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Resource allocation schemes for next generation wireless communication systems Phuyal, Umesh 2012

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Resource Allocation Schemes for Next Generation Wireless Communication Systems by Umesh Phuyal B.E., Tribhuvan University, Nepal, 2003 M.E., Asian Institute of Technology, Thailand, 2006 M.Sc., Institut National des T´el´ecommunications, France, 2006  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  Doctor of Philosophy in THE FACULTY OF GRADUATE STUDIES (Electrical and Computer Engineering)  The University Of British Columbia (Vancouver) December 2012 c Umesh Phuyal, 2012  Abstract Recent studies have indicated that spectrum scarcity in next generation wireless networks is inevitable due to the surge of mobile communication usage which offers the capability of instant access to users’ data and multimedia content anywhere anytime. Demand of mobile data traffic is found to have doubled within a year, and is expected to grow by 15 times in about five years. Fulfilling such mounting demand with the limited radio resources is a huge challenge for next generation wireless communication systems. Moreover, meeting the diverse quality of service (QoS) requirements of various types of user applications is indispensable. To tackle these challenges and to improve the spectral efficiency, radio resource management needs to be optimized for various novel systems such as relay-based cooperative transmission technique and opportunistic spectral utilization using cognitive radio (CR) technology. In addition to spectral efficiency, effective resource allocation methods need to be designed to improve the energy efficiency of such systems to achieve sustainable green communication. In this thesis, we investigate performance of certain resource allocation techniques in next generation wireless communication systems through analytical modeling and propose improved solutions using results from these models and simulations. First, we analyze the performance of resource allocation schemes for guaranteed QoS provisioning in a relay-  ii  based cooperative communication system. We introduce novel methods for precoder design for multi-antenna source and relay stations employing joint zero-forcing method. We design various schemes to allocate available transmit power to the source and relay(s) in a spectrally efficient manner. Next, we study the performance of resource allocation schemes for multicarrier multiple-input multiple-output (MIMO)-based CR system. We propose an optimal power allocation scheme for such system considering the practical CR constraints. Finally, we investigate the issues and challenges in enabling green communication in next generation wireless communication systems. We propose energy-efficient resource allocation method for guaranteed QoS provisioning by employing relay-based cooperative communication. We also analyze the intrinsic trade-off between energy and spectral efficiency using multi-objective optimization approach. For all of the proposed algorithms and schemes, we also present extensive simulation-based results for comparison with methods existing in the literature.  iii  Preface I am the primary researcher and author for all the research contributions made in this thesis. I carried out majority of the work including but not limited to performing literature review, identifying the research problems, and conducting research to address those problems. I carried out the mathematical analysis, formulation of the problems and development of novel schemes. I wrote the computer programs for analyzing the mathematical models and for simulating performances of proposed schemes. I also prepared the associated manuscripts for publication. Following are the publications that are related to the results presented in this thesis in the corresponding chapters as indicated. Other publications that are resulted from the research work conducted during this Doctoral program are listed in Appendix A. • U. Phuyal, S. C. Jha, and V. K. Bhargava, “Joint zero-forcing based precoder design for QoS-aware power allocation in MIMO cooperative cellular network,” IEEE J. Sel. Areas Commun., vol. 30, no. 2, pp. 350–358, Feb. 2012.  (appears in Chapter 2).  • U. Phuyal, S. C. Jha, and V. K. Bhargava, “QoS guaranteed resource allocation in cooperative cellular network with MIMO-based relays,” in Proc. IEEE ICC’11, June 2011, pp. 1–6.  (appears in Chapter 2).  iv  • U. Phuyal, S. C. Jha, and V. K. Bhargava, “Optimal and suboptimal relay selection and power allocation in multi-relay cooperative network,” in Proc. AH-ICI’11, Nov. 2011, pp. 1–6.  (appears in Chapter 2).  • U. Phuyal, A. Punchihewa, V. K. Bhargava, and C. Despins, “Power loading for multicarrier cognitive radio with MIMO antennas,” in Proc. IEEE WCNC’09, Apr. 2009, pp. 1–5.  (appears in Chapter 3).  • U. Phuyal, S. C. Jha, and V. K. Bhargava, “Resource allocation for green communication in relay-based cellular networks,” in Green Radio Communication Networks, E. Hossain, V. K. Bhargava, and G. Fettweis, Eds. Cambridge: UK, 2012, pp. 331– 356.  (appears in Chapter 4).  • U. Phuyal, S. C. Jha, and V. K. Bhargava, “Green resource allocation with QoS provisioning for cooperative cellular network,” in Proc. IEEE CWIT 2011, May 2011, pp. 206–210.  (appears in Chapter 4).  Satish C. Jha is a co-author for contributions in Chapters 2 and 4. I consulted him during identification of the research problems. He also provided editorial feedbacks during the preparation of the manuscripts for publication. Dr. Anjana Punchihewa and Prof. Charles Despins are co-authors for contributions in Chapter 3. I consulted them during formulation of the research problem. They provided editorial feedbacks during my preparation of the manuscript for publication. My supervisor Prof. Vijay K. Bhargava is a co-author for contributions made in Chapters 2, 3 and 4. I consulted him during the identification and formulation of the research problems. He also provided editorial feedbacks during my preparation of the manuscripts for publication. v  Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ii  Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  iv  Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  vi  List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  x  List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xi  List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv Acknowledgements  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii  Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1  1.2  1  Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1  1.1.1  Relay-based Cooperative Communication . . . . . . . . . . . . . .  2  1.1.2  Cognitive Radio . . . . . . . . . . . . . . . . . . . . . . . . . . . .  2  1.1.3  Green Communication . . . . . . . . . . . . . . . . . . . . . . . .  5  Motivation  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi  7  1.3  Objectives of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11  1.4  Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4.1  Resource Allocation Schemes for Cooperative Communication Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12  1.4.2 1.5  Resource Allocation Schemes for CR Network . . . . . . . . . . . 16  Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17  2 Resource Allocation for Relay-based Cooperative Communication Network . 20 2.1  2.2  2.3  2.4  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.1.1  Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22  2.1.2  Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23  Cooperative Communication Network With MIMO Relay . . . . . . . . . . 23 2.2.1  System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26  2.2.2  Joint Zero-Forcing Based Resource Allocation . . . . . . . . . . . 30  2.2.3  Suboptimal Power Allocation Scheme . . . . . . . . . . . . . . . . 35  2.2.4  Constraint on RS Transmit Power Budget . . . . . . . . . . . . . . 38  2.2.5  Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 39  Cooperative Communication Network With Multiple Single-antenna Relays  52  2.3.1  System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53  2.3.2  Optimal Power Allocation . . . . . . . . . . . . . . . . . . . . . . 55  2.3.3  Suboptimal Relay Selection and Power Allocation . . . . . . . . . . 58  2.3.4  Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 63  Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72  3 Resource Allocation for Cognitive Radio Network with MIMO Antennas . . 74  vii  3.1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.1.1  Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77  3.1.2  Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77  3.2  CR System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78  3.3  Power Allocation Scheme for CR Capacity Optimization . . . . . . . . . . 82  3.4  Performance Analysis and Results . . . . . . . . . . . . . . . . . . . . . . 84  3.5  3.4.1  Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 84  3.4.2  Comparison With Existing Schemes . . . . . . . . . . . . . . . . . 85  3.4.3  Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 89  Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102  4 Resource Allocation to Enable Green Communication in Wireless Networks 103 4.1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.1.1  4.2  4.3  4.4  Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105  Enabling Green Communication in Wireless Communication Networks . . 106 4.2.1  Component Level . . . . . . . . . . . . . . . . . . . . . . . . . . . 106  4.2.2  Equipment Level . . . . . . . . . . . . . . . . . . . . . . . . . . . 107  4.2.3  Network Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107  4.2.4  Computation Complexity Versus Transmit-power-saving . . . . . . 108  Relay-based Green Cooperative Communication Network . . . . . . . . . . 108 4.3.1  Implementation Issues and Challenges . . . . . . . . . . . . . . . . 110  4.3.2  Advantages of Fixed Relay–based CCN . . . . . . . . . . . . . . . 114  4.3.3  Green Performance Metrics for Resource Allocation . . . . . . . . 115  Design of a Green Power Allocation Scheme . . . . . . . . . . . . . . . . . 115 4.4.1  System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 viii  4.5  4.4.2  Green Power Allocation Scheme . . . . . . . . . . . . . . . . . . . 118  4.4.3  Performance Analysis of GPA Scheme . . . . . . . . . . . . . . . . 120  4.4.4  Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 122  Green Performance Versus System Capacity . . . . . . . . . . . . . . . . . 136 4.5.1  4.6  Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 138  Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142  5 Conclusions and Directions for Future Work . . . . . . . . . . . . . . . . . . 144 5.1  Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144  5.2  Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 5.2.1  Cooperative CR Network . . . . . . . . . . . . . . . . . . . . . . . 147  5.2.2  Effect of Uncertainty in Channel State Information . . . . . . . . . 148  5.2.3  Green CR Network . . . . . . . . . . . . . . . . . . . . . . . . . . 149  Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Appendices A List of Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 B Derivation of γk in (2.12) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 C Quasi-concavity of γk Given by (2.12) . . . . . . . . . . . . . . . . . . . . . . . 165 D Solution of Problem P2 Defined in (2.24)–(2.27) . . . . . . . . . . . . . . . . . 166 E Convexity of Problem (2.40) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 F Concavity of l(Ps, Pr ) given by (4.7) . . . . . . . . . . . . . . . . . . . . . . . . 171 ix  List of Tables Table 2.1  Performance improvement for increase in number of available relays (N) from 5 to 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72  Table 3.1  Simulation parameters for power allocation for multicarrier cognitive radio (CR) with MIMO antennas. . . . . . . . . . . . . . . . . . . . . . 85  Table 4.1  Simulation parameters for relay-based green cooperative communication network (CCN). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123  x  List of Figures Figure 1.1  Relay-based cooperative communication. . . . . . . . . . . . . . . . .  Figure 1.2  Spectrum holes created due to underutilization of licensed frequency  3  bands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  4  Figure 1.3  A simple cognitive radio (CR) scenario. . . . . . . . . . . . . . . . . .  6  Figure 1.4  Classification of resource allocation schemes for cooperative communication network (CCN). . . . . . . . . . . . . . . . . . . . . . . . . . 13  Figure 2.1  System model for CCN with MIMO relays illustrating broadcast channel with multi-antenna RSs and direct link between BS and MSs. . . . . 28  Figure 2.2  Illustration of position of relays and cell-edge MSs in simulations. . . . 40  Figure 2.3  Probability of system outage by using proposed power allocation scheme versus relative distance of RS from BS for various α . . . . . . . . . . . 42  Figure 2.4  Comparison of probability of system outage with and without using Algorithm 2.1 in the proposed power allocation scheme. . . . . . . . . 44  Figure 2.5  Comparison of outage probability by using proposed and existing schemes for different relative positions of relay. . . . . . . . . . . . . . . . . . . 45  Figure 2.6  Probability of system outage by using proposed power allocation scheme versus power budget constraint. . . . . . . . . . . . . . . . . . . . . . 47  xi  Figure 2.7  Comparison of outage probability versus power budget constraint for proposed and existing power allocation schemes. . . . . . . . . . . . . 48  Figure 2.8  Outage probability versus number of simultaneous worst case data streams per relay for proposed power allocation scheme.  Figure 2.9  . . . . . . . . . . . . 49  Comparison of outage probability versus number of simultaneous worst case data streams per relay for various power budget constraints. . . . . 50  Figure 2.10 Total power consumption by using proposed algorithm versus optimal solution by exhaustive search. . . . . . . . . . . . . . . . . . . . . . . 51 Figure 2.11 An example simulation scenario depicting position of source, destination and 30 relays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Figure 2.12 Average normalized throughput versus number of available relays for different relay selection and power allocation methods. . . . . . . . . . 66 Figure 2.13 CDF of number of relays used by optimal power allocation scheme for various total number of available relays. . . . . . . . . . . . . . . . . . 68 Figure 2.14 CDF of number of relays used by threshold based iterative relay selection and power allocation scheme for various total number of available relays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Figure 2.15 CDF of normalized throughput for different relay selection methods and various total number of available relays. . . . . . . . . . . . . . . . 