Cross-Layer Design for Cooperative Wireless Networking

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Ning Wang

B.Eng., Tianjin University, 2004

M.A.Sc., The University of British Columbia, 2010

A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of

DOCTOR OF PHILOSOPHY

in the Department of Electrical and Computer Engineering

c

Ning Wang, 2013 University of Victoria

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Cross-Layer Design for Cooperative Wireless Networking

by

Ning Wang

B.Eng., Tianjin University, 2004

M.A.Sc., The University of British Columbia, 2010

Supervisory Committee

Dr. T. Aaron Gulliver, Supervisor

(Department of Electrical and Computer Engineering)

Dr. Wu-Sheng Lu, Departmental Member

Dr. Kui Wu, Outside Member (Department of Computer Science)

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Supervisory Committee

Dr. T. Aaron Gulliver, Supervisor

Dr. Wu-Sheng Lu, Departmental Member

Dr. Kui Wu, Outside Member (Department of Computer Science)

ABSTRACT

In this dissertation, we study cross-layer design for cooperative wireless data com-munication networks. Based on the characteristics of cooperative wireless communica-tions, and the requirement of Quality of Service (QoS) provisioning for data networks, we consider cross-layer system design for cooperative wireless networking. Three ma-jor design issues which cover cooperative link establishment, information security of cooperative communications, and cross-layer cooperative transmission scheduling, are investigated. Specifically, we follow the communication procedure in cooperative wireless systems and investigate several cross-layer design problems. Considering the queueing behavior of data buffers at the candidate relays, we study relay selection from a queue-aware perspective which takes into account the queueing systems at both the source and the potential relays. With the cooperative link established, we then study the secret key establishment problem by cross-layer cooperative discus-sion. Then cross-layer transmission scheduling is investigated from two perspectives. We first look at cross-layer adaptive modulation and coding (AMC), which takes both the channel condition and traffic intensity into consideration in the scheduling design. A more general queue-aware scheduler state selection mechanism based on buffer queue occupancy is studied, and optimization by nonlinear integer program-ming is presented.

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List of Tables

Table 1.1 Cross-layer protocol design procedure. . . 7 Table 3.1 Key agreement protocol parameters . . . 53 Table 4.1 Parameters for the Convolutionally Coded Transmission Modes . 72 Table 5.1 PER of the modulation modes for different SNRs and a packet

length of Np = 256 bits/packet. . . 128

Table 5.2 Transmission schemes available after scheduler state reduction for Scenarios 1 and 2. . . 129

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List of Figures

Figure 1.1 The seven-layer OSI reference model and the TCP/IP protocol stack . . . 2 Figure 1.2 A simple relay channel model with one source, one destination,

and a single relay. . . 4 Figure 2.1 A wireless communication system with a single base station and

N + 1 mobile stations. The focus is on the performance of the uplink of the source node S0. . . 12

Figure 2.2 Time frame structure for auction-based relay node selection and cooperative transmission. . . 20 Figure 2.3 Probability of the relay buffer occupancy exceeding Qth_−co. . . . 28

Figure 2.4 Average SNR improvement for the source transmission achieved using different relaying techniques. . . 29 Figure 2.5 Packet blocking rate of different relay selection techniques under

different traffic conditions. . . 31 Figure 3.1 A three-node cooperative wireless communication system

con-sisting of Alice, Bob and the relay. . . 37 Figure 3.2 Joint PDF of SB and SR with γ1 = 10 dB, γ2 = 12 dB and

γD = 5 dB. . . 42

Figure 3.3 Mutual information between X and Y given Z. . . 45 Figure 3.4 Lower and upper bounds on the secret key rate S(X; Y||Z) under

different channel conditions with γ1 and γ2 equal. . . 49

Figure 3.5 Lower and upper bounds on the secret key rate S(X; Y||Z) for different values of γ1 and γ2. The direct Alice-Bob physical

chan-nel SNR γD is fixed at 0 dB in (a) and 10 dB in (b). . . 50

(a) . . . 50 (b) . . . 50

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Figure 3.6 The average key rate bounds given by (3.25). The average of ΓD

is set to 0 dB. The averages of Γ1 and Γ2 range from 0 dB to

16 dB. The Nakagami-m fading parameter is equal to 1.5 for all inter-node channels. . . 52 Figure 3.7 Key agreement protocol for the three-node cooperative wireless

communication system. . . 54 Figure 3.8 Compression rate q for privacy amplification and bit error rates

ǫR for the relay and ǫB for Bob before information reconciliation

for different values of γ1 and γ2. The SNR of the direct Alice to

Bob physical channel is set to γD = 5 dB. . . 62

Figure 3.9 Error correcting code rate RC and advantage distillation rate RW

for different values of γ1 and γ2. The SNR of the direct Alice to

Bob physical channel is set to γD = 5 dB. . . 64

Figure 4.1 The single-source single-destination system model with N relays. 69 Figure 4.2 Equivalent feedback queueing model at the source node. . . 75 Figure 4.3 Queue length PMF of the truncated model for the TREC

proto-col and the corresponding simulation results for the four trans-mission modes with different average SNR and packet arrival rates. 89 Figure 4.4 Source queue length PMF for the TREC and LAZY protocols

with transmission mode 2. . . 90 Figure 4.5 Feasible regions of transmission modes 1 to 4. . . 91 Figure 4.6 AMC scheduling based on network power maximization for TREC. 93 Figure 4.7 AMC scheduling based on network power maximization for LAZY

with κ = 0.5. . . 94 Figure 4.8 AMC scheduling based on network power maximization for LAZY

with κ = 1. . . 95 Figure 4.9 Channel utilization with AMC scheduling using the LAZY

pro-tocol with κ = 0.5. . . 97 Figure 4.10Channel utilization with AMC scheduling using the LAZY

pro-tocol with κ = 1. . . 98 Figure 5.1 A three-node wireless cooperative communication system model. 103 Figure 5.2 The queue-aware cooperative transmission scheduler model with

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Figure 5.3 The unit neighborhood and principal neighborhood of a discrete point X. . . 116 Figure 5.4 An example of a sub-sequential search interval (SSI). . . 122 Figure 5.5 Average queue length plus average retransmission performance

of the queue-aware cooperative transmission scheduling strate-gies. The channel condition is Scenario 1 with a direct source to destination channel SNR of 10 dB. . . 131 Figure 5.6 Average queue length plus average retransmission performance

of the queue-aware cooperative transmission scheduling strate-gies. The channel condition is Scenario 2 with a direct source to destination channel SNR of 20 dB. . . 133 Figure 5.7 Buffer occupancy plus packet retransmissions of the cooperative

systems scheduled under Rayleigh fading with fixed average re-ceived SNRs. The direct source-to-destination average channel SNR used in (a) is 10 dB. The direct source-to-destination aver-age channel SNR used in (b) is 15 dB. . . 135 (a) . . . 135 (b) . . . 135

