the nth

subcarrier at MS i, respectively. The channel is assumed to be block-fading, i.e., it is

invariant over each block period, but varies from one block to another. The channel

vectors hi,n are independent random vectors, each having elements independently

distributed as the zero-mean complex-Gaussian with unit variance. The transmitted

signal xn ∈ CM×1 consists of the unit-norm beamforming vectors bm,n ∈ C

M×1 and

4.2. MULTI-CARRIER CHANNELS WITH COOPERATION 53

the symbol sm,n for MS m on the nth subcarrier, and is given by

xn =M∑

m=1

bm,nsm,n. (4.2)

The transmit power for the total bandwidth is limited by Pt and is equally distributed

to the mth symbol at the nth subcarrier as Pt

NM. This chapter assumes that the

M most favorable MSs are selected among K MSs at each block by user-selection

algorithms such as [67]. Hence, if not stated otherwise, K is considered equal to M .

4.2 Multi-Carrier Channels with Cooperation

In this chapter, MSs operate in a dual-mode, having both macro-cellular and micro-

radio interfaces, as studied in [67]. Using this micro-radio interface, each MS coop-

erates with nearby MSs to relay the received signals from a cellular interface. As

in [33], this chapter focuses on an amplify-and-forward relaying among several other

relaying strategies such as decode-and-forward or compress-and-forward [13]. This

strategy has benefits that reduce the decoding complexity and that decrease delays

caused by relaying, because it is relatively simple and does not require processing

time to remodulate the received signals.

4.2.1 Amplify-and-Forward Relaying

The received signal for each subcarrier is first normalized before being sent to nearby

MSs. The normalized signal yi,n on the nth subcarrier at MS i is represented by

yi,n =yi,n

√

E [‖yi,n‖2]=

yi,n√

Pt

NMh†i,n

(

∑M

m=1 bm,nb†m,n

)

hi,n +N0

N

, (4.3)

and then, is forwarded to MS j with the weighted mobile power wi,nPr, where Pr is the

maximum power assigned to each MS. The weighting scalars wi,n are distributed to all


the subcarriers to improve the relaying performance. Since the sum of mobile power

at each subcarrier is limited to Pr, the weighting scalars are subject to∑N

n=1 wi,n ≤ 1.

Thus, the relayed signal from MS i to MS j is expressed as

yij,n =√

wi,nPrαij,nyi,n + nij,n

= gij,nyi + nij,n, ∀ i 6= j, (4.4)

where αij,n is a relay channel gain between two MSs on the nth subcarrier, and the

channel noise nij,n is distributed as the zero-mean complex Gaussian with the variance

N0/N . Correspondingly, the relay gain gij,n from MS i to MS j is defined from (4.3)

and (4.4) by

gij,n = αij,n

√

wi,nPr√

Pt

NMh†i,n

(

∑M

m=1 bm,nb†m,n

)

hi,n +N0

N

. (4.5)

This work assumes that the channel vector hi,n is fully known to MS i and can be

conveyed to nearby selected MSs during training periods. Also, it is assumed that

the relay channel gains are known to both MSs on the channel. To coordinate the

relayed signals from neighboring MSs, each MS divides them by the corresponding

relay gains such that the aggregate signal {¯yij,n} at MS j on the nth subcarrier is

given by

¯yij,n = yi,n +1

gij,nnij,n

=

{

h†i,nxn + ni,n +

1gij,n

nij,n ∀ i 6= j

h†i,nxn + ni,n ∀ i = j.

(4.6)

4.2. MULTI-CARRIER CHANNELS WITH COOPERATION 55

In a vector form, the aggregated signals for MS j on the nth subcarrier can be

equivalently written as

yj,n =

¯y1j,n¯y2j,n...

¯yKj,n

= H†nxn + nn +D−1

j,nnj,n

= H†nxn +Gj,nnj,n (4.7)

where Hn ∈ CM×K is a channel frequency response matrix at the nth subcarrier,

whose ith column is hi,n. The vectors nn and nj,n consist of concatenated broadcast

channel noises {ni,n}Ki=1 and concatenated relay channel noises {nij,n}i 6=j, respectively.

The jth element of nj,n is zero because there is no need for self-cooperation. The

diagonal matrix Dj,n represents the noise enhancement resulting from an amplify-

and-forward relaying strategy, and its ith diagonal element is the relay gain gij,n.

Since njj,n is equal to 0, gjj,n is not important. To combine the effects of noises from

both vectors, the matrix Gj,n ∈ CK×2K and the vector nj,n ∈ C

2K×1 are derived

as[

IK D−1j,n

]

and {nn, nj,n}, respectively. In the derivation, IK represents a K-

dimensional identity matrix.

The aggregate signal vector yj,n is now applied with the combining vector cj,n ∈C

M×1 for MS i’s nth subcarrier so that the filter output zj,n is detected with the

corresponding interference and noise as follows:

zj,n = c†j,nyj,n (4.8)

= c†j,nH

†nbj,nsj,n +

∑

m 6=j

c†j,nH

†nbm,nsm,n + c

†j,nGj,nnj,n.

Thus, the signal-to-interference and noise ratio (SINR) under the proposed scheme is

affected by two problems: The first is selection of both the beamforming vector bi,n

and the combining vector ci,n, and the second is the allocation of relaying power Pr

at each MS among subcarriers to reduce noise enhancement.


4.2.2 Transmit Beamforming and Receive Combining

To mitigate the effect of the multi-user interference and to increase the total through-

put simultaneously, this chapter uses QR decomposition (QRD) of the channel matrix

Hn as in [33]. Even though the QRD method is not necessarily optimal, it can be

simply implemented and is numerically stable [22]. Using this QRD method, the

channel matrix Hn is factored into two matrices as follows:

Hn = QnR†n, (4.9)

where Qn is a unitary matrix, and Rn is a lower triangular matrix. To preserve

information for its own and cancel the effects resulting from the beamforming vectors

of other MSs, a combining vector ci,n for MS i is chosen from the null space of the

matrix Ri,n obtained from Rn as

Ri,n = [ r1,n . . . ri−1,n ri+1,n . . . rM,n ] ∈ CK×(M−1), (4.10)

where rm,n is the mth column of Rn. This matrix consists of all the column vectors

of Rn except ri,n, and the corresponding combining vector for MS i is given by

ci,n ∈ N (Ri,n) (4.11)

where N (A) = {x : Ax = 0}. As a result, the inner-product of ci,n with Rn produces

the vector where only the ith element remains as

c†i,nRn = [ 0 . . . c†i,nri,n . . . 0 ] ∈ C

1×M . (4.12)

This result implies that only the ith column of the unitary matrix, qi,n, affects the

SINR for the nth subcarrier of MS i because the other columns are multiplied by zero.

In addition, the beamforming vectors for MS i, bi,n, should be chosen close to qi,n to

minimize the interference caused by a limited feedback. This work uses a sub-optimal

codebook created by random vector quantization (RVQ) in [3], which is well analyzed

and achieves optimality as the number of feedback bits B increases. This codebook

4.3. RELAYING POWER ALLOCATION ON CONFERENCING 57

is generated by using the codeword, fi,n, which is isotropically and independently

distributed in CM×1: F = {fi}2

B

i=1. Among these codewords, the beamforming vector

is chosen at MS i to be the closest vector to qi,n as

bi,n = argmaxf∈F

|q†i,nf|2, (4.13)

and the index of bi,n is fed back to the BS. Consequently, the SINR for MS i’s nth

subcarrier is given by

SINRi,n =

Pt

NM|c†i,nri,n|2|q†

i,nbi,n|2∑

j 6=iPt

NM|c†i,nri,n|2|q†

i,nbj,n|2 + N0

N‖c†i,nGi,n‖2

. (4.14)

It is observed that only Gi,n is adjustable to increase the SINR by allocating ap-

propriate power to each subcarrier. The following section discusses the allocation of

mobile power to subcarriers from this definition.