71 Figure 3.1  Distribution of primary and CR users in spectral domain. . . . . . . . . 79  Figure 3.2  CR system model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80  Figure 3.3  Variation of MIMO channel capacity of CR versus interference temperature threshold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90  xii  Figure 3.4  Variation of maximum permissible power transmission of CR versus interference temperature threshold. . . . . . . . . . . . . . . . . . . . . 91  Figure 3.5  Cumulative distribution function of instantaneous interference caused to PU. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93  Figure 3.6  CR capacity versus total transmit power using proposed power allocation scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95  Figure 3.7  CDF of total transmit power of SUs using proposed power allocation scheme for different interference temperature thresholds. . . . . . . . . 97  Figure 3.8  CDF of total transmit power of SUs using proposed power allocation scheme for different number of transmit antennas. . . . . . . . . . . . . 98  Figure 3.9  Capacity of CR versus total transmit power budget (Pmax ). . . . . . . . 99  Figure 3.10 Capacity of CR versus number of subcarriers using proposed power allocation scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Figure 4.1  Cellular networks with ideal hexagonal cells. . . . . . . . . . . . . . . 109  Figure 4.2  An ideal hexagonal cell of a relay-based CCN. . . . . . . . . . . . . . . 117  Figure 4.3  Variation of energy efficiency with respect to relay position for QoS satisfied users. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124  Figure 4.4  Variation of QoS outage with respect to relay position. . . . . . . . . . 126  Figure 4.5  Variation of average system throughput with respect to relay position. . 127  Figure 4.6  Total transmit power consumption for QoS satisfaction by different power allocation schemes. . . . . . . . . . . . . . . . . . . . . . . . . 129  Figure 4.7  Average power per unit throughput for different Pmax . . . . . . . . . . . 130  Figure 4.8  QoS outage for different Pmax . . . . . . . . . . . . . . . . . . . . . . . 132  Figure 4.9  Variation of QoS outage for different Rmin . . . . . . . . . . . . . . . . . 133 xiii  Figure 4.10 Average throughput for different Rmin . . . . . . . . . . . . . . . . . . . 134 Figure 4.11 Variation of energy efficiency for different Rmin . . . . . . . . . . . . . . 135 Figure 4.12 Variation of average power consumption with respect to trade-off parameter α . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Figure 4.13 Variation of average throughput with respect to trade-off parameter α . . 140 Figure 4.14 Variation of energy efficiency with respect to trade-off parameter α . . . 141  xiv  List of Abbreviations 3GPP  3rd Generation Partnership Project  AF  Amplify and forward  AMC  Adaptive modulation and coding  AWGN  Additive white Gaussian noise  BS  Base station  CCN  Cooperative communication network  CDF  Cumulative distribution function  CoMP  Coordinated multi-point  CR  Cognitive radio  CSI  Channel state information  CZ  Cell zooming  DF  Decode and forward  DL  Downlink  DRX  Discontinuous reception  FCC  Federal Communications Commission  GPA  Green power allocation  GPANQ  GPA with no QoS provisioning  xv  i.i.d.  Independent and identically distributed  ICT  Information and communication technologies  IEEE  Institute of Electrical and Electronics Engineers  KKT  Karush-Kuhn-Tucker  LTE  Long Term Evolution  MIMO  Multiple-input multiple-output  MMSE  Minimum mean square error  MRC  Maximal ratio combining  MS  Mobile station  MSPA  Multi-stage power allocation  MUI  Multi-user interference  OFDM  Orthogonal frequency division multiplexing  OFDMA  Orthogonal frequency division multiple access  PU  Primary user  QoS  Quality of service  RS  Relay station  SINR  Signal to interference-plus-noise ratio  SNR  Signal to noise ratio  SU  Secondary user  SVD  Singular value decomposition  TMPA  Throughput maximization power allocation  TV  Television  UPA  Uniform power allocation  WiMAX  Worldwide Interoperability for Microwave Access xvi  WirelessMAN Wireless Metropolitan Area Network ZF  Zero-forcing  xvii  Acknowledgements First and foremost, I would like to profoundly thank my supervisor Professor Vijay K. Bhargava for his continuous guidance, encouragement and support during my doctoral studies and this research. I would also like to thank Professor Charles Despins and Dr. Anjana Punchihewa for contributing valuable insights to this thesis work. I am very grateful to Professor Shahriar Mirabbasi and Professor Vincent Wong for serving on my supervisory committee; Professor Victor C.M. Leung and Professor Robert Schober for serving on my qualifying examination committee; Professor Z. Jane Wang and Professor Vikram Krishnamurthy for serving on my departmental examination committee; Professor David Michelson and Professor Ryozo Nagamune for serving as University Examiners, Professor John Ries for serving as Examination Chair and Professor Chengshan Xiao for serving as External Examiner for the final dissertation. The work in this thesis is supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada under various strategic project grants. I am grateful to NSERC for their support. I am grateful to my past and present colleagues in the Information Theory and Systems (ITS) laboratory for their genuine and friendly support and for providing a stimulating and fun environment during the course of my PhD research. I am equally indebted to all other  xviii  friends who have supported me in many ways during this part of my life. Special thanks goes to my family members for their love and support during this endeavour. I would like to thank my loving wife Kushum for her continuous encouragement, patience and many sacrifices she has made during my thesis work. Lastly, and most importantly, I wish to thank my parents for their unconditional love and support.  xix  To My Parents ...  xx  Chapter 1 Introduction 1.1 Background In wireless communications environment, electromagnetic spectrum is a precious and scarce resource. Studies have indicated that spectrum scarcity in next generation wireless networks is inevitable due to the surge of mobile communication which offers the capability of instant access to data from anywhere at anytime. Demand of mobile data traffic is found to have doubled in one year (during 2011), and is expected to grow by 15 times in about five years [1]. To tackle with such growing demand, various novel methods are being introduced to improve the spectral efficiency of the wireless communication systems. Relay-based cooperative transmission technique and opportunistic spectral utilization using cognitive radio (CR) technology are major examples of such new areas of exploration. The tremendous growth in wireless communications will also increase the energy consumption of such systems significantly. This requires development of novel methods to optimize the energy efficiency in addition to spectral efficiency of wireless networks. There1  fore, energy efficient (green) communication is another new but important area of research for future wireless communication systems.  1.1.1 Relay-based Cooperative Communication In recent years, data transmission with cooperation of multiple devices has attracted attention of large research community. The method of relaying was first introduced by Van der Meulen in 1971 [2], which was later studied from an information theoretic point of view by Cover and El Gamal in 1979 [3]. In the simplest form, a group of cooperating nodes relay the data being transmitted from a source towards the intended destination. As depicted in Fig. 1.1, when the direct path between the source and destination (S–D) is not reliable due to, for example, dead spots created by adverse channel conditions (e.g., blockade by an obstacle, high attenuation at cell edge), or hot spot created by higher traffic, the relay paths (S–Ri –D, i = 1, . . . , N) can offer better communication channels. In addition, cooperative communication helps in increasing transmission rate, decreasing delay across network, reducing transmission power, improving spatial frequency reuse, and extending network coverage [4].  1.1.2 Cognitive Radio Studies by the spectrum policy task force of the Federal Communications Commission (FCC) has suggested that the assigned spectrum has been very inefficiently utilized by the licensed users [5]. It was found that while some frequency bands are heavily used and crowded, others are only partially occupied and many bands are largely unoccupied. Up to 85% of allocated spectrum on average is being unutilized at certain time and geographical locations, creating large spectrum holes, as illustrated in Fig. 1.2. CR has emerged as a promising technology to improve the spectrum utilization by al2  s1 1d 1  sd s2 2d  sN  2  Nd  N  Figure 1.1: Relay-based cooperative communication. Multiple relays R1 , . . . ,RN cooperate in data transmission from source S to destination D.  3  Unused Spectrum (Spectrum Hole)  Frequency Band  Used Spectrum  Time Figure 1.2: Spectrum holes created due to underutilization of licensed frequency bands.  4  lowing unlicensed or secondary users (SUs) to use licensed or primary user (PU) bands while ensuring that no harmful interference is introduced to the PUs by the SUs [6, 7, 8]. For example, FCC has already approved rules that would allow new broadband communications to be performed in unused television (TV) bands [9]. In addition, IEEE 802.22 working group has been established to develop CR-based standards for devices operating in spectrum that is allocated to the TV broadcast service [10]. A simple CR scenario is depicted in Fig. 1.3 [11, 12]. SUs may coexist with PUs either on a non-interfering basis or an interference-tolerant basis [13, 14], i.e., SUs may use the frequency bands unoccupied (spectrum holes) or occupied by PU. However, CR has to maintain the interference limit constraint at all times, i.e., the interference introduced to PU by SUs should be below a certain threshold, generally termed as interference temperature. CR is intelligent in the sense that it is aware of its propagation environment and dynamically adapts to it. It does so by making real time changes in certain operating parameters such as transmission power, operating frequency, and by employing adaptive modulation and coding (AMC).  1.1.3 Green Communication Owing to the excessive demand of data delivery by wireless media, mobile communications is expected to contribute up to 15–20% of the overall energy consumption in information and communication technologies (ICT) [15]. This has attracted attention of a huge research community towards a new frontier, dubbed in the literature as ‘green communication’. One may wonder, what exactly is meant by the term ‘green communication’? ‘Green’ usually refers to ‘environmentally friendly,’ including but not limited to reduced energy consumption and carbon emissions, protection of ozone layer, use of natural resources,  5  SU2 PU2 PU Base Station  PU3 SU1 PU1  SU Access Point  PU Communication CR Communication  Figure 1.3: A simple CR scenario. SUs are introduced into the area of already existing PUs. A device may have both PU and SU transceivers.  6  reduction in industrial waste, etc. Therefore, green communication is a vast research area which covers energy saving at all layers in the protocol stack of wireless access networks as well as that in design of wireless architecture and techniques for future generation cellular systems [16].  1.2 Motivation Although wireless communication systems are regarded as a highly successful technology, their potential in throughput and network coverage improvement has not been fully realized. Data transmission with cooperation of multiple devices can be a key technique to harness the potential throughput and coverage gains in cellular wireless networks. Apart from throughput and coverage, cooperative communication can improve the energy saving performance at the mobile devices and increase reliability in transmission. Therefore, relay-based cooperation is already considered as an integral part in modern wireless cellular standards such as 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE) and LTE-Advanced [17, 18, 19], and IEEE 802.16 family of standards (commonly known as WiMAX) [20]. However, successful deployment and operation of a cooperative communication network (CCN) hinge on the development of advanced radio transmission and resource management techniques. Thus, cooperative transmission offers new frontiers for research, particularly in the area of resource allocation. For example, resources now need to be smartly shared between base station (BS) and relay stations (RSs) in order to achieve optimal utilization. Multiple-input multiple-output (MIMO) technique has been implemented in recent wireless communication standards such as 3GPP LTE, LTE-Advanced [21], IEEE 802.11n [22] and 802.16e [23] because of its potential to increase channel capacity via transmit spatial  7  multiplexing and/or enhanced reliability via spatial modulation and coding. Generally, user devices are equipped with single antenna due to their size and cost constraints. However, if the fixed relays are deployed by the wireless operator, they do not have strict size constraints providing them with the possibility to be equipped with multiple antennas. Therefore, fixed relays with MIMO antennas seem to be potential candidates in order to achieve higher throughput and extended coverage with higher reliability in a CCN. This motivated us to consider CCN with multiple single-antenna mobile stations (MSs) and MIMO-based fixed relays owned by the operator. In such scenario, the available resources need to be efficiently divided among the source and cooperating RSs before allocating them across multiple antennas in order to maximize the overall transmission capacity of the system. Improved performance in such scenario can be obtained by joint optimization of twofold power allocation: (i) distribution of total power among the source and cooperating relays, and (ii) distribution of power allocated to each device among its antennas. While operator-owned MIMO-RSs can significantly improve system performance, because of the fixed nature of the RSs, there exists the challenge of optimally positioning the RSs to provide coverage to all areas. It may not be feasible to install the RSs at optimal locations because of physical constraints such as unavailability of site. So, ability to use MSs, which are mobile, as relays can be more attractive option. In addition, the requirement to be able to support MS-relaying for emergency responders during disaster rescue and recovery situations has been recently identified by 3GPP [24] as FCC has announced LTE to be the communication standard for the United States nationwide public safety network [25, 26]. Therefore, cooperation of multiple