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List of Acronyms

Acronyms

Definitions

ACK ACKnowledgement

AF Amplify-and-Forward

AMC Adaptive Modulation and Coding

ARQ Automatic Repeat-reQuest

AWGN Additive White Gaussian Noise

BER Bit Error Rate

BPSK Binary Phase-Shift-Keying

BS Base Station

BSC Binary Symmetric Channel

CAQA Channel-Aware Queue-Aware

CC Coded-Cooperation

CDF Cumulative Distribution Function

CDMA Code-Division Multiple Access

CDRS Constrained Discrete Rosenbrock Search

CF Compress-and-Forward

CRC Cyclic Redundancy Check

CSI Channel State Information

CSIT Channel State Information at the Transmitter

CSMA Carrier Sense Multiple Access

CTS Clear-To-Send

DF Decode-and-Forward

DMS Discrete Memoryless Source

EGC Equal Gain Combining

EQP EQual-Partitioning

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FDMA Frequency-Division Multiple Access

FSMC Finite-State Markov Chain

i.i.d. independent and identically distributed

IIS Interval of Interest Search

ISDS Integer Steepest Descent Search

LTE Long Term Evolution

MAC Multiple Access Control; Media Access Control

MCS Modulation and Coding Scheme

MDF Multipath Decode-and-Forward

MDU Max-Delay-Utility

MFS Modified one-dimensional Fibonacci Search

MIMO Multiple-Input-Multiple-Output

MMPP Markov-Modulated Poisson Process

MRC Maximal Ratio Combining

MS Mobile Station

NACK Negative ACKnowledgement

NCC Network Coding Cooperation

NE Nash Equilibrium

OFDM Orthogonal Frequency-Division Multiplexing

OFDMA Orthogonal Frequency-Division Multiple Access

OSI Open System Interconnection

PDF Probability Density Function

PER Packet Error Rate

PHY PHYsical layer

PMF Probability Mass Function

PSK Phase-Shift-Keying

QA Queue-Aware

QAM Quadrature-Amplitude-Modulation

QoS Quality-of-Service

QPSK Quadrature Phase-Shift-Keying

QRT Queue length plus packet ReTransmissions

RD Relay-to-Destination

RF Radio Frequency

RMP RandoM-Partitioning

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RV Random Variable

SD Source-to-Destination

SNA System Network Architecture

SNR Signal-to-Nose Ratio

SR Source-to-Relay

SSI Sub-sequential Search Interval

TCP Transmission Control Protocol

TDD Time-Division Duplex

TDMA Time-Division Multiple Access

TREC TRansmit-Every-Clock-tick

VoIP Voice over IP

VP Video Telephony

WLAN Wireless Local Area Network

WMAN Wireless Metropolitan Area Network

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ACKNOWLEDGEMENTS

Firstly and foremost, I would like to take this opportunity to give my warm and grateful thanks to my supervisor, Dr. T. Aaron Gulliver, for providing me with this great opportunity to work in the field of wireless communications with him, and for his continuous support, encouragement, and guidance throughout my doctoral study. I would like to thank Dr. Ivan Fair from University of Alberta for his willingness to serve as my external examiner. I am deeply indebted to Dr. Wu-Sheng Lu from UVic ECE department and Dr. Kui Wu from UVic CS department for their great efforts and significant amount of time to serve on my Ph.D. advisory committee. I would also like to express my thanks to Dr. Lin Cai from the ECE department and Dr. Jing Huang from the Department of Mathematics for their help with my coursework, and for the helpful discussions with them on my research projects. I really appreciate their valuable time and constructive suggestions. In addition, I would like to thank Dr. Ning Zhang from Xidian University, Xi’an, China, Dr. Jun Yang from National University of Defense Technology, Changsha, China, and Dr. Yi Shi from Huawei Technologies, Beijing, China, for their feedback and valuable suggestions on my research work through our collaborations.

My thanks to all my labpartners and friends at the University of Victoria and the University of British Columbia for their help and friendship. Special thanks to Dr. Kenza Guenda, Zawar Khan, Dr. Wing-Kwan Ng, Qian Li, Dr. Tingting Lv, Xuegui Song, Min Xing, Dr. Zhe Yang, Lei Zheng, Dong Zhang, Lei Zhang and Jun Zhu for always being available for technical discussions and for sharing their academic experiences generously.

Finally, I would like to express my deepest gratitude for the constant support, understanding, inspiration and unconditional love that I have been receiving from my family! I love you!

Ning Wang 2013 Summer @ Victoria, BC, Canada

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DEDICATION To my family.

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Introduction

1.1 Background and Motivation

Wireless communications and networking has been undoubtedly the most vibrant area in the communications research community for the past few decades. Unleashed from wires, people can now enjoy the freedom of communicating with each other whenever and wherever they want through wireless devices. However, different from wireline media such as twisted wire, coaxial cable, and optical fibre etc., the open transmission media for wireless communications has much more severe attenuation and signal fluctuations, as well as noise and interference. Therefore more sophisti-cated techniques must be used to achieve satisfactory link quality for wireless systems. Spurred by the increasing demands for higher data rates and greater convenience, the research community continues to seek more flexible and more reliable wireless tech-nologies. Among all the technologies proposed to combat unfavorable wireless channel conditions, the concept of cooperation [1], which actually utilizes the “unfavorable” broadcasting nature of the wireless media, provides a novel approach to improve wireless communication links.

Developed in the mid 1970’s, IBM’s Systems Network Architecture (SNA) for peer-to-peer networking is considered as the first hierarchical architecture for data commu-nications protocol design [2]. The idea of layering and the corresponding client/server inter-layer interaction introduced by the SNA then evoked development of a number of standard data network architectures, including the seven-layer OSI model, and the most commercially successful TCP/IP model. Based on this layered architec-ture, system functions are assigned to different non-overlapping cascaded layers of

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responsibility, and interaction is only allowed between adjacent layers. This provides layered architectures with the ease for protocol development and implementation of new features. However, in wireless data networks, especially when cooperation and decentralized topology come into play, rigid layering may impede further improvement of system performance. Conversely, a cross-layer design approach, which is essentially based on information exchange between non-adjacent layers, provides a way to opti-mize overall network level performance using certain designated criteria. Successful deployment of cross-layer design in the 3G, 3G beyond, and Long Term Evolution (LTE) mobile communication systems has further encouraged research activities in this area.

In this dissertation, we study cooperative wireless networking from a cross-layer design perspective. More specifically, we consider the design of several major function-alities of cooperative wireless systems. Fundamental design problems for cooperative wireless networking, including relay selection, secret key establishment and trans-mission scheduling will be investigated using the cross-layer design approach. The resulting designs and algorithms can be applied to the implementation of practical cooperative wireless communication networks.

1.2 Cooperative Wireless Communications

The broadcast nature of the wireless communication media is often considered as an adverse characteristic of conventional wireless communication systems. This is be-cause a great amount of energy is wasted in the open space. In addition, it also raises more severe security issues than bounded wireline media because the transmitted sig-nal can be overheard by nodes other than the intended receiver. However, the concept of cooperative communications, which was first introduced by Sendonaris et al. in 1998 [1], proposes a novel approach to utilize the overheard information at a third party other than the intended source and sink nodes to aid in the communication.

The basic building block of cooperative communications is the relay channel, which is a probabilistic channel model for communications between a source and a destina-tion assisted by one or several intermediate nodes, known as relays. The relay model was first introduced by Van der Meulen [3] in a general three-node communication scenario, and was later studied systematically from the information theoretic point of view by Cover and El Gamal [4]. The simplest case of a relay channel with one source, one destination, and one relay is shown in Fig. 1.2, where S, R, and D represent the

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Figure 1.2: A simple relay channel model with one source, one destination, and a single relay.

source, the relay, and the destination, respectively.