4.3 Relaying Power Allocation on Conferencing

This section formulates the relaying power-allocation problem across different sub-

carriers for each MS, and derives the optimal weighting variables that maximize the

total throughput of K MSs. The problem is

argmaxw={wi,n}i,n

Rsum(w) =1

N

M∑

i=1

N∑

n=1

log2 (1 + SINRi,n)

subject toN∑

n=1

wi,n ≤ 1, wi,n > 0 ∀ i, n, (4.15)


where w is a set of all the weighting variables wi,n for all i and n. In (4.14), the noise

term of the SINR is a function of w and can be expanded as follows:

‖c†i,nGi,n‖2 = 1 + c†i,nD

−2i,nci,n

= 1 +M∑

j 6=i

|(ci,n)j|2|gji,n|2

= 1 +M∑

j 6=i

ϕi,j,n

wj,n

, (4.16)

where the scalar (ci,n)j is the jth element of the combining vector ci,n. The scalar

ϕi,j,n is defined by

ϕi,j,n =

|(ci,n)j|2|αji,n|2γN

h†j,n

(

∑M

m=1 bm,nb†m,n

)

hj,n

M+

1

ρ

, (4.17)

where γ is the ratio of the MS’s power to the BS’s power, i.e., Pr/Pt, and ρ is the

SNR of the received signals from the BS for all the subcarriers, i.e., Pt/N0.

This optimization problem is difficult to solve because the objective Rsum(w) is

strictly non-concave for w. Instead, the problem can be modified to maximize the

total throughput by determining the weighting variables of only one MS, where those

of other MSs are given. Then, the calculated weighting variables of each MS are

sequentially updated until they converge. This iterative algorithm transforms the

original non-concave problem into a series of concave sub-problems. Specifically,

provided that the relaying power allocations of other MSs are fixed, only the weighting

variables for MS i, wi = {wi,n}Nn=1, remain to solve the optimization problem. As a

4.3. RELAYING POWER ALLOCATION ON CONFERENCING 59

result, the objective Risum(w

i) of the sub-problem for MS i is defined as

Risum(w

i)

=1

N

N∑

n=1

M∑

j 6=i

log2

(

1 +sj,n

tj,n + 1 +∑

m 6=i,j

ϕj,m,n

wm,n+

ϕj,i,n

wi,n

)

=1

N

N∑

n=1

M∑

j 6=i

log2

(

1 +s ij,n

t ij,n + 1/wi,n

)

(4.18)

where

sj,n =Pt

NM|c†j,nrj,n|2|q†

j,nbj,n|2

tj,n =∑

m 6=j

Pt

NM|c†j,nrj,n|2|q†

j,nbm,n|2

s ij,n = sj,n/ϕj,i,n

t ij,n =tj,n + 1 +

∑

m 6=i,j

ϕj,m,n

wm,n

ϕj,i,n

. (4.19)

This problem is designed only for MS i. Therefore, there is no confusion in omitting

the index i above. Then, the problem for the proposed scheme reformulates to

argmaxwi

n={wi,n}Nn=1

Risum(w

i) =1

N

N∑

n=1

M∑

j 6=i

log2

(

1 +sj,n

tj,n + 1/wn

)

subject toN∑

n=1

wn ≤ 1, wn > 0 ∀ n. (4.20)

From the information obtained through the relay channels, MS i can determine the

optimal relaying power assignment on its own. The solution can be achieved ana-

lytically with Karush-Kuhn-Tucker (KKT) conditions when the number of MSs is 2.

Generally, the solution can be calculated with the interior-point method when the

number of MSs is larger that 2 [9].


4.3.1 M × 1 with M = 2

This condition transforms the objective Risum(w

in) in (4.20) from a double-sum func-

tion to a single-sum function and thus to a standard convex optimization problem for

MS j(= 1, 2) as follows:

argminwi

n

L0 = − 1

N

N∑

n=1

log2

(

1 +sj,n

tj,n + 1/wn

)

subject toN∑

n=1

wn ≤ 1, −wn < 0 ∀ n, (4.21)

where tj,n is now independent of any weighting variables. Hence, the iterative al-

gorithm is not needed, and the optimal wn can be directly calculated by using the

Lagrangian as

L(wn, ν, λn) = L0 + ν

(

N∑

n=1

wn − 1

)

−N∑

n=1

λnwn, (4.22)

with the following KKT conditions as

N∑

n=1

wn − 1 ≤ 0, −wn < 0, (4.23)

ν ≥ 0, λn ≥ 0, ν

(

N∑

n=1

wn − 1

)

= 0, (4.24)

λnwn = 0,dL0

dwn

+ ν − λn = 0. (4.25)

Combining both conditions in (4.25) and applying it into (4.23) and (4.24), the opti-

mal wn is derived as the water-filling-based solution

wn =1

2

[√

(a1 + a2)2 − 4

(

a1a2 − µa2 − a1N ln 2

)

− (a1 + a2)

]+


where [ x ]+ = max (0, x). The auxiliary variables a1, a2, and the Lagrange dual

variable µ are 1/(sj,n+ tj,n), 1/tj,n, and 1/ν, respectively. A unique µ can be obtained

to satisfy the condition, g(µ) = 0, where the function g(µ) is defined by

g(µ) =N∑

n=1

wn − 1. (4.26)

µ is easily determined using a root-finding algorithm such as a bisection method, and

the corresponding optimal weighting variables are obtained.

4.3.2 M × 1 case with M > 2

The optimization problem in (4.20) has a concave objective and affine constraints

so that interior-point methods can be applied to solve it. The logarithmic barrier

function is used to remove inequality constraints and to apply Newton’s method in

this interior-point method. Table. 4.1 shows the details of the proposed relaying power

allocation algorithm. The scheme starts by initializing all the weighting variables

uniformly, and obtains the optimal variables wi. Then, the algorithm repeats the

same procedure for the other weighting variables until it converges.


This section shows the results of computer simulation, using Monte Carlo methods to

evaluate the proposed relaying power allocation scheme. The number of BS antennas

M is 4, and the same number of MSs is assumed to be chosen. The number of

OFDM tones N varies from 16 to 256. According to one of the recent standards

[27], the ratio γ of the MS’s power to the BS’s power is 0.01 (= 23 dBm/43 dBm).

The power of relay channel gain αij,n between two MSs is exponentially distributed

with mean λ(= 1 to 10) under the assumption that the distance between MSs is

much smaller than their distance from the BS. Then, a new variable β denotes γλ to

indicate relaying efficiency through conferencing. The following figures compare the

performance of the proposed relaying power allocation scheme with user-cooperation


Table 4.1: Relaying Power-Allocation Algorithm

Initialization:wi = 1

N[1 1 · · · 1] for i = 1 . . .M

initialize w′ = {wi}Mi=1

Recursion:for each wi ∈ w′

wi∗ = argmaxRi(w′)

update wi = wi∗

update w = {wi}Mi=1

if ‖w−w′‖ ≤ ǫbreak

else w′ = w

Result:w∗ = w

R∗sum(w) = Rsum(w

∗)

(RPAUC) to two previously suggested schemes: The first is a broadcast scheme with

no cooperation and limited feedback, zero-forcing beamforming (ZFBF) in [28], and

the second is a broadcast scheme with user-cooperation and limited feedback under

equal relaying power allocation (EPAUC) in [33].

Fig. 4.1 demonstrates the total throughput of RPAUC, EPAUC, and ZFBF with

respect to β and with B = 3 feedback, respectively. As expected, the proposed

relaying power allocation scheme outperforms the equal power allocation scheme for

all βs. It is observed that as β decreases, the throughput gain increases. This implies

that the efficiency of power allocation on noisy relay channels is relatively superior,

and those channels have much room for improvement. On the other hand, both

RPAUC and EPAUC outperform ZFBF for large β because of cooperation among

MSs, as explained in [33]. However, as β is smaller and the SNR is lower, the amplified

noise on relay channels degrades the throughput so that the advantage from user-

cooperation becomes negligible.

Fig. 4.2 compares the asymmetric advantage by the proposed relaying power al-

location on the throughput across different MSs. It is shown that the relative gain


5 10 15 20 25 301

1.5

2

2.5

3

3.5

4

4.5

5

β = 1.00

β = 0.10

β = 0.01

SNR, ρ (dB)

Ave

rage

Thr

ough

put (

bps/

Hz)

RPAUCEPAUCZFBF

Figure 4.1: The total throughput of all the RPAUC, EPAUC, and ZFBF is comparedunder a limited feedback where M = 4, N = 16, B = 3, and β = 1, 0.1, 0.01.