mobile MSs to assist in data transmission from source to destination is not only essential but also it can be a significant performance enhancer for next generation wireless systems. This motivated us to study mobile multi-relay based  8  CCN. In a CR network, cognitive users (i.e., SUs) may coexist and opportunistically share the spectrum with PUs either on a non-interfering basis or interference tolerance basis [14, 27]. Examples of several opportunistic spectrum access methods for CR has been proposed in [14]. One of the major challenges in CR network is to ensure successful coexistence of PUs and CR users in the same frequency band while maximizing the CR users’ performance and limiting the interference introduced to the PUs within the prescribed threshold. Multicarrier communication technology such as orthogonal frequency division multiplexing (OFDM) has been identified as the transmission technology for next generation wireless systems due to its key advantages over other widely used wireless access techniques [28] such as time division multiple access, frequency division multiple access and code division multiple access. The main advantage of multicarrier communication is that the wireless channel is divided into many narrow-band, low-rate, frequency-nonselective subcarriers so that multiple symbols can be transmitted in parallel while maintaining a high spectral efficiency. Multicarrier communication introduces the issue of power and rate allocation to multiple frequency subcarriers in a communication system. As this itself is a huge research area, the issues have been well addressed in the literature for traditional communication system. Due to the co-existence of PUs and SUs in a CR network, which introduces additional constraints (such as constraint on maximum allowable interference to PU introduced by SUs) to the problem in hand, the resource allocation strategies proposed in conventional radios to improve capacity and system performance may not be optimal and not directly applicable for CR. Introduction of multiple antennas at receiver and transmitter in the multicarrier based  9  CR system introduces additional dimensions of problem resulting in requirements of allocating transmit power and rates across multiple subcarriers and multiple antennas while satisfying the CR constraints. This motivates further research in area of resource allocation for MIMO multicarrier-based CR networks. Therefore, in this thesis we also study resource allocation strategies such as power loading with the aim of improving the system performance and capacity of such CR networks. Spectral efficiency had been a major focus in the past during the design and implementation of existing wireless networks. Energy efficiency of wireless communication systems and their impact to the environment have been largely ignored. Increasing energy consumption in these networks has been recently identified as a global problem due to its adverse effects on the environment and increasing cost of operation [29, 30, 31, 32, 33, 34]. Several studies have suggested that the fraction of overall electricity consumption due to ICT infrastructure corresponded to around 7.8% in the European Union in 2005 [35], which is expected to rise to 10.9% by 2020. Around 3% of the world’s electricity consumption is attributed to ICT – contributing to about 2% of worldwide CO2 emission [29, 36, 37, 38]. Cellular system constitutes a major part of wireless communication and its use in daily life is increasing more than ever [39]. From above estimates, it is apparent that the contribution of energy consumption by mobile communications to the overall energy consumption in ICT can no longer be disregarded. Therefore, in this thesis, we also study ways to design a sustainable cellular wireless communication system and enable energy-efficient (green) communication by reducing the transmit energy consumption.  10  1.3 Objectives of the Thesis The broad objectives of this thesis are to investigate performance of certain resource allocation techniques in next generation wireless communication systems through analytical modeling, and to propose improved solutions using results from these models and simulations. The specific objectives of this thesis are are follows: i. To analyze the performance of resource allocation schemes for relay-based CCN for both single- and multi-antenna as well as single- and multi-relay cases, and to design and propose schemes to allocate available resources to the source and relay(s) in more spectrally efficient manner. ii. To study the performance of resource allocation schemes for multicarrier MIMO based CR system, and to propose power allocation scheme for such system considering the practical CR constraints. iii. To investigate the issues and challenges in enabling energy-efficient (green) communication in next generation wireless systems by employing relay-based cooperative communication, to propose energy efficient resource allocation method for guaranteed quality of service (QoS) provisioning, and to analyze the trade-off between energy efficiency and spectral efficiency in relay-based green communication system.  1.4 Literature Review In this thesis, we address the resource allocation problem in a number of emerging wireless communication systems, with special emphasis on spectral efficiency, QoS provisioning, and energy efficiency. This section provides a broad overview of related works on resource  11  allocation in these systems. Further review or literature will also be provided as per relevance in the subsequent chapters.  1.4.1 Resource Allocation Schemes for Cooperative Communication Networks In this section, we review the most notable state-of-the-art resource allocation schemes for the relay-based CCN in the literature. We then discuss the approaches and objectives of these schemes and analyze their effectiveness towards energy efficiency performance. Resource allocation in such network can be optimized to achieve various objectives such as maximization of system throughput, minimization of transmission power, guaranteed QoS provisioning, and energy efficiency. Generally, a trade-off between these objectives is needed in practice. Based on these objectives, these schemes can be broadly classified into three major categories: throughput maximization, QoS-aware transmit power minimization, and energy-aware green schemes, as illustrated in Fig. 1.4. In addition, other categories of schemes such as error rate minimization [e.g., 40] has also been discussed in the literature. Although similar classification is possible for allocation of other network resources such as frequency bands, time-slots and codewords, we mainly focus on allocation of transmit power in the following discussion. Throughput Maximization Schemes Modern cellular networks consistently face high traffic demand. As a result, capacity maximization is of prime importance for these networks. As the name suggests, throughput maximization schemes maximize the overall system throughput and generally use all of the available transmit power [e.g., 41, 42, 43]. They are effective in fulfilling the high 12  Resource Allocation Schemes  Throughput Maximization  QoS-Aware  No QoS  QoS-Aware Transmit Power Minimization  Base Station Power Minimization  Energy-Aware (Green)  QoS-Aware  No QoS  SNR/Data Rate Constraint  Relay Station Power Minimization  SNR/Data Rate Constraint  Outage Constraint  Total Transmit Power Minimization  Outage Constraint  Figure 1.4: Classification of resource allocation schemes for CCN.  13  traffic demand in the system. However, such schemes favor MSs with better direct and/or relay channels and hence may not be fair to all users in terms of data rate and outage. To combat this problem, throughput maximization schemes with QoS provisioning exist in the literature [e.g., 44] which maximize the system throughput and at the same time guarantee either a predefined data rate, or signal to noise ratio (SNR) for each user, or a predefined overall system outage. The schemes with QoS provisioning, however, offer lower overall system throughput compared to those without QoS provisioning. Both types of these schemes do not consider energy efficiency of the cellular networks. Therefore, in terms of green performance metric (e.g., J/bit1), these schemes can be unsatisfactory. QoS-aware Transmit Power Minimization Schemes The main objective of schemes in this category is to reduce power consumption in the system rather than maximizing the system capacity. They try to minimize transmit power (BS, RS, or total power) while providing a QoS guarantee in terms of data rate or SNR at each MS. Jointly minimizing sum of BS and RS powers [e.g., 45] provides better results compared to minimizing BS or RS power alone, at a cost of computational complexity. These schemes perform better than throughput maximization schemes in terms of green performance. However, the overall system throughput in this case is usually lower than that of throughput maximization schemes.  1  The green performance metric J/bit represents the amount of transmit energy required per bit of information, which is equivalent to transmit power per unit data rate. See Section 4.3.3 for more details.  14  Energy-aware Green Schemes The energy efficiency of a cellular system can be best achieved by directly optimizing the green performance metric (e.g., J/bit) during resource allocation process. Energy-aware green resource allocation is relatively a new research concept and a few work on saving energy in CCN has been reported in the literature [e.g., 46, 47, 48]. In [46], MSs are partitioned into groups. Only one RS is selected for the transmission in the next time-slot among those RSs for which at least one user in their group has BS–RS SNR higher than a threshold value (minimum end-to-end SNR required at the MS). The idea is to switch off those RSs whose first-hop transmission cannot guarantee the end-to-end SNR, and save transmit power without increasing outage probability. However, since at most one RS is active at a time, the overall system throughput and fraction of users served at a time may be very low in practice. In [47] and [48], authors proposed schemes to maximize the network life by minimizing the energy consumption. Based on the channel conditions and power requirement, [47] proposed a scheme which selects between direct non-cooperative transmission or relaybased cooperative transmission, or decides to postpone the transmission for possible future better channel conditions. The authors in [47] showed that cooperation can reduce the energy consumption in the network without disturbing the QoS performance in terms of maximum allowable system outage. On the other hand, [48] proposed a scheme that exploits the existence of BS–MS path. However, with the proposed scheme, the increase in lifetime and energy saving comes at the cost of increased outage. In addition, contrary to the assumption of [48], relay based communication is required for users at the cell-edge that do not have strong direct path in practical scenarios. When the direct path is in deep fade, the users are hidden from BS, giving the opportunity for BS to transmit data to other 15  users in second time-slot reusing the resources. These existing schemes may not optimize the green performance metric. Moreover, the effect of energy saving on the overall system throughput has not been discussed. Therefore, more research is needed to develop an efficient green resource allocation scheme for CCN.  1.4.2 Resource Allocation Schemes for CR Network Since PUs have a higher priority than the SUs while opportunistically sharing the spectrum, SUs have to maintain interference introduced to the PUs below a certain limit known as interference temperature threshold defined by regulatory bodies such as FCC. Therefore, the QoS of PUs in a CR network is maintained by introducing additional interference power constraints, measured at the PUs receivers [11, 13, 27]. The average interference power measure is appropriate for delay-insensitive communications and has been extensively exploited in the previous studies to limit the interference from SU transmission to the PUs [11, 13, 27]. By considering this setup, in [49], an optimal power allocation strategy is proposed to achieve the ergodic capacity and the outage capacity of single-antenna CR under its transmit power constraint and set of interference power constraints on the PUs. Power allocation algorithms for conventional multicarrier MIMO wireless systems exist in literature [e.g., 50, 51] but they focus on optimizing the power distribution with the constraint only on total transmit power. These algorithms do not consider the interference introduced to the PU as an optimization constraint. However, in CR, interference constraint is more important than power constraint as CR transmitter is not allowed to transmit if the interference to PU is above certain threshold predefined by the regulating bodies. Channel capacity of a class of MIMO CRs has been discussed in [52] and fundamental limits of operation of such network with a single PU and a single SU are derived. However,  16  [52] assumes that the SU has access to the PU’s messages and derives the capacity limits with constraint on combined transmission power of licensed and cognitive transmitters. In practical CR application, this may not be the case.  1.5 Outline of the Thesis A common thread between the subsequent chapters of this thesis is study of various resource allocation mechanisms for next generation wireless communication technologies to improve the efficient utilization of available resources. In Chapter 2, we analyze the performance of resource allocation schemes for relaybased CCNs. First, we study a relay-based cooperative communication scenario where multiple data streams originating from a BS targeted to multiple cell-edge MSs are transmitted via pre-installed cooperative RSs with multiple antennas. Our objective is to guarantee a QoS in terms of predefined SNR at such users within the transmit power budgets at BS and RSs while minimizing total transmit power. We propose a novel precoder design method for power allocation between multiple data streams at BS and RS by using joint zero-forcing (ZF) strategy in order to avoid multi-user interference (MUI) in the signal received by MSs via both the direct and relay links. We also propose a low-complexity suboptimal power allocation algorithm. We focus on analyzing the significance of direct link transmission in providing QoS to cell-edge MSs specially when RS is not situated directly between BS and MSs. We also present simulation results which show that considering direct link and using the proposed scheme in such case significantly improves system outage performance compared to existing schemes in the literature which do not consider direct link. In the later part of Chapter 2, we study a cooperative communication scenario where  17  multiple amplify and forward (AF) relays cooperate to transmit data from a source to