Though it originated from the relay channel model, cooperative wireless communi-cations differ significantly from basic relaying in a number of aspects. First, coopera-tion is introduced to wireless communicacoopera-tions to reduce the effects of multipath fading by creating a distributed virtual Multiple-Input Multiple-Output (MIMO) system. The information sink, or the destination node, receives signals from both the source node and the relay(s), and combines these signals using some combining technique determined by the available channel state information. Consequently, space diversity approximating that of a multi-antenna system can be achieved through multi-hop communications without the actual use of multiple antennas. Note that the classic relay channel results in [4] only deals with information forwarding in simple additive white Gaussian noise (AWGN) channels. Second, relaying is not always an active feature in cooperative wireless communications. When to use the relay(s) and how the relay(s) act in the communications process are determined by the cooperation strategy employed by the system. Last but not least, in a relay model the roles of different nodes are specified in advance, i.e. it is predetermined whether a node is one of the communication parties or just aids the communications. Conversely, in cooperative wireless networks each node can act as not only a relay to help in the information exchange between the source and the destination, but also a source node to transmit its own information. Therefore cooperative wireless communications can be considered as an integration of the advantages of relay-assisted transmission and diversity combining.

A number of cooperation strategies/protocols for wireless networking have been proposed [5]. The most widely used wireless cooperation strategies in the literature are amplify-and-forward (AF), decode-and-forward (DF) and compress-and-forward (CF). The AF and DF strategies are adopted as the primary cooperation models

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in this dissertation. Other cooperation strategies including coded cooperation (CC), network coding cooperation (NCC), and multipath decode-and-forward (MDF) etc., rely on signal processing algorithms with high complexity, and will not be discussed in this work.

From a practical system design point of view, it is technically unrealistic for a wireless device to transmit and receive simultaneously in the same radio frequency (RF) band. Therefore we always assume half-duplex within the same frequency band or time slot for the wireless communication system. The basic idea of wireless coop-eration strategies for the three-node system shown in Fig. 1.2 can be demonstrated in a two-phase slotted time division frame structure as in [6]. We assume each trans-mission time slot is further divided into two sub-timeslots, namely TS1 and TS2. In AF mode, the source node broadcasts in TS1, while the nodes D and R receive the broadcast signal from S in this sub-timeslot. Then in TS2, the relay R amplifies the signal received in TS1 from S and forwards it to the destination D. At the end of the time slot, D has two copies of the signal, the first is received directly from the source in TS1, and second is the forwarded copy from the relay. The destination can then use some combining technique, e.g. equal-gain combining (EGC) and maximal-ratio combining (MRC) to combine the two signal copies. In AF mode, the relay simply amplifies and forwards the received analog signal waveform without restoring the orig-inal information. AF is sometimes referred to as non-regenerative relaying. Note that the noise at the relay’s receiver is also amplified in the amply-and-forward process in TS2 of AF relaying; therefore the AF strategy is susceptible to noise propagation.

The communication process in TS1 of DF is essentially the same as that in the AF strategy. The major difference is that in DF mode, the relay decodes the information from its received signal in TS1; then in TS2, R re-maps the messages and forwards the re-mapped messages to the destination. Similar to AF, the destination performs combining and decoding at the end of the entire time slot. Note that in this process, a good source-to-relay channel is required to guarantee that the message encoded by the relay is the same as the source message with very high probability; otherwise an incorrect message will be forwarded to the destination from R. Thus the DF strategy is susceptible to error propagation.

Different from the DF strategy, the relay operating in CF mode uses a quantiza-tion codebook to encode the quantized samples of its received analog signal in TS1. At the destination, the receiver first decodes the quantized samples of R, and then performs combining and decoding for the original message from the source. The CF

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strategy is analogous to multiple antenna reception in that a high capacity relay-to-destination channels which can support a large quantization codebook is required to have negligible quantization error. Therefore the CF strategy is suitable for co-operative wireless systems with good relay-to-destination channels. In contrast, DF resembles multi-antenna transmission in that the relays can form a virtual transmit-ting antenna array, and the connection between the source and the relays must be very reliable to avoid error propagation. The DF strategy is thus more preferable when the source-to-relay channels are near ideal.

Implementation of cooperative wireless communications requires us at least to address two fundamental questions: whom to cooperate with and when and how to cooperate. The second question is related to cooperation mode selection or schedul-ing, which determines what cooperation strategy (AF, DF, or CF) should be used, and whether the system should perform fixed relaying, selection relaying, incremen-tal relaying, etc. The first question deals with the selection of which relay to aid in the cooperative communication process from a set of candidates. In this process, we need to consider the inter-node channel conditions between the candidate nodes and the source, and between the candidates and the destination. For wireless communica-tions, it is also critical to take into account the mobility issue because potential relays such as handsets or on-vehicle radios are very likely to be mobile. This relay selection problem will be one of the topics studied in this dissertation. Specifically, different from the aforementioned conventional approaches found in literature, we pay special attention to the queueing behavior of the candidate relays because in general coop-erative wireless communication scenarios, the relays are also active wireless devices which have their own traffic.

1.3 The Cross-Layer Design Approach

There is no strict definition of cross-layer design as early efforts on this area of study were made independently by researchers working on different layers of the protocol stack from different perspectives [7]. In general, any type of protocol design that violates the basic client/server only principle between adjacent layers and introduces other inter-layer inter-operations is considered to be cross-layer design. Several major types of cross-layer inter-operations were summarized in [7]. Note that the cross-layer design approach relies on the interaction between layers, thus the layered architecture is not abandoned completely. It was pointed out in [8] that unintended cross-layer

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Table 1.1: Cross-layer protocol design procedure.

– Develop abstract models for the layers and QoS metrics for each layer; – Determine the adaptation protocols at each layer;

– Determine the (minimal) information exchange between layers; – Formulate the joint optimization problem: optimal or heuristic; – Consider the tradeoffs: performance, complexity and scalability.

interactions may cause undesirable consequences on overall system performance; un-controlled cross-layer design may even lead to “spaghetti design,” which affects the sustainability and further development of the communication system. Therefore cross-layer design should also be based on a clear definition of cross-layering of the protocol stack, and the inter-layer interaction should be minimized to reduce the impact on system functionalities. Based on a layered architecture, the cross-layer design approach pro-vides a way to optimize overall network performance from a certain perspective (de-sign criterion), with information exchange between layers. While maintaining a basic layered structure, in the cross-layer design approach each layer is characterized by several key parameters or measurements which can be used by other layers or by a cross-layer optimization engine for decision making.

Because of the nature of wireless communications, some key design issues for wireless networking, e.g. quality-of-service (QoS) provisioning, are inherently cross-layer. Most of these reside in the design of the PHY layer, the data link layer, and the network layer. Two main categories of cross-layer design problems, namely QoS optimization and efficiency (of the energy or spectrum) optimization under QoS re-quirements have received significant attention in the literature. Because some QoS measurements are application sensitive, for a wireless data network which accom-modates different types of traffic, the corresponding protocol stack should adapt to the instantaneous traffic type. The basic cross-layer protocol design procedure for wireless communication networks is summarized in Table 1.1.