0 5 10 15 20 250

2

4

6

8

B = ∞

B = 3

SNR, ρ (dB)

Ave

rage

Thr

ough

put (

bps/

Hz)

RPAUCEPAUC

(a) MS 1

0 5 10 15 20 250

0.5

1

1.5

2

2.5

3

B = ∞

B = 3

SNR, ρ (dB)

Ave

rage

Thr

ough

put (

bps/

Hz)

RPAUCEPAUC

(b) MS 2

0 5 10 15 20 250

0.5

1

1.5

B = ∞

B = 3

SNR, ρ (dB)

Ave

rage

Thr

ough

put (

bps/

Hz)

RPAUCEPAUC

(c) MS 3

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

B = ∞

B = 3

SNR, ρ (dB)

Ave

rage

Thr

ough

put (

bps/

Hz)

RPAUCEPAUC

(d) MS 4

Figure 4.2: The per-MS throughput of both RPAUC and EPAUC is illustrated withM = 4, N = 16, β = 0.01, and B = ∞, 3.


4 8 16 32 64 128 2561.5

2

2.5

3

3.5

4

4.5

B = 5

B = 3

Number of Subcarriers, N

5 %

Out

age

Thr

ough

put (

bps/

Hz)

RPAUCEPAUCZFBF

Figure 4.3: The 5 % outage total throughput of all the RPAUC, EPAUC, and ZFBFis shown with respect to the number of subcarriers, N , where M = 4, ρ = 25 dB,β = 0.01, and B = 3, 5.

on the performance is most significant for MS 4 and decreases in the reverse order of

MS indices. The QRD used for decoding the data symbols explains the performance

asymmetry. Even though its gain from power allocation is low, MS 1 achieves the

highest throughput with the help of cooperation among MSs. This result shows that

scheduling should be considered for the proposed scheme, but is beyond the scope of

this chapter.

Fig. 4.3 shows the outage total throughput of all the RPAUC, EPAUC, and ZFBF

as the number of subcarriers N increases. The δ % outage throughput is defined such

that the probability of the throughput being less than the value at each block period

is δ %. In many applications, this outage performance can be used as criteria to

satisfy the QoS requirement. The outage throughput gain by RPAUC over EPAUC

and ZFBF increases with N because frequency diversity is more efficiently used to


2.4 2.6 2.8 3 3.2 3.4 3.60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

N = 16

N = 128

Total Throughtput (bps/Hz)

Pro

babi

lity

RPAUCEPAUC

Figure 4.4: Thd CDFs of the total throughput under both RPAUC and EPAUC arecompared to each othere for N = 16 and 128, respectively. The parameters M = 4,B = 3, ρ = 25 dB, and β = 0.01 are used.

4.5. SUMMARY 67

distribute mobile power into subcarriers at a large N . Besides, both RPAUC and

EPAUC achieve significantly higher outage throughput than ZFBF at a large B.

This is because as the multi-user interference caused by a limited feedback decreases,

the effects of the cooperation among MSs becomes more substantial in the outage

throughput. It is interesting to observe that the outage throughput of both EPAUC

and ZFBF also increase with N without any power allocation. This increase is caused

by the statistical variation of the throughput, which decreases with N irrespective of

power allocation. Thus, the outage performance is enhanced with N even though the

average throughput is still the same.

Fig. 4.4 shows the cumulative distribution function (CDF) of the total throughput

under both RPAUC and EPAUC with respect to the number of subcarrriers. This

graph helps demonstrate how the distribution of total throughput changes with N ,

and statistically how much throughput gain from power allocation can be obtained.

The proposed scheme shifts the CDF to the right so that it has a higher probability

to achieve higher throughput. In addition, for large N , the variation of the total

throughput is small so as to maintain the reliable throughput.

4.5 Summary

This chapter studied the relaying power allocation problem for OFDM systems when

MSs can cooperate through their ad-hoc radio interfaces. Using this cooperation

on relay channels, each MS was assumed to forward the received signals from the

BS to nearby selected MSs. The proposed scheme improved the performance of

user-cooperation by minimizing the effects of noise enhanced by a simple amplify-

and-forward relaying strategy. The results of computer simulation showed that the

proposed scheme reduces the throughput loss and increases the efficiency of cooper-

ation as compared to the equal power allocation scheme.

To improve this cooperation-based scheme, future work needs to consider more

effective relaying strategies and the optimal combination of beamforming and combin-

ing vectors. Even though an amplify-and-forward scheme is simple and easily reduces

delay caused by remodulating signals, the performance is limited by its inclusion of


noise in forwarding signals. It is also interesting how the combination of beamforming

and combining vectors should be chosen to optimize the total throughput. Finally,

efficient scheduling may increase the benefit of cooperation among MSs.

Chapter 5

Cooperative Strategy for

Multi-Hop Networks

Recently, multi-hop networks where each node operates independently without any

centralized base stations have been widely investigated. Using cooperation among

nodes, this network can exploit cooperative diversity to increase the total throughput

above that of a single-hop network [23, 31, 45]. However, each node is autonomous

and selfish in nature, and this fact frustrates spontaneous cooperation among nodes.

To accommodate this selfish nature of multi-hop networks, many approaches to stim-

ulate cooperation have been proposed. These approaches are roughly classified into

incentive-based schemes and pricing-based schemes.

In incentive-based schemes, nodes are rewarded for appropriate behaviors such

as being cooperative, or punished for inappropriate behaviors such as being selfish.

Depending on the types of incentive, these schemes are divided into reputation-based

models and market-based (or payment-based) models. In reputation-based models,

every node observes nearby neighbors to detect whether they forward data pack-

ets or not, for example, by using a watchdog mechanism [42]. When a node has

been deliberately dropping others’ packets, the nearby nodes evaluate the node as a

non-cooperative node, and isolate it from their route selection [25]. To increase the

credibility for a node, [43] evaluates a node with a weighted combination of three

different reputations: subjective, indirect, and functional. These reputation-based

69

70 CHAPTER 5. COOPERATIVE STRATEGY FOR MULTI-HOP NETWORKS

P1

P3P2

P4

P5

P6

P7

Figure 5.1: P4’s wrong report to P2 could isolate P5 in error.

models are analytically studied based on Bayesian games in [55] and on the tit-for-tat

strategy in [50]. However, these approaches assume that none of the nodes exhibit

any misbehavior. For example, if a malicious node accuses well-behaved relays of

being non-cooperative nodes, they would be isolated and the whole system would op-

erate in error. Fig. 5.1 shows this example that P4’s wrong report to P2 could isolate

P5 in error. Besides, as the number of isolated nodes increases, [25, 44] show that

the total network throughput decreases because isolated nodes do not contribute any

throughput to the network.

Market-based models use payments as incentives for sending or relaying traffic.

When a node sends a packet, it pays credits to relay nodes for forwarding its packet.

If a relay node actively forwards packets, it would earn many credits and send its own

packets later by spending credits [8,11]. Since credits are used as virtual money in this

approach, each node requires tamper-proof hardware or a centralized authority in the

system to ensure every payment among nodes as shown in Fig. 5.2. This condition

prevents market-based schemes from becoming a fully distributed algorithm. Instead,

[68] proposes a secure protocol to manage credits confidentially without tamper-proof

hardware or a centralized authority. Additionally, the credits vary according to several

types of resources like bandwidth as in [40]. However, these schemes do not provide

71

P1

P3

P4

P5

P6

P7

Tamper-proof

device

Bank

P2

Figure 5.2: Additional authority is required to ensure every payment.

all the nodes with equal opportunities to earn their own credits. Nodes at the edge

of network are penalized because the demand for relaying traffic is relatively low.

Another approach to stimulate cooperation is a pricing-based scheme where nodes

compete to be selected on a routing path. The pricing scheme was initially introduced

into networks as a rate-control problem in [29], and has been developed to solve

network resource allocation problems with dynamic link costs. In this scheme, relay

nodes competitively bid their resources to accommodate as much incoming traffic

as possible, and then the next-hop is decided depending on the link costs as shown

in Fig. 5.3. Since every node only cares to maximize its own profit, this approach

is usually modeled with a game-theoretic framework where each node is considered

a selfish node. In [4], the interaction among nodes is considered as a Stackelberg

competition to solve revenue-maximization problems. Recently, [62] analyzes the

multi-hop pricing game with a game-theoretic perspective where a relay competes for

traffic from multiple nodes and allocates received traffic to multiple nodes. However,

the selected routing path is not guaranteed to be the shortest path to a destination

even though it could be optimal for each node to achieve its own profit. This result

can cause a delay when packets arrive at a destination and consume more energy than

expected.