destination. We discuss an optimal power allocation method to assign transmit powers to the source and relays in order to maximize achievable data rate of the system. We propose less-complex suboptimal power allocation methods using various relay selection strategies. We also provide simulation results to demonstrate performance of the optimal power allocation and suboptimal relay selection and power allocation schemes. We show that these suboptimal schemes perform close to optimal scheme and are more reasonable for practical implementation. In Chapter 3, we study a multicarrier CR network employing MIMO antennas. We propose power allocation scheme for allocating the available transmit power within the power budget limit to different transmitting antennas within different subcarriers maximizing the total CR system capacity while maintaining the interference to PU within a prescribed limit. We formulate this as a convex optimization problem. We also compare the performance of proposed power allocation scheme with other existing schemes in the literature. We present simulation results which show that the capacity of MIMO CR using proposed scheme increases significantly with increase in interference temperature limit and the number of transmit antennas. However, we also confirm that when we include interference constraint in the conventional power allocation schemes, the capacity does not increase proportionally with increase in number of transmit antennas because the instantaneous channel condition between cognitive user transmitter and primary user receiver is not exploited by the conventional schemes. Chapter 4 focuses on resource allocation for green communication. First, various approaches to achieve green communication in a cellular network are discussed. We discuss some performance parameters for green communication that can provide a quantitative  18  measure of the green performance. Our approach is on an algorithmic and protocol design level instead of energy-efficient circuitry design for communication devices. We analyze benefits, implementation issues, and research challenges in enabling green communication in cellular networks with a focus on employing relay-based cooperative approach. We then propose a green power allocation (GPA) scheme which combats some of the identified challenges. The proposed scheme allocates power to both the source and relay using a strategy that minimizes required transmit power per unit throughput while guaranteeing a QoS requirement in terms of predefined data rate. We also present some simulation results which show that proposed GPA scheme outperforms classical power allocation schemes by reducing total transmit power required to guarantee the QoS without increasing system outage penalty. Since the improvement of green performance comes at the cost of degraded system throughput in general, a trade-off between system throughput and green performance is also analyzed in this chapter using multi-objective optimization approach. Finally, in Chapter 5, we present the major conclusions derived from the research conducted for this thesis. We discuss practical implementation aspects of the novel algorithms and system design methodologies which have resulted from this research. We also present some directions for potential future research in the related area.  19  Chapter 2 Resource Allocation for Relay-based Cooperative Communication Network1 2.1 Introduction Data transmission with cooperation among devices has attracted attention of huge research community recently. Benefits of cooperative transmission have been investigated for various types of wireless networks, such as cellular mobile, cognitive radio, and sensor networks [56, 57, 58, 59, 60]. It has been shown that cooperative communication can boost the performance of cellular networks significantly, e.g., by increasing reliability, reducing transmission power, and improving system throughput, network coverage, and spa-  1 The results of the research work presented in this chapter has been published as: U. Phuyal, S. C. Jha, and V. K. Bhargava, “Joint zero-forcing based precoder design for QoS-aware power allocation in MIMO cooperative cellular network,” IEEE J. Sel. Areas Commun., vol. 30, no. 2, pp. 350–358, Feb. 2012 [53]; U. Phuyal, S. C. Jha, and V. K. Bhargava, “QoS guaranteed resource allocation in cooperative cellular network with MIMO-based relays,” in Proc. IEEE ICC’11, June 2011, pp. 1–6 [54]; and U. Phuyal, S. C. Jha, and V. K. Bhargava, “Optimal and suboptimal relay selection and power allocation in multi-relay cooperative network,” in Proc. AH-ICI’11, Nov. 2011, pp. 1–6 [55].  20  tial frequency reuse [56, 60, 61]. Due to these potential benefits, relay-based cooperation is already being considered in modern wireless cellular standards such as 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE), LTE-Advanced [17, 18, 19] and IEEE Wireless Metropolitan Area Network (WirelessMAN), commercially known as WiMAX [20]. Successful deployment and operation of a cooperative communication network (CCN), however, hinge on the design of relaying strategies, relay deployment, relay selection and efficient resource management among the source and relays. Cooperation among the nodes can be realized in various ways based on the relay deployment strategy. For example, the user nodes can cooperate to transfer each-others’ data whenever their own transceivers are free. Hence, user nodes themselves can act as mobile relay stations (RSs). On the other hand, wireless operators can also install fixed RSs at predefined locations so as to maximize the coverage and reliability. While installing such relays, their positions are usually selected to optimize the desired system performance metric such as total system capacity and service outage probability. Discussion of various relay placement strategies can be found in literature, e.g., [62]. Real implementation of relay-based system may exist as the hybrid of the above two methods. Therefore, the system architecture of relay-based CCN can be broadly classified into three types: (a) system with fixed RSs [63, 64], (b) system with mobile RSs [65, 66], and (c) hybrid system with both types of RSs. Depending on how a RS relays the data, several types of relaying protocols are possible. For example, a RS may simply amplify the received signal and forward it towards the destination. Other RS may employ more complex signal processing steps to decode the received signal, and retransmit it after re-encoding and re-modulating. Yet another RS may lie between the above two types, which demodulates the received signal, removes the  21  noise and retransmits after re-modulating but without decoding. The relaying protocols followed by the RSs in these examples are respectively called amplify and forward (AF), decode and forward (DF), and Regenerate and Forward. Since AF relays are transparent to source/destination modulation and coding schemes and have lower complexity, they seem to be more practical compared to the other types [67, 68]. A detailed performance modeling and analysis of AF cooperative diversity using a Markov-based model can be found in [69].  2.1.1 Outline In this chapter, first, we discuss resource allocation for CCN with multi-antenna relays in Section 2.2. Section 2.2.1 presents the system model and describes the proposed relaybased transmission framework in a multiple-input multiple-output (MIMO) cellular system. A joint zero-forcing (ZF) based precoder design is proposed and analyzed in Section 2.2.2. Low-complexity suboptimal power allocation scheme for MIMO relay–based CCN is presented in Section 2.2.3. Selected simulation results are presented in Section 2.2.5 to demonstrate the performance of the proposed scheme. In later part of the chapter, in Section 2.3, we investigate the resource allocation mechanisms for network with multiple single-antenna relays. System model and considered cooperative transmission scheme for multiple relay system are presented in Section 2.3.1. In Section 2.3.2, optimal power allocation method for such system is described. Low complexity suboptimal relay selection and power allocation schemes are then discussed in Section 2.3.3. Selected simulation results and discussion are presented in Section 2.3.4. Finally, Section 2.4 presents some conclusions drawn from the research presented in this chapter.  22  2.1.2 Notations Throughout this chapter, we denote matrices and vectors by uppercase and lowercase boldface letters, respectively. Corresponding lowercase normal-face letter represents its element. AT and AH , respectively, represent transpose and conjugate transpose of a general matrix A. Trace of a square matrix S is represented by tr(S). vector, whereas ≻ and  · represents l2 norm of a  represent element-wise inequalities. 1 and 0 respectively repre-  sent vectors with all elements equal to 1 and 0. The subscripted variable ξ U represents the vector formed by taking subset of elements in vector ξ , i.e., ξ U = [ξi ∀i ∈ U]T . For a set U, |U| represents its cardinality.  2.2 Cooperative Communication Network With MIMO Relay As discussed earlier, one of the methods of realizing cooperation among the nodes in a cellular network is by installing fixed RSs at predefined locations. Fixed RSs are more suitable for cellular wireless systems due to several advantages. The main advantage of fixed relay-based approach is that it requires minimum to no hardware modification in the existing cellular architecture. Hence it is more practical as only software upgrade at base station (BS) and mobile stations (MSs) may be sufficient. In addition, deployment of fixed relays is cheaper and includes less planning than installing new BSs. MSs are generally equipped with single antenna due to their size and cost constraints. In contrary, because the fixed relays are deployed by the wireless operator, they can be equipped with multiple antennas. MIMO technique has been implemented in recent wireless communication standards such as 3GPP LTE/LTE-Advanced [21], IEEE 802.11n [22] and 802.16e [23] because of its potential to improve spectral efficiency and transmission  23  reliability [70]. Moreover, as discussed in Section 2.1, AF relaying seems to be more practical compared to other types of relaying methods [67, 68]. Therefore, in this section, we consider pre-installed fixed AF relays (i.e., architecture (a) described in Section 2.1) with MIMO antennas and MSs with single antenna to implement cooperative transmission in a more practical way. There has been extensive work on resource allocation for cellular MIMO systems [e.g., 71, 72, 73]. Most of them mainly focus on maximizing network capacity. These schemes do not favor the cell-edge MSs with poor channel conditions and hence fail to provide a specified minimum data rate to them. A smart resource allocation scheme is necessary to utilize the benefits of cooperative technique in order to guarantee the quality of service (QoS) requirements in such networks. Furthermore, MIMO technique also offers research challenges due to inherent multi-user interference (MUI) in such system. Usually, an efficiently designed precoder can significantly cancel MUI in a MIMO system [74, 75, 76]. When the channel conditions are known to MIMO transmitter, it is possible to design the precoders such that MUI at the receiver is completely nullified. This process is known as ZF or null-steering. Therefore, precoder design for power allocation can be an attractive way to optimize the performance of cooperative MIMO networks. Research efforts have been made in literature to propose source and relay precoder design methods for power allocation in CCNs. For example, recent work [77] proposed optimal ZF-based design of precoders and decoders for multiuser CCN with single antenna at MSs and RSs. On the other hand, [43, 45] assumed MIMO antennas at BS/RS and single antenna at MSs. In [43], upper and lower bounds for achievable sum-rate capacity were derived assuming ZF dirty paper coding [78] at BS and transmit power constraints at BS/RS. The authors maximized such capacity without any QoS provisioning to MSs. In contrary,  24  authors in [45] did not consider any constraint on transmit power and minimized weighted sum power consumptions at BS and RS satisfying minimum signal to interference-plusnoise ratio (SINR) at MSs. However, none of these proposals with MIMO RS considered direct link between BS and MSs. Moreover, these schemes are particularly efficient if RS is about midway between BS and MSs. In practical network where number of RSs is limited and MSs are distributed randomly throughout the cell, it may be impractical to assume such scenario, and cooperation among direct and relay transmission may significantly increase the system performance. There has been a few recent work considering the effect of direct link in MIMO relay– based system [79, 80, 81]. Authors in [79] and [80] proposed minimum mean square error (MMSE)–based joint precoder design for such system. Singular value decomposition (SVD)–based iterative joint precoder design for capacity maximization was proposed by [81]. These work considered single MS with multiple antennas and did not consider QoS guarantee for the MS. In this section, we propose joint ZF based design for BS and RS precoders in a multiuser MIMO relay–based CCN. The major contributions of this section can be summarized as follows: i. We consider direct link along with relay link and focus on analyzing the impact of direct link on relay based cooperative transmission. We show that including direct link significantly improves the system performance when relays are not located along the straight path between BS and MSs. This is more practical when each RS needs to serve multiple MSs simultaneously. ii. We particularly focus on enhancing fairness to cell-edge users by decreasing their outage probability. Cell-edge users are generally the ones with low signal to noise ratio 25  (SNR) since they suffer from higher signal attenuation. Note, however, that the users need not be (or identified to be) at cell-edge for harnessing the performance gain offered by the proposed scheme. iii. We propose a method to design precoders at BS and RS jointly such that MUIs due to both the direct and relay links are cancelled out at MS receivers. To the best of our knowledge, proposed scheme is the first approach to jointly design BS and RS precoders by zero-forcing both links for MIMO relay–based CCN. iv. We propose low-complexity suboptimal algorithm for BS/RS power allocation to multiple simultaneous data flows using proposed precoder design. We define a design parameter for performance tuneup of the algorithm and show that, with careful selection of the parameter, close to optimal performance can be achieved.  