In wireless networks where neighboring nodes can be used as relays, the benefit of cooperation is not limited to the nodes involved in the cooperation but to the entire network. This is not surprising if we consider cooperation from a cross-layer point of

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view, as local improvements can affect the optimization of the entire network. The benefits of wireless cooperative networking include, but are not limited to, higher spatial diversity, higher throughput, lower packet delay, improved energy efficiency, lower interference level, and extended coverage. Recent research papers have begun to place an emphasis on cross-layer design for cooperative wireless communication sys-tems. The topics covered include cross-layer design for cooperative beamforming [9], cross-layer design for cooperative media access control [10], distributed cooperative rate adaptation and energy efficiency [11], and QoS-aware cooperative opportunistic scheduling [12]. However, there are still many topics including cross-layer relay se-lection, cross-layer security solutions for cooperation, cross-layer queue-aware radio resource management etc., which have not been well investigated. In this dissertation, several of these topics are investigated from a system design point of view through cross-layer design.

1.4 Brief Outline of the Dissertation

This dissertation considers the design of cooperative data networks from a system design perspective, and the notion of cross-layer design is used throughout this study. Following the communication procedure of cooperative wireless communica-tions, queue-aware relay node selection, cooperative secrete key agreement, adaptive modulation and coding (AMC) for cooperative wireless systems, and queue-aware cooperative transmission scheduling, are investigated. A more detailed overview of the rest of this dissertation is outlined as follows.

Chapter 2 studies relay selection for user-cooperation in a general wireless commu-nication system with a centralized system structure. In addition to the channel conditions of the relays, both the source node and the relay buffer queueing states and QoS requirements are taken into consideration in the relay selec-tion mechanism design. A distributed, aucselec-tion game-based soluselec-tion for relay selection is proposed and analyzed.

Chapter 3 investigates the design of a practical information-theoretically secure se-cret key agreement protocol for a wireless cooperative network employing stan-dard modulation techniques. Security threats from eavesdroppers collocated with the relay node are considered. Upper and lower bounds on the secret key rate of this cooperative wireless system are derived, and are shown to be tight

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in practical communication scenarios. A practical secret key agreement proto-col for the system is then studied, and design parameter selection is examined based on the bounds derived from both security and efficiency perspectives. Chapter 4 studies the AMC problem for a cooperative wireless system using the

DF strategy. A packet feedback model is proposed to characterize packet loss in the wireless channel. With packet arrivals given by a Markov-modulated Poisson process (MMPP), queueing analysis for the packet level performance is conducted for this cooperative system. A practical cross-layer AMC algorithm is then proposed to maximize the network power metric of the system.

Chapter 5 considers generalized optimal transmission scheduling algorithm design for cooperative wireless systems. The transmission scheduling problem is for-mulated as a nonlinear integer programming problem on an integer convex set. Two discrete search algorithms, namely the integer steepest-descent search with sub-sequential interval search (ISDS-SSI) algorithm and the constrained dis-crete Rosenbrock search (CDRS) algorithm, are proposed and verified with nu-merical examples.

Chapter 6 contains a summary of the main results and major contributions of this dissertation. Possible future work for further development and extension of the results in this dissertation is also discussed.

1.5 Bibliographic Notes

The majority of Chapters 2 through 5 of this dissertation is based on our published or submitted research papers. The work in Chapter 2 is to be submitted to IEEE Transactions on Mobile Computing as [13]. Part of the work in Chapter 3 has been published as [14], and a complete version of this chapter has been submitted to IEEE Transactions on Information Forensics and Security as [15]. The work in Chapter 4 has been published in CWIT’11 and in IEEE Transactions on Wireless Communica-tions as [16] and [17], respectively. The algorithm design part of Chapter 5 has been submitted to IEEE Transactions on Wireless Communications as [18], and applica-tion of the proposed algorithms to cooperaapplica-tion scheduling presented in this chapter has been submitted to IEEE Transactions on Vehicular Technology as [19].

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Chapter 2 Distributed Queue-Aware Relay

Node Selection for Cooperative

Wireless Networks via Auction

Game

The problem of queue-aware relay selection for uplink of a user cooperation multi-ple access wireless system is investigated in this chapter. In order to achieve better quality-of-service (QoS) provisioning for the entire system, queueing states of the transmission buffers of the potential relays are considered in the relay selection pro-cess. A distributed relay node selection mechanism based on a Vickrey auction game is proposed. It is shown that with a strictly positive reserve value in the game mech-anism design, the unique Nash equilibrium (NE) of the auction game achieved by a truthful bidding strategy is the best response of the relays under the QoS constraint set by a queue length requirement. The proposed relay selection mechanism is im-plemented and evaluated using simulation. Numerical results show that a significant improvement in QoS provisioning can be achieved by the proposed auction game-based distributed queue-aware relay selection strategy, compared with fixed relaying and channel-aware relay selection policies. The resulting SNR improvement to the source transmission achieved by the proposed method is significantly greater than that with fixed relaying. It is also shown to be superior to the SNR-based schemes in terms of the source SNR improvement when the relay traffic load is high.

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2.1 Background and Motivation

Cooperative wireless communications have been attracting an increasing amount of interest in the research community because it can provide spatial diversity in wire-less systems when multiple antennas are not available. The basic building block of cooperation is the relay channel, which was first studied by Van der Meulen [3] and Cover and El Gamal [4]. Based on these studies on the capacity of different coopera-tion strategies in wireless relay networks, Kramer et al. pointed out that cooperacoopera-tion performance largely depends on the location of the relay(s), and the applicability of cooperation strategies is also determined by where the selected relays are. For example, it was demonstrated in [20] that decode-and-forward (DF) strategies are es-pecially good when the relays are close to the source node, i.e. in a system with good source-to-relay channel quality. Conversely, when the selected relays are close to the destination, compress-and-forward is especially useful in improving system capacity. Because of the possibility of error propagation (for DF) and noise propagation (for amplify-and-forward (AF)), it is not beneficial to always have certain relay(s) partic-ipating in the communication. Therefore, finding suitable relays to cooperate with is critical to taking full advantage of a relaying mechanism.

A rich body of research emphasizing relay node selection can be found in the recent literature. The basic relay selection procedure has two phases, candidate selection and relay node assignment, which can be viewed as two subproblems. In the first phase, a number of nearby nodes are selected as candidates for relaying. The candidate set can be a predetermined set which does not change during communication, or a dynamic set which is adaptively updated by some algorithm based on measurements. Pre-assigned schemes are usually incorporated with routing algorithms for cooperative networking [21], which is beyond the scope of this study. On the other hand, adaptive candidate set selection can be achieved by utilizing signaling messages in the media access control (MAC) layer like request-to-send (RTS) and clear-to-send (CTS) [22]. After the candidate set is determined, one node in the set is assigned for coop-eration based on some criteria. The simplest strategies are pre-defined assignment and random assignment. However, it can be shown that those schemes, although they have low design complexity, are far from optimal. A number of works in com-munications literature have studied this relay assignment problem from different per-spectives. Based on channel conditions, distance or geographical information-based schemes [23] and SNR-based schemes [24][25] have been studied in the literature.

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Figure 2.1: A wireless communication system with a single base station and N + 1 mobile stations. The focus is on the performance of the uplink of the source node S0.

Distributed algorithms based on game theory [26] [27] have also been proposed to perform relay selection without knowledge of the channel state information at the transmitter (CSIT).