To mitigate the delay effects, this chapter assumes that a routing path is decided

with the help of a shortest-path algorithm. Given a path, both a sender and a relay


P1

P3P2

P4

P5

P6

P7

Figure 5.3: P2, P3 and P4 are competing for being selected as a next hop of P1.

cooperate to forward traffic by using the relative reputation of each node. The main

differences from the previous approaches are as follows. Instead of isolating non-

cooperative nodes on the path, this proposed method provides non-cooperative nodes

with more chances to contribute to the overall network throughput. To encourage

them to be cooperative, this method allows mutual bidding of cooperative willingness

of a sender and a relay to decide the forwarding probability of packets. Rather than

competing for traffic, a relay decides its bidding amount considering the available

energy status and the sender’s reputation. This inter-relation procedure not only

makes a relay conditionally cooperate, but also allows a cooperative sender to be

treated well, and to encourage a non-cooperative sender to be cooperative.

This chapter proposes a cooperative relay scheme under an energy-limited condi-

tion in multi-hop networks. The main foci are 1) to motivate each node to cooperate,

2) to decide optimally the amount of cooperation, 3) to analyze an equilibrium for the

proposed scheme, and thus 4) to maximize the overall throughput. First, each node

is treated according to its relative reputation. Unlike the previous mechanisms, this

relative reputation increases only when cooperative behavior is in accordance with the

proposed rule so that helping a cooperative node is encouraged while helping a selfish

node is discouraged. Second, this chapter formulates a mutual-bidding problem of

5.1. SYSTEM MODEL 73

Stackelberg competition. By embedding a sequential-move game, the inter-relation

between two nodes is modeled as an optimization problem. Third, an equilibrium of

the optimal solution is compared to a simultaneous-move game of Cournot competi-

tion [20]. Simulation results show that each node is encouraged to be a cooperative

node and the total network throughput is effectively improved as opposed to a con-

ventional scheme where selfish nodes are isolated, and thus, are not allowed to relay

packets any longer. The key contributions of this work are

• The cooperative rule is a novel approach where only conditional cooperation is

encouraged.

• The proposed scheme does not isolate selfish nodes. Instead, the mutual-bidding

scheme provides them with more chances to participate in the network.

• The cooperation between nodes is modeled under energy-limited constraint in

a game-theoretic framework.

• A two-stage Stackelberg equilibrium is analyzed compared to a one-stage Cournot

equilibrium.

The rest of this chapter is organized as follows: Sec. 5.1 introduces a system

model. Sec. 5.2 formally describes the proposed cooperative scheme, and Sec. 5.3

provides an equilibrium analysis of the scheme. Sec. 5.4 explains the underlying relay

protocol as a series of successive games. In Sec. 5.5, simulation results demonstrate

the performance of the proposed scheme, and then this chapter concludes in Sec. 5.6.

5.1 System Model

This dissertation considers stationary multi-hop networks where a source sends traffic

to a destination through multiple relays with fixed power. It is assumed that a routing

path is discovered by Dijkstra’s shortest-path algorithm and consists of loop-free links.

Fig. 5.4 illustrates 100 distributed nodes in a multi-hop network.

This work assumes that a sender can precisely estimate its own channel gain for

a specific relay [54]. Since a block fading channel is considered, the channel gain on a


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

2627

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

4748

49

50

51

5253

54

55

56

57

58

59

6061

6263

64

65

66

67

68

6970

71

72 73

74

75

7677

78

79

80

81

82

83

84

8586

87

88

89

90

9192

9394

95

96

97

9899

100

Figure 5.4: Illustration of 100 nodes uniformly distributed.

link is invariant over the block period so that a sender can be reasonably aware of it.

The corresponding signal-to-noise ratio (SNR) can be calculated, and accordingly, the

network throughput of each link can be obtained. In the network, it is also assumed

that each node overhears control packets from neighboring nodes. By overhearing the

packets, each node can monitor its neighbors and record their cooperative activities

in its look-up table. In the proposed scheme, this look-up table is utilized by itself in

order to avoid any security concerns among nodes.

5.2 Cooperative Relay Scheme

The proposed cooperative scheme is based on the Stackelberg competition between a

sender and a relay. In multi-hop networks, a sender needs to ask a relay to forward its

packets toward the destination. The relay responds to the sender about whether or

not to relay the packet. This sequential procedure can be modeled by the Stackelberg

competition, and the optimal strategy is solved by backward-induction.

To encourage a relay to forward a packet, the proposed scheme provides an incen-

tive if it transmits the packet successfully. However, it is possible that a malicious

5.2. COOPERATIVE RELAY SCHEME 75

Table 5.1: The Credit Table of Relay

sender action ∆crcooperative forward rewarded (+)cooperative drop punished (-)selfish forward punished (-)selfish drop rewarded (+)

node takes advantage of the scheme such that it transmits only its own packets as

a selfish sender and does not participate in forwarding any other packets as a relay.

Therefore, a new game rule provides an incentive only when a relay helps a coopera-

tive sender or denies to help a non-cooperative sender. To determine how cooperative

a sender is, this paper re-defines the term, credit, not as virtual money, but as a

history of how well a node follows the proposed scheme’s rule. This credit is in the

range of [−1,+1]. The most cooperative node has a credit of +1 and the most selfish

node has a credit of −1. The credit is updated after each game is over as follows:

ci,n+1 = ci,n +∆ci (5.1)

where ci,n is the credit of node i at time n and ∆ci is the amount of the incentive

credit, which is achieved by the chosen action. The updated credit ci,n+1 is bounded

at ±1.

Table 5.1 shows how the credit of a relay changes depending on its action. The

credit is given only when it helps forward a packet from a cooperative node and denies

help to a selfish node. This scheme encourages nodes to be cooperative in order to

avoid being treated as a selfish sender later.

The credit of a sender represents the reputation it has achieved from other nodes.

The reputation declines for neighbors when a request to forward a packet is refused by

the relay. Since a sender cares about only whether its packet is successfully delivered

or not, the incentive credit to a sender depends only on the action of the relay, as in


Table 5.2: The Credit Table of Sender

relay action ∆cs- forward gain reputation (+)- drop lose reputation (-)

Table 5.2.

Based on the incentive strategy, this paper addresses the problem of how cooper-

ative a node is each time. The game introduces a new variable wi to represent the

willingness to participate in the game. Both a sender and a relay should be able to

decide their own willingness, and correspondingly, the forwarding probability at time

n is expressed in terms of credits and willingness as

pn = pbase + pconst∑

i=r,s

wic−i,n (5.2)

where pbase and pconst are tuning parameters, and the subscript −i represents the

opposite player. Each node looks at the credit of the opposite player and decides how

much it weighs. If a node meets a cooperative player, then it would weigh more to

increase the forwarding probability, and vice versa.

With these parameters, the game between a sender and a relay is established. Each

node has two utilities consisting of three reputation components: Shannon capacity

as the measure of the throughput, the cost of transmission power consumption, and

the credit accumulation. Given the transmission cost β, and the SNRs in the game,

both throughput utility and credit utility are expressed as

ut,i(wi, w−i) = pn (log (1 + SNRi)− β) , (5.3)

uc,i(wi, w−i) = fi(pn, c−i,n)wi (5.4)

where SNRs is the SNR between a sender and a relay, and SNRr is the SNR between

a relay and the next hop of the relay. The amount of credit is calculated based on

5.2. COOPERATIVE RELAY SCHEME 77

Table 2 and 3. When a relay weights its willingness wr, it gains or loses additional

credit depending on a sender’s current credit and on whether the packet is actually

forwarded after the game is over. Therefore, ∆cr = ±cswr and fr(x, y) = (2x − 1)y

where ± signs follow Table 1, and [0, 1] is mapped to [−1, 1] by (2x − 1), allowing

the credit utility uc,i to be positive, i.e., providing incentive, or negative, i.e., costing

a penalty. From the perspective of a sender, the additional credit relies only on its

willingness ws, and the result of the actual packet delivery regardless of the relay’s

current credit. Thus, ∆cs = ±ws and fs(x, y) = (2x− 1) where ± signs follow Table

2.

Furthermore, the game has one constraint that a node should operate under the

available battery condition. Each time, a node can be requested or can request to

join in the game. According to the result of each game, the remaining energy of node

i at time n, notated as βrem,i,n, varies as

βrem,i,n = βtot −n−1∑

k=1

I(pk)β > 0 for i = r, s (5.5)

where βtot is the node’s total energy available, and I(·) is the function to indicate the

result of packet delivery.