2.2.1 System Model We study downlink (DL) transmission from a multi-antenna BS to multiple single-antenna MSs with cooperative transmission via fixed multi-antenna RSs. The MSs get served directly from BS as well as via RSs. As described above and illustrated in Fig. 2.1, multiple fixed RSs may be installed by operator at predetermined locations. There may be multiple RSs which are capable of serving a particular BS–MS communication. Although selecting multiple relays may provide better communication opportunities, price may need to be paid in terms of system complexity including requirement of complex operations such as RSs synchronization, coordination, and joint resource allocation, as well as capability of MS to simultaneously detect and combine signals from multiple transmitters. Moreover, since there are limited number of fixed RSs deployed by the operator in practice, it is reasonable to say that generally each MS finds one of the RSs much better than others. Therefore, 26  for less-complex practical system implementation, we assume only one RS is selected to assist any MS at a particular time [59]. There may be several ways to choose the ‘best’ RS for an MS. BS selects such RS using the implemented relay selection strategy, which is essentially a routing issue [82]. Some relay selection strategies will be discussed later in Sections 2.3.2 and 2.3.3. Detailed description of various relay selection strategies in relay-based CCNs can be found in [82] and references therein. For the system described above, BS–RS channel is a point-to-point MIMO link whereas channel between BS/RS and multiple MSs is a Multiple-input Single-output Broadcast Channel (MISO-BC). This is illustrated in Fig. 2.1. The BS and RS are equipped with MB and MR antennas, respectively. The precoding operation at the BS for kth user’s data stream is represented by wk,B ∈ CMB ×1 . We stack such vectors column-wise for all K MSs and call it WB which is a MB × K matrix with complex elements. The transmitted signal vector at the BS is represented by  xB = W B s =  ∑ wk,B sk ,  (2.1)  k∈K  where K = {1, . . . , K} represents the set of indices of MSs (or data streams) being served by RS under consideration, and s = [s1 , . . . , sK ]T , where sk denotes the modulated symbol for kth MS drawn from a unit variance constellation. Note that without loss of generality, we ignore the time index. The transmit power of BS, therefore, is given by  PB = E [ xB 2 ] = tr(WB WH B ), where E [·] represents expectation operation. 27  (2.2)  1  hB,1 hR,1 hB,2 hR,2  2  HBR RS  hB,3  hR,3  BS  3  Figure 2.1: System model for CCN with MIMO relays illustrating broadcast channel with multi-antenna RSs and direct link between BS and MSs.  28  The received signal vector at RS is given as  yBR = HBR xB + nR ,  (2.3)  where HBR ∈ CMR ×MB represents the MIMO channel gain between BS and RS where each element is modeled as an independent and identically distributed (i.i.d.) Rayleigh variable, and nR is the noise vector at the RS receiver where each term is assumed to be i.i.d. zeromean complex Gaussian random variable with unit variance. The channel between BS and kth MS can be represented by a vector hBM,k ∈ C1×MB . The received signal at kth MS due to BS transmission is therefore given by  yBM,k = hBM,k xB + n1,k ,  ∀k ∈ K,  (2.4)  where n1,k represents noise at kth MS receiver assumed to be i.i.d. zero-mean complex Gaussian random variable with unit variance. We stack vectors hBM,k , ∀k ∈ K row-wise to form HBM ∈ CK×MB . Therefore, received signal vector at MSs due to direct transmission from BS can be written as yBM = HBM WB s + n1 ,  (2.5)  where n1 is noise vector with elements n1,k , ∀k ∈ K. We consider AF processing at the RS. The signal transmitted by RS (either in next time slot or in orthogonal frequency band depending on implementation) is given by  xR = WR yBR ,  (2.6)  where WR ∈ CMR ×MR is the RS precoding matrix. Therefore, RS transmit power is given 29  by H H PR = E [ xR 2 ] = tr(WR (HBR WB WH B HBR + I)WR ).  (2.7)  The channel between RS and kth MS can be represented by a vector hRM,k ∈ C1×MR . The received signal at kth MS due to RS transmission is therefore given by  yRM,k = hRM,k xR + n2,k ,  ∀k ∈ K.  (2.8)  where n2,k is noise at kth MS receiver assumed to have same distribution as n1,k . Therefore, received signal vector at MSs via RS transmission can be represented as  yRM = HRM WR HBR WB s + HRM WR nR + n2 ,  (2.9)  where HRM = [hTRM,1 , . . ., hTRM,K ]T , and n2 is noise vector with elements n2,k , ∀k ∈ K. Joint ZF based resource allocation scheme for such system will be proposed in the next section.  2.2.2 Joint Zero-Forcing Based Resource Allocation We are interested in jointly designing precoder matrices WB and WR such that there is no MUI at each MS due to transmission of data streams intended to other MSs. For such design, from (2.5) and (2.9), the result of matrix products HBM WB and HRM WR HBR WB need to have non-zero elements only at their diagonal entries. This is known as nullsteering or ZF criterion. In the following, we assume that BS and RSs have same number of antennas, say M, i.e., MB = MR = M. This is a reasonable assumption when RSs are pre-installed at fixed locations by the operator. Generally, each RS is responsible to serve a group of MSs based on implemented relay selection strategy. From among the pool of users being served by a RS in the cell, BS selects a set of users, say K, for simultaneous 30  data transmission via the RS at a particular time such that |K| = M. While better strategy may be implemented in selecting K, for simplicity we choose K randomly among all the sets satisfying feasibility problem (2.21) defined later assuming at least one such set exists. Without loss of generality, suppose K = {1, . . ., K} after the user selection. Assuming the knowledge of channel matrices HBM , HBR , and HRM to be available at BS and RSs and the matrices to be nonsingular, the joint ZF can be achieved by choosing WB = H−1 BM Λ  (2.10)  WR = H−1 RM QH,  (2.11)  and  H where Λ , Q ∈ RK×K are diagonal matrices, and H = HBM H−1 BR . Let Λ Λ = diag{λ1 , . . . , λK }  and QQH = diag{q1 , . . . , qK }, where diag{c1 , . . ., cK } represents a K × K diagonal matrix with diagonal elements c1 , . . . , cK . Note that λk , qk ≥ 0, ∀k ∈ K. Using these precoders, total SNR at kth MS receiver (k ∈ K) performing maximal ratio combining (MRC) of signals received directly from BS and via RS is given by (see Appendix B)  γk = λ k +  λ k qk , qk hTk 2 + 1  (2.12)  where hk represents kth row of H. Let us define a vector of received SNRs, γ = [γ1 , . . . , γK ]T which will be used later. Our objective is to minimize the sum power consumption at BS and RS while guaranteeing the QoS for each MS and considering power budget constraints of both the BS and RS, say PB,max and PR,max , respectively. Therefore, the optimization problem P can be  31  formulated as  minimize Pt = PB + PR  (2.13)  subject to γ  (2.14)  {WB ,WR }  γ min  0 ≤ PB ≤ PB,max  (2.15)  0 ≤ PR ≤ PR,max ,  (2.16)  where Pt represents the total transmit power and γ min = [γ1,min , . . ., γK,min ]T where γk,min is the required minimum SNR to guarantee a predefined QoS for user k. Now, from (2.2) and (2.10), we can write  PB =  ∑ λk  gBM,k 2 ,  (2.17)  k∈K  where gBM,k is kth column of H−1 BM . From (2.7), (2.10), and (2.11), we have H −1 H H −1 H ΛΛ H QH (H−1 PR = tr(H−1 RM QΛ RM ) ) + tr(HRM Q H H Q (HRM ) )  =  ∑ λ k qk  k∈K  gRM,k  2  +  ∑  √ ai j qi q j ,  (2.18)  i, j∈K  where gRM,k is kth column of H−1 RM , and ai j ∀i, j ∈ K are nonnegative real coefficients. Therefore, optimization variables in problem P are λ = [λ1 , . . . , λK ]T and q = [q1, . . . , qK ]T .  In Appendix C, we show that γk given by (2.12) is quasi-concave function of (λk , qk ). Thus, constraint (2.14) for each k defines a convex set since it is a superlevel set of a quasiconcave function [83]. As seen in (2.17), PB is linear function of the variable λ . However, PR given by (2.18) is neither convex nor concave function of the optimization variables  32  since the Hessian of this function is neither guaranteed to be positive- nor to be negativesemidefinite [83]. Consequently, objective function (2.13) is neither convex nor concave for these variables. Optimal solution for such problem is difficult to calculate efficiently. Therefore we propose suboptimal solutions below. Let us first define a reduced optimization problem without constraint (2.16) as P1: minimize Pt {λ , q}  (2.19)  subject to (2.14) and (2.15). Based on the discussion above, it is easy to see that the feasible region of P1 is convex. Constraint (2.16) will be dealt with later in Section 2.2.4. Feasibility of Problem P1 First we discuss about feasibility of problem P1 and then propose an algorithm to find its suboptimal solution. We establish following propositions which will be useful in designing the algorithm. Proposition 1. If the condition  ∑ γk,min  gBM,k  k∈K  2  ≤ PB,max  (2.20)  holds, then problem P1 is always feasible. Proof. This condition means that QoS for all MSs can be guaranteed by the BS direct path transmission by assigning λ = γ min and q = 0. We propose this as a suboptimal solution for this case because it saves second time slot (or frequency band) by avoiding relay transmission, thereby contributing to increased throughput while guaranteeing the 33  QoS. Proposition 2. If condition (2.20) does not hold, i.e.,  ∑ γk,min  gBM,k  2  > PB,max , then  k∈K  problem P1 is feasible when linear problem find λ  (2.21)  subject to (2.15) hTk  λk > γk,min  hTk  2  2+1  ,  ∀k ∈ K  (2.22)  .  (2.23)  is feasible. Proof. We can rewrite kth constraint in (2.14) as  qk ≥  λk (  γk,min − λk T hk 2 + 1) − γk,min  hTk  2  For qk ≥ 0, we must have λk ≤ γk,min , resulting in non-negative numerator on the right hand side. Therefore, the denominator must also be positive which is equivalent to constraint (2.22). As long as we have a λ satisfying (2.22) and (2.15), we can choose appropriate q to satisfy (2.14). It is obvious from (2.22) that λk must be positive as γk,min is always positive. This is because the power consumed by BS to transmit data stream for user k is determined by  λk . Constraint (2.22) also defines the minimum value of λk required for each flow, below which the required SNR cannot be obtained even by letting qk → ∞ because of the inherent noise amplification in AF relaying.  34  2.2.3 Suboptimal Power Allocation Scheme As described in the proof of Proposition 1, when (2.20) is true, we can take λ = γ min and q = 0 as a suboptimal solution of P1. In the following, we propose algorithms to find suboptimal solution of P1 when (2.20) is not true. From (2.17) and (2.18), we see that PB depends linearly on λ whereas PR depends on both λ and q. Therefore, minimizing the objective function of P1 requires minimizing both  λ and q. We can achieve this by minimizing weighted sum of λ and q with careful choices of weights. With this in mind, let us define an optimization problem for a subset of users U ⊆ K and arbitrary BS power constraint P˜B,max ≤ PB,max as P2(U, P˜B,max ): minimize {λ U , qU }  ∑  f (λ U , qU ) =  αi λi2 + q2i  (2.24)  i∈U  subject to γi ≥ γi,min ,  ∑ λi  gBM,i  λU  0,  ∀i ∈ U  (2.25)  2  (2.26)  i∈U  qU  ≤ P˜B,max 0,  (2.27)  where αi is nonnegative weight factor associated with λi which we will discuss shortly, and the choice of objective function f (·) is motivated by the fact that when αi = 1 ∀i, optimal solution of above problem represents the feasible point which is nearest to the origin of 2|U|-dimensional space, and the optimal value represents its distance from the origin. Let  α denote the vector with elements αi ∀i ∈ K. Note that the weights of qi ∀i are normalized to unit; in this case, αi represents the relative weight of λi with respect to qi .  35  From (2.22) and (2.26), we see that P2 is feasible only when  ∑ γi,min  i∈U  hTi  2  hTi 2 + 1  gBM,i  2  < P˜B,max.  (2.28)  Note that for U = K and P˜B,max = PB,max , P2 is always feasible based on the user selection criterion described in Section 2.2.2. Also note that P2 is a convex optimization problem and can be solved efficiently using standard algorithms [83]. For example, Lagrangian-based solution for this problem when α = 0 is shown in Appendix D. Now, we propose Algorithm 2.1 to find suboptimal solution of P1 with a greedy approach in assigning BS power to multiple data streams. It is clear from the algorithm that proposed suboptimal solution is obtained by assigning part of BS power to such a user that requires least power to guarantee its QoS via direct (BS–MS) link. Then we check whether this step decreases the overall power consumption. If the overall power consumption is not decreased, then this step is discarded and the algorithm is stopped; otherwise this step is repeated for the user needing next least BS power and so on. For each step, we solve P2 to find the power allocation between BS and RS for data streams in set U. Note that if (2.20) does not hold for set of users K, the remaining power P˜B,max will not be enough for users U to satisfy (2.20). In the next section, via exhaustive search based simulations, we show that the solution obtained by this suboptimal algorithm is very close to optimal solution. Choice of Weight Vector α The positive weight factors αi in (2.24) can be chosen in various ways. One of the simple choices is α = 1, which results in equal weights to all elements of λ and q. Another choice is to take α = 0, which means that we are interested in reducing the RS power as BS power is already limited by (2.26). 36  Algorithm 2.1 Joint ZF based power allocation algorithm 1: Given γ min , PB,max , HBM , HBR , HRM . 2:  if  ∑ γk,min  gBM,k  2  k∈K  3: 4: 5: 6: 7: 8: 9:  ≤ PB,max then  λ˜ = γ min , q˜ = 0 else Set U ← K, P˜B,max ← PB,max Solve P2(U, P˜B,max) to obtain λ˜ u , q˜u , ∀u ∈ U. Calculate required total power P˜t using (2.17) and (2.18). while |U| ≥ 2 do l ← argmin gBM,i 2 i∈U  10: 11:  P˜B,max ← P˜B,max − γmin,l gBM,l if P˜B,max > 0 then  2  14:  U ← U\{l} if P2(U, P˜B,max) infeasible then return λ˜ , q˜  15:  end if  12: 13:  16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29:  Solve P2(U, P˜B,max) to obtain λˆ u , qˆu ∀u ∈ U. Calculate required power Pˆt using (2.17) and (2.18). if Pˆt > P˜t then return λ˜ , q˜ else λ˜ l ← γmin,l ,  λ˜ u ← λˆ u , end if else return λ˜ , q˜ end if end while end if return λ˜ , q˜  q˜l ← 0, P˜t ← Pˆt q˜u ← qˆu , ∀u ∈ U  37  It is obvious that the performance can be increased if the value of αi adapts to the change in channel conditions. From (2.17) we see that PB may be decreased by decreasing  λi gBM,i 2 , and from (2.18), PR may be decreased by decreasing qi gRM,i 2 . Therefore, we define  α¯ i =  gBM,i gRM,i  2 2  ,  ∀i ∈ K.  (2.29)  It is clear that previous proposed values of α (i.e., 0 and 1) result in simpler system implementation compared to α = α¯ . To illustrate the effect of choice of α with the help of comparative results, let us also define  αˇ i = 1/α¯ i ,  ∀i ∈ K.  (2.30)  Note that the complexities involved in calculating both these values of α (i.e., α¯ and αˇ ) are equal.  