In most of the existing studies on relay selection for wireless cooperation, queueing behavior of the candidate relays is ignored. Since the candidate relays also have their own traffic and buffer queue in many practical communication scenarios, e.g. in user-cooperative wireless systems where the relays and the source are peer nodes, the queueing behavior of the relays will also contribute to the system QoS provisioning. Then if the amount of data to be transmitted via cooperation is too much for the selected relay, i.e. the relay does not have sufficient radio resources to transmit the data in the current time slot, packet loss and relay buffer overflow may occur. With this assumption, the relays tend to be “selfish” as they do not have any motivation to provide assistance to other transmissions, especially when they have heavy traffic of their own to handle. Therefore, a good relay selection strategy should evaluate the “capability” of the relays to help from both the channel state and queue state perspectives, and also give the relays some “rewards” to encourage relaying when they have extra resources.

In this chapter, the queue-aware relay selection problem is investigated for uplink user cooperation in a centralized wireless communication network. The system shown in Fig. 2.1 is considered where a single network center, i.e., a base station (BS), is

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the destination of the cooperative communication system. Both the source node and potential relays are mobile stations (MS) in this network. The impact of relaying on the queueing behavior of the candidate relays will be analyzed, and efficient queue-aware relay selection which achieves good QoS provisioning from the entire system point of view will be studied. An idea similar to RTS-CTS signaling will be employed in the relay selection mechanism design. An auction game-based distributed algorithm is proposed to find the optimal relay from a QoS provisioning perspective. More specifically, a source with saturated traffic broadcasts an RTS-like message such that the nearby MS nodes who can receive this message are invited to join the auction game to be potential relays. Virtual money which can be used to “purchase” assistance from other nodes is introduced in this auction game as an incentive for cooperation, and the potential relays are assumed to be risk neutral and try to maximize their payoff when placing bids via CTS-like messages. A second-price Vickrey game with positive reserve value is used, and we optimize the reserve value in our mechanism design such that the Nash equilibrium (NE) achieved by truthful bidding is also optimal from a source perspective. After the bidding period is over, the source announces the winner of the auction game, which is selected as the relay node for this period of cooperation. The rest of this chapter is organized as follows. In Section 2.2 we present the system model and give basic assumptions for traffic and channel conditions. The auction game used for relay selection is introduced in Section 2.3, and auction mech-anism design is discussed. Numerical examples are given in Section 2.4 to demonstrate the auction game-based queue-aware relay selection. Some concluding remarks are presented in Section 2.5 which summarize the contributions of this chapter.

2.2 System Model

Uplink transmission and user cooperation of an infrastructure-based wireless commu-nication system with a network center as shown in Fig. 2.1 is considered in this work. This wireless system contains one BS and N + 1 MS nodes communicating with the BS. Normally, all MS nodes communicate with the BS directly using a multiple access technique such as frequency-division multiple access (FDMA), code-division multiple access (CDMA), or orthogonal frequency division multiple access (OFDMA). Once an MS node has a large packet arrival burst or a special need to improve its quality-of-service, it initiates a relay node selection process and seeks another MS node to forward its packets to the BS, which will help improve its communication link quality

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and therefore its QoS. In this section, the assumptions about the cooperative system model are discussed.

2.2.1 Basic physical layer assumptions

We focus on the uplink of one MS which is assumed to have special QoS needs. This node is considered as the source node S0 in the cooperation model. Then the BS

is the destination node of the cooperative system, and the other N MS nodes are the potential relays. We denote the potential relay nodes by R1, R2, . . . , RN. The

objective of relay selection is to improve the communication link of the target MS, i.e., the source node S0, with the best relay selected from the other N MS nodes.

The relay selection criteria will be discussed in detail in Section 2.3. The selected relay performs fixed-power amplify-and-forward (AF) for the source packets to the destination in a two-phase cooperation frame structure as proposed in [6]. Frequency division multiple access (FDMA) and frequency division duplex (FDD) are considered in this wireless system such that the selected relay can still transmit its own packets with full transmission power while receiving packets from the source in another radio frequency band in the first phase of the cooperation time slot.

We assume flat Rayleigh fading and quasi-static channel conditions for this wireless system. More specifically, all the uplink channels are independent and identically distributed (i.i.d.) Rayleigh fading channels with the same average channel power gain H0, and the wireless channels between the MS nodes are modeled as i.i.d. Rayleigh

fading channels with the same average channel power gain G0. A random variable

(RV) H is used to denote the source node uplink channel gain, and RV Hi to denote

the ith potential relay uplink channel gain. Similarly, the random gain of the channel between the source and the ith potential relay is denoted as Gi. The random variables

H, Hi and Gi are thus exponentially distributed. Note that in order to simplify

the analysis, channel power gain here is referred to as the aggregated effect of the transmitter antenna gain, the radio propagation gain and the receiver antenna gain. Based on the quasi-static channel assumption, we assume the channel power gains remain constant within one cooperation time slot. All the MS nodes are assumed to have the same constant full transmission power level P , and the additive white Gaussian noise (AWGN) at all locations in the system has the same noise variance σ2_{. The average received signal-to-noise ratio (SNR) of a direct uplink transmission}

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is therefore given as

¯ Γ0 =

P H0

σ2 , (2.1)

and the average received SNR of the inter-MS channels linking S0 and the other MS

nodes is

¯

Γ = P G0

σ2 . (2.2)

By the Rayleigh fading channel assumption, the received SNR ΓH of any uplink

channel is an exponential RV with probability density function (PDF) given by

fH(γ) = 1 ¯ Γ0 exp −_¯γ Γ0 = σ 2 P H0 exp −σ 2_γ P H0 . (2.3)

Similarly, the PDF of the inter-MS channel SNR ΓG is

fG(γ) = 1 ¯ Γexp −γ_¯ Γ = σ 2 P G0 exp −σ 2_γ P G0 . (2.4)

The ergodic capacity of the uplink Rayleigh fading channel, which is the channel capacity averaged over the Rayleigh fading distribution, is given by

CeH = Z ∞ 0 log₂(1 + γ)fH(γ)dγ = Z ∞ 0 log2(1 + γ) σ2 P H0 exp −σ 2_γ P H0 dγ = _{P H}1 0 σ2 ln 2 Z ∞ 0 exp −σ 2_γ P H0 ln(1 + γ)dγ =−exp σ2 P H0 ln 2 Ei − σ 2 P H0 bits/s/Hz, (2.5)

where Ei(_{·) is the exponential integral function defined as}

Ei(x) = Z x −∞ exp(t) t dt =− Z ∞ −x exp(−t) t dt. (2.6)

The ergodic capacity CeGof the inter-MS Rayleigh fading channels has the same form

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2.2.2 Queueing system assumptions

It is assumed that all the MS nodes are communicating with the BS, i.e., each has its own packets to transmit and they are equally important to the overall performance of the system. Conventional relay selection algorithms [23] [24] [25] focus on physical layer channel conditions, so the best relay selected may be an MS node with intensive traffic or a large packet backlog in its buffer, in which case the QoS of this relay will be degraded if help is provided to others. Sometimes the selected relay may not even have enough buffer space for the incoming source packets, which will require the relay to further sacrifice its own QoS by dropping its own packets. Otherwise the performance improvement for the source transmission evaluated based on the physical channel condition of the relay cannot be achieved. Thus a trade-off between source performance improvement and the packet level performance degradation of the selected relay is introduced. Therefore, in order to ensure good QoS from the perspective of overall system performance, it is important to consider this trade-off and take into account the packet level conditions of the potential relays when conducting relay node selection. This is the basic idea for the queue-aware relay selection studied in this chapter.