I(pn) =

{

1 if packet is successfully delivered under pn

0 otherwise

The objective function of each node is then the sum of the physical utility ut,i

and the virtual utility uc,i above under the condition that each node is alive. The

cooperation factor α controls the weight of the virtual utility. Accordingly, the game

between a sender and a relay leads to two sequential optimization problems so as to

maximize the objective function. For a relay, the best response w∗r is a function of

given ws, i.e., w∗r = w∗

r(ws). This optimization problem is

maxwr∈W

πr(wr, ws) = ut,r(wr, ws) + αuc,r(wr, ws)

subject to βrem,r,n − pnβ > 0, (5.6)


where W is the feasible set bounded by the maximum and minimum limit of the

willingness variable. W = [wmin, wmax] where 0 ≤ wmin, wmax ≤ 1. On the other

hand, a sender anticipates how a relay would behave given ws, i.e., w∗r = w∗

r(ws) by

backward-induction as shown before. The sender’s optimization is expressed as

maxws∈W

πs(ws, w∗r) = ut,s(ws, w

∗r) + αuc,s(ws, w

∗r)

subject to βrem,s,n − pnβ > 0. (5.7)

By solving two sequential optimization problems, both sender and relay can decide

their best strategies to maximize their own payoffs.

5.3 Equilibrium Analysis

This section shows that the proposed Stackelberg sequential-move strategy achieves

a Nash Equilibrium, and this equilibrium is unique for each player. Additionally,

strategies by a simultaneous-move game through Cournot competition cannot be

achieved in practice.

At the first stage of the Stackelberg game, a sender anticipates that a relay ra-

tionally decides its best strategy based on the proposed rule. Given all the available

information, a sender estimates the relay’s response by solving its optimization prob-

lem in Eq. (5.6). This problem can be rewritten as a quadratic form of wr by

maxwr∈W

πr(wr, ws) = aw2r + bwr + c

subject to wr ≤ d if cs,n > 0

wr ≥ d if cs,n < 0

βrem,r,n − (pbase + pconstwscr,n)β ≥ 0 if cs,n = 0,

5.3. EQUILIBRIUM ANALYSIS 79

where the variables, a, b, c, and d, are defined respectively as

a = 2αpconstc2s,n,

b = (2αpconstcr,ncs,n)ws + pconstcs,nAr + αcs,n(2pbase − 1),

c = (pbase + pconstwscr,n)Ar,

d = −cr,nws/cs,n + (βrem,r,n − pbaseβ) / (cs,nβpconst) ,

Ar = (log (1 + SNRr)− β) .

Then, the optimal strategy of a relay w∗r(ws) is expected to be one of three solutions

below as a function of ws depending on certain conditions (which are omitted because

of space constraints).

w∗r(ws) =

wmax

wmin

− cr,ncs,n

ws +βrem,r−pbaseβ

cs,nβpconst

At the next stage, a sender applies the solution of w∗r(ws) to its own objective func-

tion maxws∈W πs (ws, w∗r(ws)) and decides the best strategy w∗

s by solving a similar

quadratic optimization problem. Sequentially, a relay decides its strategy w∗r(w

∗s)

after receiving a sender’s response w∗s .

5.3.1 Stackelberg Equilibrium

Proposition 1 In the proposed two-stage game, the backward-induction solution w =

(w∗s , w

∗r(w

∗s)) is a Nash equilibrium.

Proof The solution set w = (w∗s , w

∗r(ws)) of two nodes is a Nash equilibrium be-

cause both strategies of the nodes are the best responses to each other. At the first

stage, w∗s is the best response to w∗

r(ws) so that it maximizes the objective func-

tion πs(ws, w∗r(ws)). At the second stage, w∗

r(ws) is also the best response to ws so

that it maximizes the objective function πr(ws, wr). The backward-induction solution

w = (w∗s , w

∗r(w

∗s)) is achieved when the best response w∗

s of a sender to a relay is given.


Since a set w is a subset of the set w, the backward-induction solution achieves a

Nash equilibrium.

Theorem 2 The proposed two-stage game guarantees the existence of a solution if

βrem,i,n ≥ β for i = r, s

and the solution is unique unless the following two conditions occur: cs,n = 0 or

a = −b, d /∈ W .

Proof The optimization problem for a relay is a quadratic problem of wr with an

affine energy constraint. As long as the available transmission energy remains, the

solution of a quadratic objective function πr(wr, ws) is on a valid finite set W . This

condition verifies the existence of the solution w∗r . Since the sender’s optimization

problem consists of a linear function w∗r of ws for an expected response from a relay, the

objective function πs(ws, w∗r) is still quadratic. Therefore, provided the valid energy

constraint is met, the finite set W also guarantees the existence of the solution w∗s .

The backward-induction solution w = (w∗s , w

∗r(w

∗s)) is unique except under two

conditions: The first is that a sender is exactly neutral. According to Table 1, a relay’s

action is decided depending on the credit of a sender. Thus, a node with a neutral

credit can be both cooperative and selfish so that a relay is confused about whether

to help or not. The second is that d is outside a region W so that a whole region

W is valid in an energy constraint, i.e., d /∈ W , and simultaneously the quadratic

objective function is symmetric in a feasible set W , i.e., a = −b. This condition gives

a symmetric quadratic form within a feasible set W . Similarly, the same condition is

applied when a sender solves its own optimization problem. Except for these cases,

the convexity or concavity of a quadratic problem is maintained so that a unique

solution is obtained from an asymmetric region of a feasible set.

5.3. EQUILIBRIUM ANALYSIS 81

5.3.2 Cournot Equilibrium

The proposed scheme is based on a sequential-move game that decides the best strate-

gies for a sender and a relay. From a game-theoretic perspective, two nodes can simul-

taneously exchange their biddings. This simultaneous-move game is explained by the

Cournot competition where each player decides his own strategy without seeing other

players’ actions. However, this subsection shows that the proposed scheme cannot

achieve a solution from the Cournot competition.

Theorem 3 The simultaneous one-stage game for the proposed model does not guar-

antee that the best response (w∗s , w

∗r) for both nodes exists or is unique even if it exists.

Proof Provided that the proposed scheme is operated in a one-stage game, a sender

seeks its solution w∗s directly from the optimization problem in Eq. (5.7) as a function

of wr. Using its own quadratic problem, the optimal strategy for a sender w∗s(wr) is

developed as one of four options as follows:

w∗s(wr) =

wmax

wmin

− cs,ncr,n

wr +βrem,s−pbaseβ

cr,nβpconst

− cs,n2cr,n

wr +cs,nAs

4αcr,n− 2pbase−1

4pconstcr,n,

where As = log (1 + SNRs)−β. Since two functions of w∗r(ws) and w∗

s(wr) are the best

responses to each other, any crossing points become optimal for both. However, the

slopes of the linear regions of w∗r(ws) and w∗

s(wr) are the same, or have the same sign

depending on their parameters. Under this condition, two linear regions of w∗r(ws)

and w∗s(wr) could be parallel, overlapped, or unmatched.

Thus, the simultaneous one-stage game may not have a solution or may have

multiple solutions. When the strategy of each node is not unique, another node

cannot decide its own strategy, and thus, should decide at random. This simultaneous

setting prevents the proposed model from obtaining the optimal solution.


5.4 Relay Protocol and Successive Games

This section explains the underlying relay protocol for the proposed cooperative

scheme. The proposed scheme is based on a two-stage game between a sender and a

relay, and this game is repeated along a given routing path toward a destination.

A game between a sender and a relay is established with two phases as in Fig. 5.5.

When a sender is ready to send its messages, it sends a control signal to its next-

hop in the first phase. If the designated relay is in the powerless state, it would

reject the game and remain selfish because it is more important to save energy for

its own transmission later. Otherwise, the relay responds with an ACK signal with

the associated game parameters such as the next link’s SNR. In the second phase,

a sender searches the relay’s credit and cooperative activities in its look-up table,

which has been constructed by overhearing its neighbors. Then, it decides the best

response to maximize its own profit, and sends the best response to the relay. Using

this procedure, the proposed cooperative scheme continues until the packet reaches

the destination.

If the destination directly receives a packet from the prior game, no additional

procedure is necessary. On the other hand, if a relay’s next relay is the final desti-

nation, the relay just forwards the packet to the destination without a subsequent

game and accumulates the maximum credit. This is because the packet was originally

headed to the destination, so a game does not need to be established.