2.2.4 Constraint on RS Transmit Power Budget As described above, the resulting solution of P1 would first assign BS transmit power satisfying its budget constraint and then assign RS transmit power so as to satisfy QoS constraint of each MS. When we have additional constraint (2.16) in P1, all of the above discussion does not change as long as the solution derived above satisfies (2.16). Otherwise, we can say that the QoS constraint cannot be satisfied for at least one MS. Such situation is considered as system outage event in the succeeding analysis and discussion.  38  2.2.5 Results and Discussion We analyze the performance of proposed scheme with support of simulation results. We find the precoding matrices using proposed Algorithm 2.1. We use interior point method to solve the convex optimization problem P2. Only for the purpose of analyzing optimality of proposed algorithm, we solve P1 using exhaustive search method. We assume that RSs and MSs can estimate the channels with the help of pilot signals transmitted by BS and RSs, or using blind channel estimation methods and send it to BS by using feedback channels, directly or via RSs. Simulation Setup The elements of channel matrices HBM , HBR , and HRM are modeled as zero mean i.i.d. Rayleigh variables assumed to be constant over two time slots. Without loss of generality, we normalize the average distance between BS and MSs to a unit and average power gain of elements of HBM to 0 dB. We then incorporate the effect of relative path losses in HBR and HRM by changing their variances according to the relative distance of RS from BS and MSs taking path loss exponent of four. We simulate scenarios where number of antennas at BS/RS (M) varies from 2 to 5. Minimum SNR threshold of 0 dB is considered for QoS guarantee of each MS. As there may be large number of users and limited number of RSs in each cell, the relay position may not be directly between the BS and MSs. We consider a scenario where the operator installs three fixed RSs in a cell symmetrically as illustrated in Fig. 2.2. Each RS needs to serve one third of the cell. Since we are interested in guaranteeing QoS of users at the cell-edge, we define two cases of MSs’ location, namely, worst case, and average case cell-edge locations, as depicted in Fig. 2.2. We assume that the group of selected users are  39  Worst case cell-edge MSs  Average case cell-edge MSs  RS1  RS2 BS  RS3  Figure 2.2: Illustration of position of relays and cell-edge MSs in simulations. RS1 is responsible for transmission within the shaded region.  40  distributed randomly around the specified location for respective simulations. Performance Analysis To demonstrate the performance of proposed scheme and effect of direct link in cooperative transmission, we compare it with a precoding and power allocation method existing in the literature [43, 45] which does not consider direct link between BS and MSs. The existing method uses SVD-based approach and has been shown to outperform uniform power allocation (UPA) in BS and water-filling based loading in RS [43]. We simulate the proposed scheme for following four different values of α as discussed in Section 2.2.3: i)  α = 0, ii) α = 1, iii) α = α¯ given by (2.29), and iv) α = αˇ given by (2.30). For all of the proposed and existing schemes under consideration, we limit BS and RS transmit power within their budget constraints PB,max and PR,max, respectively. We record an outage event when available RS transmit power in not enough to guarantee QoS requirement (i.e., RS transmit power required to fulfil QoS constraints is more than PR,max ). For simplicity, we take PR,max = PB,max = Pmax in all simulation results presented in this section. Simulation Results First, we analyze the effect of relay position on probability of system outage by using proposed power allocation scheme with different values of α . For this purpose, we move the RS towards cell-boundary starting from near the BS and plot the corresponding outage probabilities in Fig. 2.3. It is obvious that the performance of proposed scheme depends on the choice of α for both the average as well as worst case users; however, all values of  α exhibit similar trend. The sensitivity of outage probability with respect to α is found to be higher for worst case users compared to average case users. As observed in Fig. 2.3,  α = α¯ consistently outperforms other choices of α for both types of users regardless of the 41  30  Worst Case  Outage Probability (%)  25  α=α ¯  20  α=0 α=1 α=α ˇ  15  Pmax = 3.0 K =3  Average Case 10  5 0.3  0.4  0.5  0.6  0.7  Relative Distance of RS from BS Figure 2.3: Probability of system outage by using proposed power allocation scheme versus relative distance of RS from BS for various α .  42  position of relay. It is also clear that α = αˇ does not seem to be as good as other studied values of α . This illustrates the effect of choice of α on the performance of proposed scheme. It should be noted that there is a small penalty in terms of outage probability to pay for choosing simpler values of α for proposed scheme. For example, by selecting  α = 0, the problem P2 can be made much easier to solve offering less computational requirements. However, this results in approximately 0.6% increase in outage probability (from 22.6% to 23.2%) for worst case users when RS is about midway between BS and MSs, PB,max = 3, and K = 3. The increase in outage probability for average users is 0.4% for the same scenario. Next, to analyze the performance enhancement provided by proposed Algorithm 2.1, we compare system outage resulting with and without using the algorithm. In other words, we directly solve P2 in the latter case. Since α = α¯ seems to be better choice among the chosen values of α , we use this value while plotting Fig. 2.4. It is observed that significant improvement in terms of outage probability is offered by Algorithm 2.1. Based on these results, in the rest of the simulations, we use Algorithm 2.1 with α = α¯ for the proposed scheme. In Fig. 2.5, we plot the performance of our scheme alongside the outage performance of existing scheme for both types of users. It is clear from the plot that for existing scheme with no direct link, worst case users perform better when RS is nearer to BS, and average users want it farther from BS (i.e., nearer to themselves). In contrast, proposed scheme is found to be more robust against change in RS position. Therefore, for fair comparison in rest of the simulations, RSs are positioned midway between BS and cell boundary. It is also seen from Figs. 2.3 and 2.5 that proposed scheme outperforms the existing scheme with any of the four choices of α discussed above.  43  35 Without using Algorithm 2.1 Using Algorithm 2.1  Outage Probability (%)  30 Worst Case 25  20 Pmax = 3.0 K =3 α=α ¯  15 Average Case 10  5 0.1  0.2  0.3  0.4  0.5  0.6  0.7  Relative Distance of RS from BS Figure 2.4: Comparison of probability of system outage with and without using Algorithm 2.1 in the proposed power allocation scheme.  44  100 No direct link, average case  Outage Probability (%)  90  Proposed, average case, α = α ¯  80  No direct link, worst case  70  Proposed, worst case, α = α ¯  60 50  Pmax = 3.0 K =3  40 30 20 10 0 0.1  0.2  0.3  0.4  0.5  0.6  0.7  Relative Distance of RS from BS Figure 2.5: Comparison of outage probability by using proposed and existing schemes for different relative positions of relay.  45  Now we present the variation of outage probability of proposed scheme with different power budget constraints for different choices of α in Fig. 2.6. Similar results as discussed above are observed in terms of performance variation with various values of α for different power budget constraints, α¯ being the best choice among the considered ones. In Fig. 2.7, we compare outage probability of proposed scheme with α = α¯ with that of existing scheme for average as well as worst case users. It is observed that the proposed scheme outperforms the existing one. The performance gain is higher for worst case users. This is because the contribution of direct link is also significant for such users. As expected, for all cases the outage probability decreases if transmit power limit is increased. In Figs. 2.8 and 2.9, we study the effect of number of simultaneous worst case data streams per relay on the outage performance. From Fig. 2.8, it is clear that the proposed scheme performs better with α = α¯ in all cases. Fig. 2.9 compares effect of number of simultaneous worst case data streams per relay on the outage performance of proposed scheme with α = α¯ and existing scheme for various power budgets at BS/RS. Although obvious trends of increased outage due to increase in number of simultaneous data streams or decrease in available transmit power are observed, it is worthwhile to note that the proposed scheme continuously outperforms the existing scheme even for increased number of simultaneous data flows. From the above results, it is clear that proposed power allocation scheme performs better with α = α¯ in all cases. Moreover, it is also observed that the proposed scheme outperforms existing SVD-based scheme in terms of system outage probability in all cases with any choice of α discussed above. Finally, we study the performance of our suboptimal algorithm in terms of optimality of the result. In the scatter graph in Fig. 2.10, we plot total transmit power resulted from pro-  46  45 α=α ¯  Worst Case  40  α=0 α=1  35  Outage Probability (%)  α=α ˇ 30  K =3  25 20 Average Case 15 10 5 0  2  2.5  3  3.5  4  4.5  Power Budget Constraint (Pmax ) Figure 2.6: Probability of system outage by using proposed power allocation scheme versus power budget constraint.  47  100 No direct Link Proposed, α = α ¯  90 Worst Case  Outage Probability (%)  80 K =3  70 60 50 40 30 Average Case  20 10 0  2  2.5  3  3.5  4  4.5  Power Budget Constraint (Pmax ) Figure 2.7: Comparison of outage probability versus power budget constraint for proposed and existing power allocation schemes.  48  60 α=α ¯ α=0 50  α=1  Outage Probability (%)  α=α ˇ 40 Pmax = 4.0  Pmax = 3.0 30  20  10 Pmax = 5.0 0  2  3  4  5  Number of Simultaneous Data Streams Per Relay (K) Figure 2.8: Outage probability versus number of simultaneous worst case data streams per relay for proposed power allocation scheme.  49  100 Pmax = 3.0  90  Pmax = 4.0 80  Pmax = 5.0  Outage Probability (%)  70 60 No direct link 50 40 30 20 10 Proposed, α = α ¯ 0  2  3  4  5  Number of Simultaneous Data Streams Per Relay (K) Figure 2.9: Comparison of outage probability versus number of simultaneous worst case data streams per relay for various power budget constraints.  50  Total Transmit Power Using Proposed Algorithm  4 3.5 3 2.5  Reference line with unit slope  2 1.5 α=α ¯  1 0.5 0.5  1  1.5 2 2.5 3 Optimal Total Transmit Power  3.5  4  Figure 2.10: Total power consumption by using proposed algorithm versus optimal solution by exhaustive search. Dashed reference line has a unit slope.  51  posed algorithm with α = α¯ against the optimal solution found by using exhaustive search for several random realizations of the system. We observe from Fig. 2.10 that most of the data points on the graph are scattered nearby the unit-slope reference line. The coefficient of variation of the root mean squared error is found to be 0.14. From this observation, it can be concluded that the power allocation results obtained by using proposed algorithm is very close to the optimal solution.  2.3 Cooperative Communication Network With Multiple Single-antenna Relays In the previous section, we mainly focused on a fixed single relay scenario. In this section, we study resource allocation for CCN with multiple mobile relays. As discussed earlier, cooperative communication can be a key technique to harness the potential throughput and coverage gains in modern wireless networks. Since system with mobile relays does not need any modification in existing network architecture, it seems relatively attractive approach to enable cooperation in wireless network. In addition, Federal Communications Commission (FCC) has recently announced LTE to be the communication standard for the United States nationwide public safety network [25, 26]. Since the public safety devices are required to be operable even during wireless network failure, the requirement to be able to support MS-relaying for emergency responders during disaster rescue and recovery situations has been recently identified by 3GPP [24]. Therefore, efficient resource allocation schemes with MS relays is essential for such CCNs. Thus, our focus in this section is on mobile relay–based CCN (i.e., architecture (b) described in Section 2.1). Relay selection strategy and resource distribution among source and relays are crucial  52  to optimize the performance of mobile relay–based CCN [84]. Most of the work in the literature, including our work discussed in previous section, focuses on resource allocation between source and a single relay assuming only one relay assists in the cooperative transmission [85, 86, 87, 88]. Selection of multiple relays to assist in transmission may significantly boost the system performance. In this section, we explore the performance enhancement of CCN by selecting multiple AF relays and optimally distributing the available transmission power among them as compared to the single relay case.  2.3.1 System Model We study a simple relay-based CCN consisting of a source S, a destination D, and N relays R1 , . . . , RN , as shown in Fig. 1.1. All nodes in this system are equipped with single antenna. In the considered system model, there are N + 1 possible links between the source and the destination: N links via relays plus a direct link. We assume single-carrier based transmission between all nodes. Suppose hsd represents direct link between S and D (S–D), and hsk and hkd represent channel coefficient of S–Rk and Rk –D links, respectively. We assume that the cooperative transmission in this system takes place in two consecutive time-slots2. In the first time-slot, S broadcasts the information towards the relays and D; in second time-slot, the relays amplify the information received in first time-slot and forward to D. Moreover, we assume that each time-slot is small in duration compared to channel coherence time and therefore the channel gains are constant for the duration of a particular time-slot.  2 Note  that the following discussion is not limited to using two time-slots. It is also possible to use two orthogonal sets of transmission resources such as frequency bands within the same time-slot. In such case, the first and second time-slots correspond to first and second frequency bands, respectively, in the following discussion.  53  The signals received by Rk and D in first time-slot are given by  Ysk =  √  Ysd =  √  Pshsk Xs + nk  (2.31)  Pshsd Xs + nd ,  (2.32)  and  respectively, where Ps represents the transmit power of S, Xs represents the unit-energy information symbol transmitted by S, and nk and nd are zero-mean additive white Gaussian noises (AWGNs) at the respective receivers with variances σk2 and σd2 . In the second time-slot, Rk amplifies Ysk with power Pk and forwards it towards D. Therefore, the signal received by D in second time-slot from Rk is given by  Pk hkd Xk + nd ,  Ykd =  (2.33)  where Xk = Ysk /|Ysk | is the unit-energy symbol transmitted by Rk . From (2.31) and (2.33), Ykd =  √  Pk hkd  √  Ps hsk Xs + nk  Ps|hsk |2 + σk2  + nd .  (2.34)  Therefore, SNR at D due to transmission link via relay k (i.e., S–Rk –D) is given by  SNRk =  αk βk Ps Pk , αk Ps + βk Pk + 1  (2.35)  where αk = |hsk |2 /σk2 and βk = |hkd |2 /σd2 , both of which are non-negative constants. From  54  (2.32), SNR at D due to direct transmission from S (i.e., S–D) is given by  SNRsd =  |hsd |2 Ps . σd2  (2.36)  Assuming MRC of signals received in both time-slots, the total SNR at D is given by N  SNR = SNRsd + ∑ SNRk .  (2.37)  k=1  The corresponding achievable normalized data rate is, therefore,  R=  where the factor  1 2  N αk βk PsPk |hsd |2 Ps 1 + log 1 + ∑ 2 2 σd k=1 αk Ps + βk Pk + 1  ,  (2.38)  represents the fact that two time-slots are used per transmission cycle.  2.3.2 Optimal Power Allocation Under the transmit power constrained scenario, we assume that S transmits with a fixed power Ps in the first time-slot; the same amount of power is shared by relays in the second time-slot in such a way that maximum data rate is achieved. Therefore, the problem of allocating the available transmission power to maximize the data rate can be written as max  R  P1 ,...,PN N  subject to:  ∑ Pk ≤ Ps  (2.39)  k=1  Pk ≥ 0,  k = 1, . . . , N.  Note that log(·) is a monotonically increasing function for positive argument, and Ps ,  55  |hsd |2 , and σd2 are positive and independent of optimization variables in problem (2.39). So, we can safely assume that objective function R attains its maximum when the power constraint tightly holds (i.e., ∑N k=1 Pk = Ps ). Therefore, we can equivalently represent problem (2.39) as  αk βk Pk k=1 αk Ps + βk Pk + 1 N  min  P1 ,...,PN  f =−∑ N  subject to:  ∑ Pk = Ps  (2.40)  k=1  Pk ≥ 0,  k = 1, . . . , N.  As shown in Appendix E, this is a convex optimization problem. In the following, we obtain its analytical solution by using Karush-Kuhn-Tucker (KKT) conditions. Let Pk∗ ∀k be an optimal solution for the above problem. Introducing Lagrange multipliers  λk∗ , k = 1, . . ., N for the inequality constraints and a Lagrange multiplier ν ∗ for the equality constraint, the KKT conditions are  N  Pk∗ ≥ 0, k = 1, . . ., N  ∑ Pk∗ = Ps,  (2.41) (2.42)  k=1  ∂f ∂ Pk  Pk =Pk∗  λk∗ Pk∗ = 0, k = 1, . . ., N  (2.43)  λk∗ ≥ 0, k = 1, . . ., N  (2.44)  − λk∗ + ν ∗ = 0, k = 1, . . ., N.  (2.45)  After some simplification, (2.45) can be written as  λk∗ = ν ∗ −  αk βk (αk Ps + 1) , k = 1, . . . , N, (αk Ps + βk Pk∗ + 1)2  56  (2.46)  which can further be reduced, using (2.44), to  ν∗ ≥  αk βk (αk Ps + 1) , k = 1, . . . , N. (αk Ps + βk Pk∗ + 1)2  (2.47)  It is clear from (2.47) that ν ∗ is non-negative. First, let us consider the case when  ν∗ <  αk β k . αk Ps + 1  (2.48)  In this case, (2.47) does not hold for Pk∗ = 0. Since Pk∗ is non-negative from (2.41), we conclude that Pk∗ > 0 for case (2.48). Therefore, from (2.43), λk∗ = 0 ∀k. Using this and (2.41) on (2.46), we can write Pk∗ =  1 βk  αk βk (αk Ps + 1) − (αk Ps + 1) . ν∗  (2.49)  Now, consider the case  ν∗ ≥  αk β k . αk Ps + 1  (2.50)  Under this condition, if Pk∗ > 0 then from (2.46), λk∗ > 0 which is contradictory to (2.43). This means that Pk∗ must be 0 for this condition. Combining both the results, we obtain  Pk∗  =      1 βk  αk βk (αk Ps +1) ν∗  − (αk Ps + 1)    0  if ν ∗ <  αk βk (αk Ps +1) ,  (2.51)  otherwise,  which can be re-written as Pk∗ = max 0,  1 βk  αk βk (αk Ps + 1) − (αk Ps + 1) ν∗ 57  , k = 1, . . . , N.  (2.52)  We see that the calculated values of Pk∗ depend on ν ∗ . We choose ν ∗ such that (2.42) is satisfied. Note that only and all of those relays which have non-zero transmit power ∗ ∗ allocated to them are selected. It is clear that ∑N k=1 Pk is monotonically decreasing with ν  and hence is a quasiconvex function of ν ∗ . Therefore, bisection method can be applied to find values of transmission power of relays (Pk∗ ) iteratively, as described below. Optimal Relay Selection and Power Allocation Algorithm As ν ∗ is non-zero, we can safely assume the lower bound of ν ∗ to be νl = 0. We need to find the upper bound of ν ∗ ; we can assume its initial value to be νu = 1. For simplicity in representation, let us define f P (ψ ) =  N  ∑ Pk∗  k=1  ν ∗ =ψ  ,  (2.53)  where Pk∗ is given by (2.52). Based on the description above, Algorithm 2.2 outlines the steps to iteratively find values of Pk∗ . In Algorithm 2.2, step 2 finds the upper and lower bounds of ν ∗ and step 6 computes ν ∗ using bisection method up to a tolerance level specified by ε . Once ν ∗ is found, the optimal relay transmit power values Pk∗ , k = 1, . . ., N can be calculated using (2.52), and all the relays for which Pk∗ > 0 are selected.  2.3.3 Suboptimal Relay Selection and Power Allocation It is obvious that the value of transmit powers allocated for some of the relays by Algorithm 2.2 may be very low. In practice, it may be reasonable to avoid transmitting through such relays reducing the communication complexity at a cost of performance degradation. In this section, we discuss some methods of selecting only a subset of relays and allocating transmit powers only to them. The penalty in performance introduced by selecting only a  58  Algorithm 2.2 Optimal Relay Selection and Power Allocation for Multi-relay CCN. 1: Given νl = 0, νu = 1, tolerance ε > 0 while fP (νu ) > Ps do νl ← νu 3: νu ← 2 νu 4: 2:  end while 6: repeat 5:  7: 8: 9: 10: 11: 12: 13: 14: 15: 16:  νmid ← (νl + νu )/2 if fP (νmid ) > Ps then νl ← νmid else νu ← νmid end if until ( fP (νl ) − fP (νu )) ≤ ε ν ∗ ← νmid Calculate Pk∗ , k = 1, . . . , N using (2.52). Select all the relays for which Pk∗ > 0.  59  subset of relays will be discussed in Section 2.3.4. Relay Selection Strategies 1. Best Relay(s) Selection: A predefined number, say K, of relays can be selected from N relays (K ≤ N) such that the selected subset results in maximum system throughput. Denoting the set of all N relays by N = {1, . . ., N} and K arbitrary relays by K, we can write the best K-relays selection problem as arg max RK K  subject to:  ∑ Pk ≤ Ps  k∈K  Pk ≥ 0, K∈  (2.54)  k∈K  N , K  where  αk βk Ps Pk 1 |hsd |2 Ps RK = log 1 + +∑ , 2 2 σd k∈K αk Ps + βk Pk + 1 and  N K  solving  (2.55)  represents the set of all K-combinations of N. This problem can be solved by N K  subproblems similar to (2.40) for each element in K, and choosing such  element of K which maximizes RK . 2. S–R Channel–based Selection: In the absence of R–D channel information, relays may be selected by the source by sorting S–R channel gains |hsk |2 and selecting K best ones. 3. Threshold-based Selection: As discussed earlier, it may not be always reasonable to transmit data through all available relays because of added complexity and from global utilization point of view. If some relays are not used by a particular S–D pair, they may 60  be utilized by other S–D pairs to increase overall network utilization. Therefore, it may be a better idea to select relays such that utility per relay is improved. This may be achieved by performing optimal power allocation on a reduced subset of relays where the subset reduction is based on a threshold on transmit power. In other words, only those relays which are allocated transmit power Pk ≥ Pthr (where Pthr ≤ Ps ) are selected. There are at least two methods of achieving this: (i) select all those relays for which Pk ≥ Pthr (discard all those relays for which Pk ≤ Pthr ) in one step, and re-allocate the power from discarded relays to the selected relays, (ii) iteratively discard such relay that is allocated the least non-zero power if such power is less than threshold and allocate this power to remaining relays repeating until all the remaining relays satisfy the threshold. The threshold Pthr is a design parameter which can be chosen based on performance requirement. Note that among the two example methods of threshold-based selection described above, as long as Pthr ≤ Ps, method (ii) makes sure that at least one relay is selected. However, it may happen in method (i) that, when Pthr is high, no relay is selected. In such scenario, Pthr may need to be lowered, or the method can be designed to fallback on to other method. 4. Random Selection: The easiest way to select relays is to select K relays randomly following a uniform distribution. We use this method to compare performance of other schemes in the results section later. Special Case: Single Relay System As discussed in Section 2.2.1, to reduce the hardware complexity, a single relay may be selected out of the available relays. Such relay can be selected by using any of the abovementioned selection methods by setting K = 1. Now, we briefly analyze each selection 61  strategy described above for K = 1. Note that, in such case, the selected relay’s transmission power will also be Ps in order to maximize end-to-end throughput. 1. Best Relay Selection: The best relay kbest which maximizes the end-to-end throughput for single relay system can be found from  kbest = arg max  Rk , k ∈ N,  k  (2.56)  where Rk = RK |K={k}, Pk =Ps , i.e., Rk =  αk βk Ps2 1 |hsd |2 Ps log 1 + + . 2 (αk + βk )Ps + 1 σd2  (2.57)  Removing the constant terms from Rk , we can reduce (2.56) to  αk β k , k ∈ N. (αk + βk )Ps + 1  kbest = arg max k  (2.58)  For high transmit power case, (αk + βk )Ps >> 1. Then, we can ignore the last term in the denominator in (2.58) and write  kˆ best = arg max k  1 αk  1 , k ∈ N. + β1  (2.59)  k  In other words, such relay that maximizes the harmonic mean of S–R and R–D channel gains is chosen as best relay in high transmit power case. 2. S–R Channel–based Single Relay: When R–D channel knowledge is not available at S,  62  the relay kSR can be chosen as  kSR = arg max k  |hsk |2 , k ∈ N.  (2.60)  3. Threshold-based Selection: Since the selected single relay will be assigned all the available transmission power, the relay selected by any other selection method (including the random selection) will pass the threshold-based selection criterion. 4. Random Selection: In this method, one relay is chosen randomly among the available relays following a uniform distribution.  2.3.4 Results and Discussion We assume a scenario where S and D are fixed at a distance of 1000 m in an urban environment. N relays are randomly distributed within 1000 m of the source following a uniform distribution. A snapshot of the relay positions for N = 30 is shown in Fig. 2.11. Note, however, that this is just an example; the relay positions may change during different scenarios because of the random distribution. The channels hsk , hkd ∀k ∈ N and hsd suffer from Rayleigh fading. The distance-based path loss with path loss exponent three is incorporated by changing the variance of the channel fading coefficients. We assume carrier frequency of 2 GHz, channel bandwidth of 5 MHz, and receiver noise figure of 5 dB. We assume Ps = 5 W and Pthr = 1 W in all simulations in this section. In addition to the relay selection and power allocation methods described above in Sections 2.3.2 and 2.3.3, for comparison purposes, we also simulate UPA method where equal power Ps /N is allocated for transmission through all available relays. 63  1000 Relay Source Destination  y Co-ordinate (m)  500  0  −500  −1000 −1000  −500  0 x Co-ordinate (m)  500  1000  Figure 2.11: An example simulation scenario depicting position of source, destination and 30 relays.  64  In Fig. 2.12, we plot the variation of average normalized throughput for different number of relays uniformly distributed around the source. The result confirms that throughput obtained by the optimal power allocation using all available relays is indeed the highest among all considered schemes. The next highest performance is offered by the method which selects two best relays (i.e., best relays selection with K = 2) and allocates available power to only those two relays. The performance of threshold-based relay selection method is lower than that of two best relays but better than that of selecting a single best relay. Among the two thresholdbased methods, iterative method (i.e., method (ii)) has slightly higher average throughput compared to static (one-step) method (i.e., method (i)). Performance of these two methods is almost same for lower number of available relays (N). However, iterative thresholdbased method provides higher performance enhancement when higher number of relays are available. This is because many relays will be selected for transmission by optimal power allocation method when N is high, resulting in less power for each relay. On the other hand, one-step threshold-based method tends to reject many better relays in such case. Since performance enhancement due to iterative method is not significant compared to one-step method when low to moderate number of relays are available, the latter may be more reasonable than the former due to reduced complexity for practical implementation. Performance of single best relay selection method is lower than threshold-based selection methods. It is observed that performance is similar for the two methods of selecting the single best relay: i) finding kbest directly using (2.56), and ii) finding kˆ best by harmonic mean approximation using (2.59). The UPA method using all relays offers significantly less throughput than all of the methods discussed above (i.e., optimal selection, best relay(s) selection, and threshold-  65  Optimal Selection Best Relays Selection, K=2 S-R Based Selection, K=2 Threshold-based, Method (i) Threshold-based, Iterative Random Selection, K=2 Single Best Relay Selection Single Best Relay, Approximation Single Relay, S-R Based Selection Single Relay, Random Selection  Normalized Average Throughput (bit/s/Hz)  UPA Using All Relays  3.5  3  2.5  2  5  10  15  20  25  30  Total Number of Available Relays (N) Figure 2.12: Average normalized throughput versus number of available relays for different relay selection and power allocation methods. 