A homogeneous symmetric queueing condition for all potential relays is assumed. All potential relay MS nodes have the same Poisson packet arrival rate λ, a coopera-tion period Tco, and the same buffer size B packets. Bulk packet arrivals are assumed

at the end of each time slot, and the maximum number of simultaneous packet ar-rivals is A packets, so A ≤ B is required to ensure only meaningful packet arrival events are considered. The corresponding probability mass function (PMF) of relay packet arrivals is given by

fP(k; λTco) =

(λTco)k

k! exp(−λTco), k = 0, 1, . . . , A. (2.7) Under stability constraints of the buffer queues, the average packet arrival rate of a potential relay is limited by the ergodic channel capacity CeH of its uplink channel

given by (2.5). Because the source is assumed to be experiencing a large packet arrival burst, we consider a saturated source traffic model which has unlimited packets for transmission. The relay selection algorithm therefore aims to choose a potential relay node which can provide the maximum possible transmission rate improvement for the source node while introducing constrained additional delay to its own packets.

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rates such that the stability constraints can be quantified based on the capacity, we consider a system with bandwidth W , packet length L bits/packet, cooperation time slot period Tcoand capacity achieving code of rate η. A physical channel with capacity

C bits/s/Hz can thus be transformed into a packet level channel model which can support successful packet transmissions up to

Npk,C =

W TcoC

ηL

packets/Tco, (2.8)

where ⌊·⌋ is the floor operator which takes the largest integer value smaller than or equal to the argument. This transformation method can also be used to calculate packet transmission rates in a quasi-static fading block (cooperation time slot). For example, the number of packets that can be successfully transmitted in one coopera-tion time slot via direct uplink transmission for Ri is

Npk,i =

W Tcolog2(1 + Γid)

ηL

, (2.9)

where Γidis the quasi-static random instantaneous uplink SNR of Ri for the time slot

of interest. Similar results are used in this work for other quasi-static channels with constant SNR.

Under the homogeneous assumptions made on the channel and queueing condi-tions, all potential relays are statistically independent and have identical statistics. Therefore relay selection needs to be conducted on a regular basis; otherwise any tech-nique will perform the same as fixed relaying or random relay node selection. In this work, we consider relay selection for each quasi-static transmission time slot. This coincides with the motivation of cooperation which aims to improve performance of wireless communications in the presence of fading. However, special attention must be paid to the overhead issue. Since physical channel conditions and queueing be-havior are jointly considered, a large amount of information exchange is required for centralized algorithms, which introduces significant system overhead. Therefore we propose a distributed approach to solve this queue-aware relay selection problem. Three fundamental questions for cooperation:

1. When to use a relay,

2. Whom to cooperate with, and 3. How to perform relaying,

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will be addressed by an auction-based distributed queue-aware relay node selection algorithm developed in this chapter.

2.3 Auction Game and Mechanism Design

2.3.1 Relay selection by auction

Denote the instantaneous channel SNR of the direct uplink channel from the source S0 to the BS by Γ0, and that of the ith potential relay Ri uplink channel by Γid. By

assumption, Γ0 and Γids are i.i.d. exponential RVs with average ¯Γ0 and PDF (2.3).

We also have the instantaneous source-to-relay channel SNR for the ith potential relay Γsi, i = 1, 2, . . . , N, which are i.i.d. exponential RVs following the distribution

characterized by the PDF (2.4). Lower case notation, i.e., γ0, γid, γsi, are used to

denote specific realizations of the random channel SNRs. The fixed-power AF-relayed SNR of the received signal at the BS achieved by the assistance of Ri is

Γs,i,d= PidHi· PsiGi σ2_(P idHi + PsiGi+ σ2) = αP Hi· P Gi σ2_{(αP H} i+ P Gi+ σ2) = αΓid· Γsi αΓid+ Γsi+ 1 , (2.10)

where α_{∈ [0, 1] is the fraction of the selected relay’s transmission power allocated for} cooperation in the second phase of the cooperation time slot, which will be determined later. The resulting instantaneous cooperative channel capacity achieved by maximal ratio combining (MRC) is therefore given by

Rco = 1 2log2(1 + Γ0+ Γs,i,d) = 1 2log2(1 + Γ0+ Γs,i,d) = 1 2log2 1 + Γ0+ αΓid Γsi αΓid+ Γsi+ 1 bits/s/Hz. (2.11)

The coefficient 1₂ in front of the logarithm is due to the classic two-phase coopera-tion frame structure [6] which only uses half of the time slot to transmit. The rate

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improvement achieved by cooperation is therefore Rimpr= Rco− Rsd = 1 2log2 1 + Γ0+ αΓid Γsi αΓid+ Γsi+ 1 − log2(1 + Γ0) = 1 2log2 1 + Γ0 +_αΓαΓ_idid_+ΓΓ_sisi₊₁ (1 + Γ0)2 ! bits/s/Hz. (2.12)

For a given cooperation time slot of length Tco (in which the channel SNR remain

constant by the quasi-static channel assumption), different potential relays have inde-pendent channel gains. In addition, an indeinde-pendent queueing state is also experienced by each potential relay. Therefore, the reserved power (or time slots, subcarriers), of a potential relay for their own transmissions, i.e., (1_{− α)P , will be different, so the} rate improvement for the source to BS transmission also varies. It is then unrealistic for the source node to collect channel and queue state information from all poten-tial relays due to the significant system overhead this will introduce. Centralized optimization is therefore not suitable for this queue-aware relay selection problem.

An auction game approach is used here to conduct scheduling for relay node selection and relay resource allocation. Specifically, the source node is the auctioneer, and the potential relays are participants in the auction game. The item for sale is the cooperation opportunity in the current cooperation time slot (fading block). The winner of the auction game is selected to help the source transmission by providing an SNR improvement as given in (2.10). As a return, the selected relay node will receive a certain amount of “virtual money,” which can be used to “purchase” assistance from other MS nodes when needed. Both the relay resources to be allocated for cooperation and the amount of virtual money received are determined by the auction mechanism that will be discussed in detail in Sections 2.3.2 and 2.3.3.

Following game theory convention, the auction game in strategic form is denoted as Ω = [N , Si, Πi], i∈ N , where N is the set of players, i.e., the N potential relays

in this problem; _Si is a nonempty set of actions (bidding strategies in this scenario)

of player i, and Πi is the payoff function for player i. The auction and cooperation

process is described as in Fig. 2.2. Note that an efficient design should have Tin and

Tbd much smaller than Tco so that the auction mechanism induced system overhead

is negligible.

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Figure 2.2: Time frame structure for auction-based relay node selection and cooper-ative transmission.

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potential relays randomly pick a point within the bidding period Tbdto asynchronously

access the channel and place their bids to the source node S0. Since in practical

user cooperation scenarios the number of accessible potential relays N is not very large, we do not consider bidding collision here. It is then reasonable to make the assumption that the bidders cannot respond to bids from other potential relays and change their own bids accordingly. Therefore we consider a sealed-bid auction game for this distributed queue-aware relay node selection design problem. The system overhead of the bidding process is minimized in this case because of the one-shot nature of the auction considered. The winner, i.e., the node who submitted the highest bid, is selected to assist with source node transmission in the cooperation period following the auction. The bidding process and the subsequent cooperation time slot structure is shown in Fig. 2.2. Because of the continuous nature of the bidding strategy, the probability of a tie is near zero. Whenever a tie occurs, one of the highest bidders can be chosen randomly to break the tie.