In this series of successive games, the next hop of a relay plays the role of a sender

according to Table 2. For example, when a routing path, 1 → 2 → 3 → 4 · · · , isdecided, node 1 initiates the first game with node 2 and relays the packet to node 3

according to the forwarding probability of the game. If node 3 successfully receives

the packet from node 2, node 3 then begins a successive game as a sender with node

4. This work assumes that once a node receives a packet, it broadcasts an ACK signal

to its neighbors so that the neighboring nodes can monitor whether the relay node

intentionally drops the packet at the next supposed transmission. If the node does

not begin the successive game, i.e., drops the packet intentionally, it will lose credits

because it is monitored by its neighbors. Through this framework, all the nodes on


Sender Relay

Phase 1:

Initializing a game

ACK

Phase 2:

Sending the best response

Game result

Figure 5.5: The proposed two-stage game is established with two phases betweena sender and a relay. The packet is relayed according to the calculated forwardingprobability at the second phase.

the routing path are encouraged to participate in the proposed game.


This section presents the simulation results for evaluating the performance of the

proposed relay scheme. The proposed scheme is implemented in MATLAB for the

purpose of algorithmic validation. A network with 100 nodes is simulated with uni-

form distribution of the nodes over the area of 1000 m × 1000 m. Although the

simulations do not take into account networking issues such as packet losses caused

by the volatility of wireless links or congestions, the simulations empirically verify

the correctness of the algorithm and the feasibility of the protocol. A simple unit-

disk graph model is used for network connectivity, and the maximum radio range for

successful transmission is set to 200 m. The transmission power level of each node is

set to 0 dBm, and the environmental noise is assumed to be additive white Gaussian

with mean zero and variation −90 dBm. The propagation model obeys a path-loss


−1 −0.5 0 0.5 10

0.1

0.2

0.3

0.4

0.5

Credit

Dis

trib

utio

n

(a) Normalized time = 0.00

−1 −0.5 0 0.5 10

0.1

0.2

0.3

0.4

0.5

Credit

Dis

trib

utio

n

(b) Normalized time = 0.16

−1 −0.5 0 0.5 10

0.1

0.2

0.3

0.4

0.5

Credit

Dis

trib

utio

n

(c) Normalized time = 0.25

−1 −0.5 0 0.5 10

0.1

0.2

0.3

0.4

0.5

Credit

Dis

trib

utio

n

(d) Normalized time = 1.00

Figure 5.6: Illustration showing how the distribution of nodes’ credit changes underthe proposed scheme as the normalized time goes from 0.00 to 1.00.

model with a constant path-loss factor K = −31.54 dB, a reference distance d0 = 1

m, and a path-loss exponent γ = 3.71 from the set of the empirical measurements

for an indoor system at 900 MHz [21], and a log-normal model with zero mean and

a standard deviation of 3.65 dB. For each transport path, source and destination

pair are selected at each time, and this end-to-end transmission is repeated for 1000

runs. The total run time is normalized to 1.00. Regarding the game parameters,

pbase = wmax/2, pconst = 0.25 are used where wmin = 0.1 and wmax = 0.9. The route

between a source and a destination is searched by Dijkstra’s shortest-path algorithm.

Fig. 5.6 shows the change of the distribution of the nodes’ credit over time. Ini-

tially, the credits are uniformly distributed in Fig. 5.6(a) from the most selfish, −1 to

the most cooperative, +1. As the proposed relay scheme provides incentives to nodes


−1 −0.5 0 0.5 10

0.1

0.2

0.3

0.4

0.5

0.6

Credit

Dis

trib

utio

n

(a) Normalized time = 0.00

−1 −0.5 0 0.5 10

0.1

0.2

0.3

0.4

0.5

0.6

Credit

Dis

trib

utio

n

(b) Normalized time = 0.16

−1 −0.5 0 0.5 10

0.1

0.2

0.3

0.4

0.5

0.6

Credit

Dis

trib

utio

n

(c) Normalized time = 0.25

−1 −0.5 0 0.5 10

0.1

0.2

0.3

0.4

0.5

0.6

Credit

Dis

trib

utio

n

(d) Normalized time = 1.00

Figure 5.7: Illustration showing how the distribution of nodes’ credit changes underthe reputation-based model as the normalized time goes from 0.00 to 1.00.


30 35 40 45 50 55 600.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

Nor

mal

ized

Tim

e

Initial Cooperative Percentage

Figure 5.8: Required time to reach 70 percent cooperative nodes over all the nodeswhere α = 1, β = 0.1, and βtot = 100.

obeying the game rules, the distribution moves toward the right as in Fig. 5.6(b) and

Fig. 5.6(c). This movement means that many nodes are changed into cooperative

nodes whose credits are greater than 0. At the end of the simulation run, most of the

nodes are willing to cooperate as in Fig. 5.6(d).

The benefit of the proposed scheme becomes clear in comparison with the reputation-

based model’s credit distribution, as shown in Fig. 5.7. Likewise, the nodes’ credits

also start at the uniform distribution in Fig. 5.7(a). However, as time goes by, the

distribution is moved toward both directions as in Fig. 5.7(b) and Fig. 5.7(c). This

means that cooperative nodes become more cooperative and non-cooperative nodes

become more non-cooperative. Thus, at the end, only originally cooperative nodes

can contribute to the total throughput at the system.

Fig. 5.8 shows the required time to reach a certain cooperative-percentage level of

all the nodes. The time needed to obtain 70 percent cooperative nodes decreases as


0 0.2 0.4 0.6 0.8 130

40

50

60

70

80

90

Coo

pera

tive

Per

cent

age

Normalized Time

α = 1.00α = 0.10α = 0.01

(a) β = 0.1 and βtot = 100

0 0.2 0.4 0.6 0.8 130

40

50

60

70

80

90

Coo

pera

tive

Per

cent

age

Normalized Time

β = 0.01β = 0.10β = 1.00

(b) α = 0.1 and βtot = 100

Figure 5.9: The effect of each parameter: cooperation factor α and transmission costβ, respectively, on the cooperative percentage.

the initial percentage of cooperative nodes increases. This means that the initial co-

operative percentage impacts how fast the nodes in the network become cooperative.

The effect of parameters used in payoff functions is shown in Fig. 5.9. As the

cooperation factor α increases, the curve of cooperative percentage of nodes increases

steeply in Fig. 5.9(a). This reveals that it takes less time to make nodes cooperative

because each node puts more weight on the accumulation of the credit rather than

other utilities. Fig. 5.9(b) shows the effect of transmission cost β. As β increases,

the node should carefully decide to join the game as a relay because it costs much to

forward a packet from a sender. Thus, the increase of β makes it slower to encourage

nodes to be cooperative.

Fig. 5.10 shows the average forward probability as simulation continues. Under

the proposed scheme, the number of cooperative nodes increases in Fig. 5.6. As the

entire network gets more cooperative, the forward probability also increases because

each node is more willing to help cooperative nodes. This implies that the network

is increasingly cooperative and forwards packets with higher probability.

Fig. 5.11 compares the total throughput utility of a willingness decision wi and

a conventional scheme to isolate selfish nodes as in [44]. The result demonstrates

that the proposed game-theoretic scheme outperforms the other schemes, i.e., the

random selection of wi in [wmin, wmax] or the fixed use of wi = 0.5, confirming that


0 0.2 0.4 0.6 0.8 10.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Ave

rage

of f

orw

ardi

ng p

roba

bilit

y

Normalized Time

Figure 5.10: The forward probability increases as time goes by under the proposedscheme where α = 1, β = 0.1, and βtot = 100.


0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Tot

al T

hrou

ghpu

t util

ity

Normalized Time

game−theoreticrandomizedfixedhybrid

Figure 5.11: The total throughput utility under different schemes to decide the will-ingness wi with α = 1, β = 0.1, and βtot = 100, and a hybrid scheme.


the game-theoretic wi selection is the best response for optimization. It is observed

that the randomized algorithm has an advantage over the fixed-value method because

randomized behavior avoids the worst case of wi selection. In addition, the total

throughput utility of the conventional reputation-based scheme is relatively low since

it isolates non-cooperative nodes from the network and inherently prevents them from

contributing to relay packets at all. On the other hand, the game-theoretic scheme

turns non-cooperative nodes into cooperative nodes, allowing them to contribute to

relay packets.

5.6 Summary

This chapter investigated an incentive-based relay scheme to encourage nodes to be

cooperative in wireless ad-hoc networks. The proposed scheme takes a game-theoretic

perspective so that each node’s payoff can be maximized given the condition that

its energy remains available. As a result, the distribution of nodes’ credit becomes

increasingly cooperative and most nodes become willing to help one another under

the proposed scheme.

