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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
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
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.
Fouad Tobagi, Co-Adviser
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.
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.
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iv
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
4.4 Simulation Results and Discussion . . . . . . . . . . . . . . . . . . . . 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
5.5 Simulation Results and Discussion . . . . . . . . . . . . . . . . . . . . 83
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
xvi
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.
4 CHAPTER 1. INTRODUCTION
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.
6 CHAPTER 1. INTRODUCTION
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.
8 CHAPTER 1. INTRODUCTION
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
10 CHAPTER 1. INTRODUCTION
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
16CHAPTER 2. THEORETIC BACKGROUND FOR COOPERATIVE COMMUNICATION
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
18CHAPTER 2. THEORETIC BACKGROUND FOR COOPERATIVE COMMUNICATION
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)
2.3. COOPERATIVE COMMUNICATION 19
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
20CHAPTER 2. THEORETIC BACKGROUND FOR COOPERATIVE COMMUNICATION
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
2.3. COOPERATIVE COMMUNICATION 21
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
22CHAPTER 2. THEORETIC BACKGROUND FOR COOPERATIVE COMMUNICATION
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
28CHAPTER 3. MULTI-USER BC USING CONFERENCING AND LIMITED FEEDBACK
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.
30CHAPTER 3. MULTI-USER BC USING CONFERENCING AND LIMITED FEEDBACK
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
32CHAPTER 3. MULTI-USER BC USING CONFERENCING AND LIMITED FEEDBACK
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
34CHAPTER 3. MULTI-USER BC USING CONFERENCING AND LIMITED FEEDBACK
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)
3.3. LIMITED FEEDBACK AND PARTIAL COOPERATION 35
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,
36CHAPTER 3. MULTI-USER BC USING CONFERENCING AND LIMITED FEEDBACK
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.
3.3. LIMITED FEEDBACK AND PARTIAL COOPERATION 37
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.
38CHAPTER 3. MULTI-USER BC USING CONFERENCING AND LIMITED FEEDBACK
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)
3.3. LIMITED FEEDBACK AND PARTIAL COOPERATION 39
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.
40CHAPTER 3. MULTI-USER BC USING CONFERENCING AND LIMITED FEEDBACK
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
42CHAPTER 3. MULTI-USER BC USING CONFERENCING AND LIMITED FEEDBACK
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
3.4. SIMULATION RESULTS AND DISCUSSION 43
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.
44CHAPTER 3. MULTI-USER BC USING CONFERENCING AND LIMITED FEEDBACK
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
3.4. SIMULATION RESULTS AND DISCUSSION 45
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.
46CHAPTER 3. MULTI-USER BC USING CONFERENCING AND LIMITED FEEDBACK
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
3.4. SIMULATION RESULTS AND DISCUSSION 47
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
48CHAPTER 3. MULTI-USER BC USING CONFERENCING AND LIMITED FEEDBACK
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
54CHAPTER 4. RELAYING POWERALLOCATIONON CONFERENCING FOROFDMCHANNELS
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.
56CHAPTER 4. RELAYING POWERALLOCATIONON CONFERENCING FOROFDMCHANNELS
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)
58CHAPTER 4. RELAYING POWERALLOCATIONON CONFERENCING FOROFDMCHANNELS
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].
60CHAPTER 4. RELAYING POWERALLOCATIONON CONFERENCING FOROFDMCHANNELS
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)
]+
4.4. SIMULATION RESULTS AND DISCUSSION 61
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.
4.4 Simulation Results and Discussion
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
62CHAPTER 4. RELAYING POWERALLOCATIONON CONFERENCING FOROFDMCHANNELS
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
4.4. SIMULATION RESULTS AND DISCUSSION 63
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.
64CHAPTER 4. RELAYING POWERALLOCATIONON CONFERENCING FOROFDMCHANNELS
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.
4.4. SIMULATION RESULTS AND DISCUSSION 65
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
66CHAPTER 4. RELAYING POWERALLOCATIONON CONFERENCING FOROFDMCHANNELS
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
68CHAPTER 4. RELAYING POWERALLOCATIONON CONFERENCING FOROFDMCHANNELS
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
72 CHAPTER 5. COOPERATIVE STRATEGY FOR MULTI-HOP NETWORKS
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
74 CHAPTER 5. COOPERATIVE STRATEGY FOR MULTI-HOP NETWORKS
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
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6061
6263
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6970
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7677
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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
76 CHAPTER 5. COOPERATIVE STRATEGY FOR MULTI-HOP NETWORKS
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)
78 CHAPTER 5. COOPERATIVE STRATEGY FOR MULTI-HOP NETWORKS
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.
80 CHAPTER 5. COOPERATIVE STRATEGY FOR MULTI-HOP NETWORKS
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.
82 CHAPTER 5. COOPERATIVE STRATEGY FOR MULTI-HOP NETWORKS
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
5.5. SIMULATION RESULTS AND DISCUSSION 83
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.
5.5 Simulation Results and Discussion
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
84 CHAPTER 5. COOPERATIVE STRATEGY FOR MULTI-HOP NETWORKS
−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
5.5. SIMULATION RESULTS AND DISCUSSION 85
−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.
86 CHAPTER 5. COOPERATIVE STRATEGY FOR MULTI-HOP NETWORKS
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
5.5. SIMULATION RESULTS AND DISCUSSION 87
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
88 CHAPTER 5. COOPERATIVE STRATEGY FOR MULTI-HOP NETWORKS
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.
5.5. SIMULATION RESULTS AND DISCUSSION 89
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.
90 CHAPTER 5. COOPERATIVE STRATEGY FOR MULTI-HOP NETWORKS
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.
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