2.3.2 Bidder private values

Next we study bidder private values, denoted by the RV Vi, i ∈ N , in this auction

game. Consider the amount of SNR improvement a relay can provide to the source transmission, i.e., the fixed-power AF-relayed SNR given in (2.10), as the relay’s valuation. Based on the virtual money concept introduced in Section 2.3.1, bidder Ri’s valuation is the amount of virtual money it expects to receive for providing

help to the source transmission, which reflects the value of the cooperation oppor-tunity to this node. From (2.10), this value depends on both the specific channel realization and the fraction of power α a relay would like to allocate for cooperation. With awareness, α is jointly determined by the channel state and the queue-ing state. On the other hand, the auctioneer’s valuation is the instantaneous direct source-to-destination link SNR Γ0, which is the SNR improvement given by simple

retransmission in the second phase. The auction game is thus a private-value auction. By symmetry assumption for the potential relays, Vi should be i.i.d. RVs for

different i. We denote Ri’s queue length at the beginning of the cooperation frame by

Qi, which is also an RV, and the lower case notation qi is a specific realization of Qi.

For queue-aware relay selection algorithm design, the queue length Qi at the end of

the cooperation time slot is used to define the QoS requirement of Ri. Specifically, Ri

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reduce its buffer occupancy to a prescribed threshold Qth_−cobefore it is able to allocate

transmission power for cooperation. Given Γid, this QoS requirement is described as

W Tco

2ηL {log2(1 + Γid) + log2[1 + (1− α)Γid]}

≥ Qi− Qth_−co. (2.13)

Note that sufficient buffer space should be reserved for packet arrivals of the potential relay in the current cooperation time slot when determining the value of Qth−co. For

example, in order to completely avoid buffer overflow in the current cooperation time slot, the difference between the potential relay’s buffer size and the maximum number of packet arrivals in a time slot can be used for Qth_−co.

Solving (2.13) for α at equality, we obtain

α(Qi; Γid) =        0 Qi− Qth_−co≥ 2ξ; 1− 2 2ηL W Tco(Qi−Qth−co)−log2(1+Γid)₋₁ Γid , ξ ≤ Qi− Qth−co < 2ξ; 1, Qi− Qth_−co< ξ; = max ( 0, min ( 1, 1− 2 2ηL

W Tco(Qi−Qco−th)−log2(1+Γid)_{− 1}

Γid

)) .

(2.14)

where ξ = W Tco

2ηL log2(1 + Γid). The queue-aware interpretation of (2.14) is as follows.

When the queue length Qi is smaller than a threshold determined by both the QoS

requirement Qth−co and Ri’s channel condition, Qi < W T_2ηLcolog2(1 + Γid) + Qth−co,

which indicates that the QoS requirement of Ri can be met only by transmitting in

the first phase of the cooperation time slot, so Ri is able to cooperate with its full

power P in the second phase. Otherwise, only a fraction of the transmission power can be allocated for relaying. Once Qi− Qth_−co goes beyond 2ξ = W T_ηLcolog2(1 + Γid),

this MS node is no longer able to act as a relay due to not satisfying its own QoS requirement.

The private value Vi of the ith potential relay with power allocation coefficient αi

given by (2.14) is evaluated by putting its own channel SNR realization and value of αi into (2.10).

2.3.3 Auction mechanism design

From a cooperative communications point of view, the best relay node selected should be the one that benefits the source transmission most, given the relay’s QoS

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require-ment (based on queue length here). Therefore the auction mechanism should be designed based on the auctioneer, i.e., the source node’s profit. That means the op-timal auction mechanism should maximize the expected SNR improvement in the source-to-destination link by cooperation.

As discussed in Section 2.3.1, a sealed-bid model is considered for the auction game. The relay nodes thus cannot respond to others’ bids and modify their bids accordingly. The second-price, sealed-bid auction, also known as a Vickrey auction due to the pioneering work of Vickrey [28], has the distinct advantage of assigning the item for sale to the bidder who values it most. Because the private value in this work is the SNR improvement for the source transmission due to cooperation, the Vickrey auction is a suitable model in that it chooses the relay who is most capable of improving the source transmission link SNR under QoS constraints for cooperation. However, as pointed out in both the work of Vickrey [28] and Ausubel and Cramton [29], the conventional second-price sealed-bid auction may yield low revenue for the auctioneer, which is not desirable for our relay node selection problem from the cooperative communications perspective. A simple and effective way to address this issue, as demonstrated in [29], is to introduce positive reserve pricing to the auction game. Therefore, in this work the second-price, sealed-bid auction with a positive reserve r for all bidders is considered as the auction model.

Different from the first-price auction, in a second-price auction the winner who placed the highest bid wins the auction but is only required to provide an SNR improvement for the source transmission according to the second highest bid. The amount of virtual money awarded to the selected relay for contributing in the cooper-ation is equal to its own valucooper-ation Vi. As a result, a total number of potential relays

N is assumed to be no less than 3. This auction mechanism is described as follows: 1. All bidders with private value Vi < r are rejected immediately.

2. If all bidders are rejected, no relays are selected, i.e., the source chooses to conduct a direct retransmission in the second phase of the cooperation time slot. Otherwise the relay who placed the highest bid is selected for relaying. 3. The winning bidder provides the source with the SNR improvement determined

by the maximum of the second highest bid and the reserve price r. In return, the selected relay is granted by the system its private SNR improvement valuation, Vi = Γs,i,d. The bidders who did not win pay nothing.

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4. Ties are broken by randomly selecting with equal probability one of the highest bidders for relaying.

The joint bidding strategy space, denoted by _{S, is the Cartesian product of the} action sets _Si, i.e. S = S1 × S2 × . . . × SN. We use bi to denote the ith potential

relay’s bid, and b_−i the bidding profile of the other nodes. The bidding profile of the system is given by b =_{bi, b−i}, and the corresponding payoff function of Ri is

Πi =

(

Γs,i,d(αi)− max{r, b−i}, if bi > max{r, b−i};

0 otherwise. (2.15)

The expected profit of the auctioneer, i.e. the source node, is given by

Ψ = E " X i Mixi− Γ0 # =X i E[Mi]xi− ¯Γ0 = E[Mi]xco− ¯Γ0, (2.16)

where Mi denotes the payment of bidder i if it wins, xi is the probability of bidder i

winning, and xcois the overall probability of cooperation. Note that the third equality

in (2.16) is due to the symmetry assumption of all relays.

Denote the cumulative distribution function (CDF) of Vi by FV(v), evaluation of

the term E [Mi] xcoin (2.16) is considered in two basic scenarios corresponding to the

two cases when cooperation occurs. The first scenario is when only one potential relay has its private valuation Vi greater than the reserve value r = Γ0. The corresponding

probability of cooperation is xco1 = N 1 (1_{− F}V(r)) (FV(r)) N₋₁ , (2.17)

and the payment of the winning MS in this case is Mi = r.

In the second scenario, at least two relay nodes have private values Vi greater than r.