There are two main benefits of this scheme: First, the proposed scheme is de-

centralized. Even if there is no central authority, the network is driven to relay

packets from neighbor nodes so that it becomes actively operated. Second, each node

adaptively decides its best response depending on the network environment. In every

game, each node can control the amount of its participation in relaying packets. Both

the forward probability of a relaying packet and the amount of energy consumption

can be effectively managed by rational behavior. For these reasons, the proposed

scheme fits well into wireless ad-hoc networks where each node is self-operating.

Chapter 6

Conclusion

The use of wireless devices has widely increased over the world and the demands

for wireless networks has substantially grown for the support of a variety of higher

data-rate broadband services. Thus, proper algorithms for efficient exploitation of

wireless resources become important in future wireless networks. This thesis focused

on a novel strategy – cooperation in wireless networks –, and promotes it as a key to

improve performance in multi-user cellular systems and multi-hop networks.

In cellular networks, cooperation between MSs was proposed as an alternative

resource to overcome finite-rate feedback channels. The limited feedback becomes an

obstacle for a BS to achieve uncorrupted channel information of MSs, and degrades

the total throughput of cellular systems. To reduce the degradation, this thesis in-

vestigated MS cooperation algorithms that exploit relaying resources between MSs,

and revealed the derivation of cooperative gains in terms of other resources such as

the number of feedback bits or the number of MSs. As a result, the proposed scheme

outperforms zero-forcing beamforming under the same number of feedback bits. The

proposed scheme also has the benefit of imposing any additional costs on the BS

because cooperation is enabled by just the MSs. Thereby, the proposed scheme can

be implemented without changing the existing infrastructure. An additional feature

of the proposed scheme is that the amount of two resources, cooperative gain and

feedback rates, is highly inter-dependent. As shown in this thesis, the number of

feedback bits is inversely related to the cooperative gain given the number of MSs.

91

92 CHAPTER 6. CONCLUSION

Hence, closely co-located MSs are capable of reducing feedback load because of strong

cooperative gain.

The first part of this thesis considered relaying between MSs to cooperate. Even

though an amplify-and-forward relaying strategy has several benefits such as being

simple and having small remodulation time, the performance can be limited by the

nature of the relaying method. Therefore, future research needs to consider a novel

method of relaying to cooperate more efficiently.

Contrary to cellular channels, every node independently operates without any

central authority in multi-hop networks. Thus, spontaneous cooperation between

nodes is challenging, even though it is essentially required in order to support reliable

communication. The second part of this thesis employed game theory as a emerging

powerful tool to design distributed algorithms, and proposed a cooperative relay strat-

egy to increase total throughput as well as traffic reliability. The proposed scheme

adaptively controls the cooperative strategy, and decides whether to cooperate or

not. This method is denoted as conditional cooperation between nodes, and conse-

quently helps each node manage its energy consumption and its cooperative activity.

Therefore, the proposed scheme is advantageous to self-organizing multi-hop networks

under energy constraint. This thesis showed the credit distribution of all nodes as

time goes by, and found that the proposed scheme encourages non-cooperative nodes

more quickly to cooperative nodes. Furthermore, this thesis demonstrated that the

total throughput increases with the proposed distributed algorithm based on the syn-

chronous credit information. However, each node is practically difficult to synchronize

every credit information with neighbor nodes because of nodes’ mobility and control

packets’ latency. Therefore, this work considers to extend into distributed algorithms

using asynchronous channel information for future topics.

Wireless communication systems always pursue two objectives, higher data-rates

and more reliable traffic, to support various broadband services seamlessly. This the-

sis studied potential advantages to use cooperation as a next application for future

wireless networks. Thus, instead of building costly infrastructure for wireless com-

munication, cooperation between wireless devices will be more efficient alternative to

enhance the performance as well as increase the reliability.

Bibliography

[1] R. Ahlswede. Multiway communication channels. Proc. 2nd Int. Symp. Inf.

Theory, Tsahkadsor, Armenian S.S.R.:23–52, 1971.

[2] S. Alamouti. A simple transmit diversity technique for wireless communications.

IEEE J. Select. Areas Commun., 16(8):1451–1458, Oct. 1998.

[3] C. K. Au-Yeung and D. J. Love. On the performance of random vector quanti-

zation limited feedback beamforming in a MISO system. IEEE Trans. Wireless

Comm., 6(2):458–462, Feb. 2007.

[4] T. Basar and R. Srikant. Revenue-maximizing pricing and capacity expansion

in a many-users regime. In IEEE Infocom, 2002.

[5] E. V. Belmega, B. Djeumou, and S. Lasaulce. Gaussian broadcast channels with

an orthogonal and bidirectional cooperation link. EURASIP Journal on Wireless

Communications and Networking, 2008(9), 2007.

[6] R. Bhatia, Li Li, Haiyun Luo, and R. Ramjee. ICAM: integrated cellular and ad

hoc multicast. IEEE Trans. Mobile Comp., 5(8):1004–1015, Aug. 2006.

[7] J.A.C. Bingham. Multicarrier modulation for data transmission: an idea whose

time has come. IEEE Commun. Mag., 28(5):5–14, May 1990.

[8] L. Blazevic, L. Buttyan, S. Capkun, S. Giordano, J. P. Hubaux, and J.-Y. Le

Boudec. Self-organization in mobile ad-hoc networks: the approach of termin-

odes. IEEE Communications Magazine, 39(6):166–174, June 2001.

93

94 BIBLIOGRAPHY

[9] S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge, 2004.

[10] S. I. Bross, A. Lapidoth, and M. A. Wigger. The gaussian MAC with conferencing

encoders. In IEEE ISIT, pages 1520–1524, July 2008.

[11] L. Buttyan and J.-P. Hubaux. Stimulating cooperation in self-organizing mobile

ad hoc networks. ACM/Kluwer Mobile Networks and Applications, 8(5):579–592,

October 2003.

[12] L. J. Cimini and N. R. Sollenberger. OFDM with diversity and coding for ad-

vanced cellular internet services. In IEEE Global Telecommun. Conf., volume 1,

pages 305–309, Phoenix, AZ, Nov. 1997.

[13] T. Cover and A. El Gamal. Capacity theorems for the relay channel. IEEE

Trans. on Information Theory, 25(5):572–584, Sep. 1979.

[14] T. M. Cover. Broadcast channels. IEEE Trans. Inf. Thoery, IT-18(1):2–14, Jan.

[15] T. M. Cover. Some advances in broadcast channels. Advances in Communication

Systems, 4:229–260, 1975.

[16] R. Dabora and A. Goldsmith. Capacity theorems for the finite-state broadcast

channel with feedback. In IEEE ISIT, pages 1716–1720, July 2008.

[17] R. Dabora and S. Servetto. Broadcast channels with cooperating decoders. IEEE

Trans. Inf. Theory, 52(12):5438–5454, Dec. 2006.

[18] H. A. David. Order Statistics. Wiley, New York, 3rd edition, 1970.

[19] G. J. Foschini and M. J. Gans. On limits of wireless communications in a fading

environment when using multiple antennas. Wireless Personal Commun., 6:311–

335, 1998.

[20] Robert Gibbons. Game Theory for Applied Economists. Princeton University

Press, 1992.

BIBLIOGRAPHY 95

[21] Andrea Goldsmith. Wireless Communications. Cambridge University Press, New

York, NY, USA, 2005.

[22] G.H. Golub and C.F. Van Loan. Matrix Computations, 3rd ed. Baltimore. MD:

Johns Hopkins, 1996.

[23] Z. J. Haas, M. Gerla, D. B. Johnson, C. E. Perkins, M. B. Pursley, M. Steenstrup,

and Eds. C.-K. Toh. IEEE J. Select. Areas Commun., Special Issue on Wireless

Ad Hoc Networks, 17(8), Aug. 1999.

[24] A. Haghi, R. Khosravi-Farsani, M. R. Aref, and F. Marvasti. The capacity region

of fading multiple access channels with cooperative encoders and partial csit. In

IEEE ISIT, Austin, TX, June. 2010.

[25] Q. He, D. Wu, and P. Khosla. SORI: A secure and objective. reputation-based

incentive scheme for ad-hoc networks. In IEEE WCNC’04, 2004.