The probability of this case is given by

xco2 = 1− xco1− (FV(r))N. (2.18)

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relays, whose CDF is given by F2(x) = N 2 (1− FV(x))2F_VN−2(x). (2.19)

By letting x > r in (2.19), we obtain the truncated CDF which describes the distri-bution of the payment Mi in this case

F2T R(x) =

F2(x)− F2(r)

1_{− F}2(r)

. (2.20)

The corresponding expected value of payment can then be calculated and used to evaluate the expected profit of the auctioneer given by (2.16).

According to the auction mechanism proposed for queue-aware relay selection and the system assumptions, we give the following Proposition 1 and a sketch of the proof. Proposition 1. Truthful bidding is a Nash equilibrium of the second-price sealed-bid auction for the queue-aware relay node selection.

Proof. By the symmetry assumption, the private values Vi are i.i.d. random variables

on a common support (0,∞). A strictly positive and finite reserve price r is therefore always within the support of Vi. Since an SNR improvement of Γ0 can be achieved

by simple retransmission if the source decides to not use relaying, the reserve price r should be no less than the auctioneer’s valuation Γ0, so that whenever

coopera-tion is used it can only increase the auccoopera-tioneer’s profit by providing a greater SNR improvement.

As shown in [30], with a second-price, sealed-bid auction run by the system, truth-ful bidding is a weakly dominant strategy, which gives a unique Nash equilibrium. Note that for a Vickrey auction, secrecy of the reserve price does not affect the NE of the auction game [31, Chapter 8]. In addition, since in this work the auction may end up with selecting no relay and using direct retransmission, there is no com-mitment problem in this auction. The mechanism design problem therefore reduces to the problem of finding a suitable reserve price r regarding the auctioneer’s profit (2.16).

It was found from the simulation results that in the user cooperation system where all uplink channels experience i.i.d. Rayleigh fading, if simple retransmission is adopted when all relay bids fail to meet a positive reserve price, using r = Γ0 as

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improvement. Because the fraction of power actually allocated for cooperation is less than that calculated by (2.14) the selected relay’s QoS requirement (2.13) must be satisfied. Given the second highest private value VL2, the fraction of power allocated

by the winner for cooperation can be calculated from (2.10) as

αw =

max_{VL2, r}(Γsi+ 1)

Γid(Γsi− max{VL2, r})

. (2.21)

On the other hand, based on the auction mechanism there is no QoS degradation for the losers of the auction. Therefore the system QoS requirement is guaranteed with this relay selection mechanism.

2.4 Numerical Results and Discussion

In this section, we present numerical results of the proposed Vickrey auction game-based distributed relay selection algorithm. An FDD FDMA multiple access system is considered with a total of N = 10 potential relay nodes in the system. All uplink wireless channels are i.i.d. Rayleigh fading channels with average received SNR ¯Γ0 =

10 dB. The inter-MS channels are also Rayleigh fading, and the average SNR is set to ¯Γ = 15 dB. We assume a system bandwidth of W = 200 kHz, the cooperation time slot period is Tco = 10 ms, and the Doppler frequency is fd = 20 Hz. The

packet length is set to L = 1024 bits/packet, and a capacity achieving coding scheme is assumed with code rate η = 3/4. Therefore the coefficient ξ is ξ = 1.302. The ergodic capacity of the i.i.d. uplink channels is transformed to approximately 7.56 packets/time slot. Therefore we consider packet arrival rates λTco ranging from 0.5

to 8 packets per time slot. Furthermore, we assume that the maximum number of simultaneous packet arrivals to be A = 30 packets. The buffer size of all relays is set to B = 100 packets. The QoS requirement Qth−co is 10 packets.

We first evaluate the performance of the proposed auction game-based queue-aware relay selection scheme. The packet blocking rate and the average SNR im-provement compared to the source transmission are used as performance metrics. In addition, we also consider the probability of the event with relay buffer occupancy greater than the QoS threshold Qth_−co. Performance of the SNR-based channel aware

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the SNR-based Policy I selects the relay node with the largest value of

Hri1 = min(Γsi, Γid), i = 1, 2, . . . , N. (2.22)

In Policy II, the harmonic mean of the two single hop SNRs (source-to-relay and relay-to-destination) is used as the link quality indicator, which is given by

Hri2 =

2ΓsiΓid

Γsi+ Γid

, i = 1, 2, . . . , N. (2.23) Performance of the fixed relaying scheme is also provided.

Since all relay nodes are assumed to be selfish in nature, we require that if a relay node Ri is selected for cooperation by the SNR-based or fixed relaying algorithm,

it must first guarantee its own QoS requirement before allocating power to relaying. Thus, even if it is chosen as the relay node for cooperation, Ri must first reduce its

own buffer occupancy to Qth−co. Only the remaining power can be used for relaying

of source packets. If the relay node selected cannot meet its own QoS requirement in the current time slot, relaying is not done and a retransmission of the source packets is used in the second phase of the cooperation time slot.

Fig. 2.3 shows the probability of relay buffer occupancy exceeding the QoS re-quirement Qth_−co. When the traffic load is low (below 2 packets/time slot), this is

almost 0 for all schemes. As the traffic load increases, the probability of the queue length exceeding Qth−co also increases due to the change in the steady state queue

length distribution. It can be observed from Fig. 2.3 that with queue-awareness, the proposed distributed queue-aware relay selection algorithm can better reduce the average buffer queue length, especially at higher packet arrival rates, compared with fixed relaying and SNR-based relay selection.

The cost of achieving better QoS provisioning, i.e., maintaining a buffer occupancy smaller than Qth_−co, using the proposed relay selection scheme is a slight

degrada-tion in SNR improvement for the source transmission, which is shown in Fig. 2.4. The horizontal straight line in the plot shows the average SNR improvement with simple retransmission, which is equal to the average SNR ¯Γ0 of the direct

source-to-destination channel. From this figure, it can be observed that in the low traffic regime, the SNR-based Policy II achieves the largest SNR improvement for source transmission. However, the performance gap between Policy II and the proposed queue-aware scheme is marginal (0.6 in the very low traffic regime and reducing

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0 1 2 3 4 5 6 7 8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Packet arrival rate λ T

co (packets/time slot)

Prob{Relay queue length > Q

th−co } SNR−based Policy I SNR−based Policy II Fixed relaying QA auction−based

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1 2 3 4 5 6 7 8 5 6 7 8 9 10 11 12 13 14 15

Packet arrival rate λ T

co (packets/time slot)

Sorurce transmission SNR improvement

SNR−based Policy I SNR−based Policy II Fixed relaying

QA auction−based Retransmission

Figure 2.4: Average SNR improvement for the source transmission achieved using different relaying techniques.

Cross-Layer Design for Cooperative Wireless Networking

Contents

List of Tables

List of Figures

List of Acronyms

Acronyms

Definitions

Introduction

1.1

Background and Motivation

1.2

Cooperative Wireless Communications

1.3

The Cross-Layer Design Approach

1.4

Brief Outline of the Dissertation

1.5

Bibliographic Notes

Chapter 2

Distributed Queue-Aware Relay

Node Selection for Cooperative

Wireless Networks via Auction

Game

2.1

Background and Motivation

2.2

System Model

2.2.1

Basic physical layer assumptions

2.2.2

Queueing system assumptions

2.3

Auction Game and Mechanism Design

2.3.1

Relay selection by auction

2.3.2

Bidder private values

2.3.3

Auction mechanism design

2.4

Numerical Results and Discussion