[26] K. Huang, J. G. Andrews, and Jr. R. W. Heath. Performance of orthogonal beam-

forming for SDMA with limited feedback. IEEE Trans. Veh. Tech., 58(1):152–

164, Jan. 2009.

[27] IEEE 802.16m-07/037r2 (Draft). IEEE 802.16m Evaluation Methodology Doc-

ument. [Online] Available: http://www.ieee802.org/16/tgm.

[28] N. Jindal. MIMO broadcast channels with finite-rate feedback. IEEE Trans.

Info. Theory, 52(11):5045–5059, Nov. 2006.

[29] F. Kelly, A. Maulloo, and D. Tan. Rate control in communication networks:

shadow prices, proportional fairness and stability. Journal of the Operational

Research Society, 49, 1998.

[30] J.-Y. Ko, D.-C. Oh, and Y.-H. Lee. Coherent opportunistic beamforming with

partial channel information in multiuser wireless systems. IEEE Trans. Wireless

Commun., 7(2):705–713, Feb. 2008.

96 BIBLIOGRAPHY

[31] G. Kramer, M. Gastpar, and P. Gupta. Cooperative strategies and capacity

theorems for relay networks. IEEE Trans. on Information Theory, 51(9):3037–

3063, Sep. 2005.

[32] H. Kwon and J. M. Cioffi. Multi-user MISO Broadcast Channel with User-

Cooperating Decoder. In IEEE VTC 2008-Fall, pages 1–5, Calgary, Canada,

Sep. 2008.

[33] H. Kwon and J. M. Cioffi. MISO broadcast channel with user-cooperation and

limited feedback. accepted to IEEE Intern. Symp. on Info. Theory, 2009.

[34] H. Kwon, H. Je, and J. M. Cioffi. Relaying power allocation with user-

cooperation for OFDM-based MISO broadcast channels. Honolulu, HI, 2009.

IEEE Globecom.

[35] H. Kwon, H. Je, and J. M. Cioffi. Multi-user broadcast channels using confer-

encing with limited feedback and user-selection. submitted to Asilomar Confer-

encing, 2010.

[36] H. Kwon, H. Lee, and J. M. Cioffi. Cooperative strategy by stackelberg games

under energy constraint in multi-hop relay networks. Honolulu, HI, 2009. IEEE

Globecom.

[37] S. Lasaulce and A. G. Klein. Gaussian broadcast channels with cooperating

receivers: the single common message case. In IEEE ICASSP, volume 4, pages

45–48, Toulouse, France, May. 2006.

[38] Long Le and E Hossain. Multihop cellular networks: Potential gains, research

challenges, and a resource allocation framework. IEEE Commun. Mag., 45(9):66–

73, Sep. 2007.

[39] H. H. J. Liao. Multiple access channels. Ph.d. thesis, University of Hawaii, Sept.

[40] P. Marbach and Y. Qiu. Cooperation in wireless ad hoc networks: a market-based

approach. IEEE/ACM Tran. on Networking, 13:1325–1338, Dec. 2005.

BIBLIOGRAPHY 97

[41] I. Maric, R. D. Yates, and G. Kramer. The discrete memoryless compound

multiple access channel with conferencing encoders. In IEEE ISIT, Adelaide,

Sept. 2005.

[42] S. Marti, T. J. Giuli, K. Lai, and M. Baker. Mitigating routing misbehavior in

mobile ad hoc networks. In 6th Annu. ACM/IEEE Int. Conf. Mobile Computing

and Networking, pages 255–265, 2000.

[43] P. Micardi and R. Molva. CORE: a collaborative reputation mechanism to en-

force node cooperation in mobile ad hoc networks. In IFIP Conf. Security Com-

munications, and Multimedia, 2002.

[44] M. T. Refaei, V. Srivastava, L. DaSilva, and M. Eltoweissy. A reputation-based

mechanism for isolating selfish nodes in ad hoc networks. In MobiQuitous’05,

2005.

[45] Andrew Sendonaris, Elza Erkip, and Behnaam Aazhang. User cooperation di-

versity - Part I: System description. IEEE Trans. on Communications, 51(11),

Nov. 2003.

[46] C. E. Shannon. A mathematical theory of communication. Bell System Tech.

J., 27:379–423, 623–656, 1948.

[47] C. E. Shannon. Coding theorems for a discrete source with a fidelity criteiron.

IRE Int. Conv. Rec., 7:142–163, 1959.

[48] O. Simeone, O. Somekh, G. Kramer, H. V. Poor, and S. Shamai (Shitz). Three-

user gaussian multiple access channel with. partially cooperating encoders. In

Asilomar Conf. Signals, Systems and Computers, Monterey, CA, Oct. 2008.

[49] I. Sohn, C. S. Park, and K. B. Lee. Dynamic channel feedback control for

limited-feedback multi-user MIMO systems. In IEEE ICC, June 2009.

[50] V. Srinivasan, P. Nuggehalli, C. F. Chiasserini, and R. R. Rao. Cooperation in

wireless ad hoc networks. In IEEE Infocom’03, 2003.

98 BIBLIOGRAPHY

[51] V. Tarokh, N. Seshadri, and A. Calderbank. Space-time codes for high data rate

wireless communication: performance criterion and code construction. IEEE

Trans. on Information Theory, 44(2):744–765, Mar. 1998.

[52] I. E. Telatar. Capacity of multi-antenna gaussian channels. Eur. Trans. Telecom-

mun., 10(6):585–595, Nov. 1999.

[53] D. Tse and P. Viswanath. Diversity-multiplexing tradeoff in multiple-access

channels. IEEE Trans. Info. Theory, 50(9):1859–1874, Sep. 2004.

[54] D. Tse and P. Viswanath. Fundamentals of Wireless Communication. Cambridge

University Press, New York, NY, USA, 2005.

[55] A. Urpi, M. Bonucelli, and S. Giordano. Modeling cooperation in mobile ad hoc

networks: A formal description of selfishness. 2003.

[56] B. Wang, J. Zhang, and A. Host-Madsen. On the capacity of mimo relay chan-

nels. IEEE Trans. on Information Theory, 51:29–43, Jan. 2005.

[57] H. Weingarten, Y. Steinberg, and S. Shamai. The capacity region of the Gaussian

multiple-input multiple-output broadcast channel. IEEE Trans. Info. Theory,

52(9):3946–3964, Sep. 2006.

[58] M. A. Wigger and G. Kramer. Three-user mimo macs with cooperation. In ITW

2009 (Invited), Volos, Greece, June 2009.

[59] F. M. J. Willems. The discrete memoryless multiple access channel with partially

cooperating encoders. IEEE Trans. Info. Theory, IT-29(3):441–445, May 1983.

[60] Hongyi Wu, Chunming Qiao, S. De, and O. Tonguz. Integrated cellular and ad

hoc relaying systems: iCAR. IEEE J. Select. Areas Commun., 19(10):2105–2115,

Oct. 2001.

[61] A. D. Wyner. Recent results in the shannon theory. IEEE Trans. Inf. Thoery,

IT-20:2–10, 1974.

BIBLIOGRAPHY 99

[62] Y. Xi and E. M. Yeh. Pricing, competition, and routing for selfish and strategic

nodes in multi-hop relay networks. In IEEE Infocom, 2008.

[63] L. L. Xie and P. R. Kumar. An achievable rate for the multiple-level relay

channel. IEEE Trans. on Information Theory, 51(4):1348–1358, 2005.

[64] T. Yoo and A. Goldsmith. On the optimality of multiantenna broadcast schedul-

ing using zero-forcing beamforming. IEEE J. Select. Areas Commun., 24(3):528–

541, Mar. 2006.

[65] T. Yoo and A. Goldsmith. Multi-antenna downlink channels with limited feed-

back and user selection. IEEE J. Select. Areas Commun., 25(7):1478–1491, Sept.

2007.

[66] W. Yu and J. M. Cioffi. Sum capacity of Gaussian vector broadcast channels.

IEEE Trans. Info. Theory, 50(9):1857–1892, Sep. 2004.

[67] D. Zhao and T. D. Todd. Cellular CDMA capacity with out-of-band multihop

relaying. IEEE Trans. Mobile Comp., 5(2):170–178, Feb. 2006.

[68] S. Zhong, J. Chen, and Y. R. Yang. Sprite: A simple, cheat-proof, credit-based

system for mobile ad hoc networks. In IEEE Infocom’03.

cooperative wireless communication for cellular …ck548xg6061/... · 2011. 9. 22. · cho, and...

Documents