66  based selection). In all the above schemes and UPA, the throughput increases with increase in total number of available relays. This is because the presence of more relays increases the probability of having better channel conditions via some of the relays. As expected, performance of random relay(s) selection does not depend on N. However, selecting two relays provides better performance than selecting one relay due to the additional cooperative and spatial diversity. It is interesting to note that S–R channel–based selection is also independent of N for moderate to high N. This is because the decision is made solely depending on S–R channels, which may be independent of the quality of R–D channels. For example, the relay with best S–R channel may be on the opposite direction of the destination having a very weak R–D channel. The availability of large number of relays alone cannot be fruitful in such case. However, S–R channel–based relay selection outperforms random relay selection. This is because the quality of first-hop (S–R) channel is always better (or at least similar) in S–R channel-based relay selection compared to random selection. Fig. 2.13 shows the cumulative distribution function (CDF) of number of relays used by optimal power allocation scheme for various N. It is observed, as expected, that number of selected relays increases with increase in N. For example, using optimal relay selection and power allocation scheme, at least four relays are selected for transmission almost half of the time when N is 15 (i.e., CDF value corresponding to three relays is approximately 0.5), and for more than 65% of the time when N is 30 (i.e., CDF value corresponding to three relays is less than 0.35). Now, comparing the performance curves in Fig. 2.12, we observe that the performance improvement of optimal relay selection and power allocation over two best relays selection for N = 15 is only about 1.3%. For a practical scenario, this improvement may not justify the added complexity in transmitting through four or more  67  1  Cumulative Distribution Function  0.9 0.8 0.7 0.6 0.5 0.4 0.3  Optimal power allocation method  0.2 0.1 0  N=5 N = 15 N = 30 1  2  3  4  5  6  7  8  9  10  11  Number of Relays Used Figure 2.13: CDF of number of relays used by optimal power allocation scheme for various total number of available relays.  68  relays instead of only two relays. Moreover, for N = 15, the performance improvement of optimal relay selection and power allocation over single best relay selection method is found to be about 5%. Therefore, selection among one-relay, two-relays or multiplerelays methods is governed by a tradeoff between performance requirement and system complexity. Fig. 2.14 shows the CDF of number of relays used by iterative threshold-based relay selection and power allocation scheme for various N. Comparison of plots in Figs. 2.13 and 2.14 reveals that iterative threshold-based method uses significantly less number of relays compared to optimal relay selection method. For example, for N = 30, iterative threshold-based scheme selects only up to two relays for more than 75% of the time while optimal method selects up to six relays for the same CDF value. Comparing the performance improvement offered by optimal selection method compared to iterative threshold based method in Fig. 2.12, it is clear that selection among these methods is also a matter of tradeoff between performance requirement and system complexity. Fig. 2.15 depicts the CDF of normalized throughput obtained by different schemes for different N. It is observed that CDFs for optimal, two best relays, and iterative thresholdbased relay selection schemes are almost same when N is small (e.g., N = 5). The performance gap between them increases with increase in N. It is also observed that the slopes of curves increase for higher value of N. This means that, with increase in N, the QoS perceived by the destination in terms of minimum throughput guarantee improves more than the average throughput (shown in Fig. 2.12). This is also illustrated in Table 2.1 where the improvement in average normalized throughput and minimum throughput guarantee with 95% confidence level due to increase in N from 5 to 30 are listed for different relay selection methods.  69  1  Cumulative Distribution Function  0.9 0.8 0.7 0.6 0.5 0.4 Threshold-based iterative method  0.3 0.2 0.1 0  N=5 N = 15 N = 30 1  2  3  4  5  Number of Relays Used Figure 2.14: CDF of number of relays used by threshold based iterative relay selection and power allocation scheme for various total number of available relays.  70  1  Cumulative Distribution Function  Optimal Selection 0.9  Two Best Relays Selection  0.8  Iterative Threshold-based  0.7 N=15 0.6 0.5  N=5  0.4 N=30 0.3 0.2 0.1 0 1.5  2  2.5  3  3.5  4  Normalized Throughput (bit/s/Hz) Figure 2.15: CDF of normalized throughput for different relay selection methods and various total number of available relays.  71  Table 2.1: Performance improvement for increase in number of available relays (N) from 5 to 30. Improvement in Average Minimum throughput throughput (95%)  Method Optimal selection and power allocation Two best relays selection Iterative threshold-based method  25.2% 22.4% 21.8%  52.3% 48.4% 47.9%  2.4 Conclusion In this chapter, we first investigated fixed multi-antenna relay based cooperative communication in a cellular system. A novel joint ZF based power allocation scheme was proposed which considers BS–MS direct link as well as transmission via RS to provide QoS guarantee to cell-edge MSs. We formulated power allocation problem and proposed a suboptimal scheme which offers close to optimal performance. Simulation results verified that proposed scheme outperforms an existing scheme which ignores BS–MS direct link by keeping system outage probability lower for cell-edge MSs. Performance gain of the proposed scheme is significantly higher in practical scenarios where RS is not located along the direct path between BS and MSs. Moreover, performance of the proposed scheme is found to be less sensitive to the position of RS. Therefore, we conclude that jointly optimizing direct and relay links while allocating available resources can significantly improve performance of relay-based CCN. Then we explored relay selection strategies and power allocation schemes to maximize the overall system throughput in a CCN with multiple single-antenna mobile relays. We discussed optimal relay selection and power allocation scheme followed by various low complexity suboptimal relay selection schemes. The optimal scheme maximizes the sys72  tem throughput by selecting higher number of relays. However, selecting more relays increases the computational and hardware complexity of destination node. Therefore, we also proposed and analyzed near-optimal schemes which select less number of relays. Simulation results confirmed that proposed suboptimal schemes can achieve near-optimal system throughput with lower system complexity.  73  Chapter 3 Resource Allocation for Cognitive Radio Network with MIMO Antennas1 3.1 Introduction As discussed in Chapter 1, studies by the spectrum policy task force of the Federal Communications Commission (FCC) has suggested that the assigned spectrum has been very inefficiently utilized by the licensed users [5]. Field measurements have indicated that while some frequency bands are heavily used and crowded, others are only partially occupied and many bands are largely unoccupied. Up to 85% of allocated spectrum on average is being unutilized at certain time and geographical locations, creating large spectrum holes. Cognitive radio (CR) technology has been identified as an intelligent way to increase spectral efficiency of future wireless communication systems by opportunistically utilizing  1 Parts of the results of the research work presented in this chapter has been published as: U. Phuyal, A. Punchihewa, V. K. Bhargava, and C. Despins, “Power loading for multicarrier cognitive radio with MIMO antennas,” in Proc. IEEE WCNC’09, Apr. 2009, pp. 1–5 [89].  74  the licensed band. CR nodes can access the licensed bands either using a portion of the spectrum that has not been used (spectrum holes) or using spread spectrum techniques such that the transmission of the CR node is regarded by PUs as noise [14, 90]. The former method is known as overlay spectrum sharing while the later is known as underlay spectrum sharing. As an example of overlay spectrum sharing, FCC has approved rules that would allow new broadband communications utilizing unused television (TV) bands [9]. In addition, IEEE 802.22 working group has been established to develop CR-based standards for devices to operate in spectrum allocated to the TV broadcast service [10]. One of the various challenges in the design of CR networks is that the interference introduced to a primary user (PU) by secondary users (SUs) should be below a certain threshold, generally referred to as interference temperature, at all times [91]. It is worthwhile here to mention that when the SUs are communicating using the spectrum holes, the interference introduced to a PU by SUs is mainly due to the spillage energy of SU transmission band on PU bands due to non-ideal filter realizations if SU and PU transmissions are not orthogonal to each other. Multiple-input multiple-output (MIMO) technique have drawn a considerable attention in last two decades due to its advantage of a linear increase in data rate [92] through spatial multiplexing compared to single antenna systems. It has been implemented in recent wireless communication standards such as 3GPP Long Term Evolution (LTE)/LTE-Advanced [21], IEEE 802.11n [22] and 802.16e [23]. The requirement of efficient power allocation algorithm arises when we introduce multiple antennas at SU transceivers. Furthermore, the advantages associated with multicarrier communication, e.g., ability to effectively convert frequency-selective wide-band channel to a set of parallel frequency-flat subchannels [93] by dividing it into many narrow-band subcarriers, have presented multicarrier technology  75  such as orthogonal frequency division multiplexing (OFDM) as a potential candidate for next generation wireless systems. The fact that efficiency of CR depends on its ability to use spectrum holes sparsely available throughout the spectrum further strengthens the applicability of multicarrier transmission technology in CR. In such case, the available spectrum holes at different positions along the spectrum can be made useful by dividing them into multiple subcarriers and allocating them among multiple users resulting in a simple and efficient multiple access scheme such as orthogonal frequency division multiple access (OFDMA). This also enables the transmission of multiple media with varying quality of service (QoS) requirements within the same radio link. Different modulation and/or coding schemes may be employed for different subcarriers (and thus different users) depending upon their instantaneous channel gain on the particular subcarrier. There has been several work in literature considering single-antenna CR network [e.g., 11, 27, 49]. In [11], authors consider a single-antenna multicarrier CR scenario. In [27], single-carrier uplink channel model is assumed. In [49], authors propose power allocation strategies to achieve the ergodic capacity and the outage capacity of single-carrier singleantenna CR. Power allocation algorithms for conventional multicarrier MIMO wireless systems exist in literature [e.g., 50, 51] but they focus on optimizing the power distribution with the constraint only on total transmit power. These algorithms do not consider the interference introduced to the PU as an optimization constraint. As described above and in Section 1.4.2, these power allocation schemes existing in the literature are not directly applicable to the MIMO CR scenario due to the additional CR constraints. Channel capacity of a class of MIMO CRs has been discussed in [52] and fundamental limits of operation of such network with a single PU and a single SU are derived. However, [52] assumes  76  that the SU has access to the PU’s messages and derives the capacity limits with constraint on combined transmission power of licensed and cognitive transmitters. In practical CR application, this may not be the case. Therefore, in this chapter, we are interested in optimum assignment of available transmit power of CR transmitter to available subcarriers, and different antennas within the same subcarrier such that it maximizes the total capacity of muticarrier MIMO-based CR system.  3.1.1 Outline The rest of this chapter is organized as follows. In Section 3.2, we describe the system model used in this chapter including the description of channel models. In Section 3.3, we formulate the optimal power allocation problem for channel capacity maximization of multicarrier MIMO CR network considering the interference and total power constraints. Performance analysis of proposed power allocation scheme and selected simulation results showing the comparison with existing schemes in the literature are given in Section 3.4. Finally, in Section 3.5, we derive some conclusions of this chapter.  3.1.2 Notations Throughout this chapter, we use boldface letters to denote a vector or matrix while the corresponding regular lowercase letter represents its element. For a square matrix A, det(A) denotes the determinant, (A)∗ denotes the conjugate transpose and tr(A) denotes the trace. IN denotes the N × N identity matrix. We use SU and CR user interchangeably throughout this chapter.  77  3.2 CR System Model We assume a CR scenario similar to one in [11, 12, 90, 94], as depicted in Fig. 1.3 (in Chapter 1). The PU and SU transceivers coexist in the same geographical location. In the spectral domain, SU and PU use the side-by-side bands. It is assumed that L PUs use the frequency bands Bl ∀l = 1, . . ., L, and remaining (unused) band (also known as spectrum holes) is divided into K equal subbands for use by SUs. In general, the interference introduced to PUs is dependent on the channel condition of each subcarrier between the SU transmitter and PU receiver but not on the number of SUs as long as the spectrum holes are not re-used among the SUs simultaneously. Thus, we assume multicarrier transmission system with K subcarriers and a single SU. Without loss of generality, we do not consider PU transmitters in our analysis as we are concerned about the power allocation at SU transmitter and interference from CR transmitter to the PU receiver only. Fig. 3.1 further clarifies this scenario in the spectral domain. We consider MIMO wireless channel with additive white Gaussian noise (AWGN). The SU transmitter has M transmit antennas whereas the SU receiver has N receive antennas as shown in Fig. 3.2. The SU MIMO channel for kth subcarrier (k = 1, . . ., K) is denoted by an N × M matrix H(k) where its element hn,m (k) denotes the channel gain of the path between mth transmit and nth receive antenna for kth subcarrier. The channel gain between the SU transmitter and lth PU receiver for kth subcarrier is denoted by an 1 × M vector gl (k) where its mth element denotes channel gain between SU’s mth transmit antenna and the lth PU’s receiver antenna. The received signal at SU receiver on kth subcarrier is given by  Ys (k) = H(k)X(k) + n(k), 78  (3.1)  SU subcarriers  . PU Band 1  PU PU Band 2 Band 3  PU Band L  .  1 2 ….  …..K f  B1  B2  B3  BL  Figure 3.1: Distribution of primary and CR users in spectral domain.  79  1  1 H(N×M)  SU Transmitter  2  2  . .  . .  M  N  SU Receiver  g(1× M)  PU Receiver Figure 3.2: CR system model. Antenna pattern and modulation/transmission schemes of PU may not be known to the SUs.  80  where X(k) is the transmit symbol vector of length M and n(k) is the AWGN vector at the receiver for kth subcarrier. The interference signal to the lth PU due to SU transmission in kth subcarrier is given by Y p (k) = gl (k)X(k).  (3.2)  Therefore, interference power at the lth PU due to SU transmission in kth subcarrier is Il (k) = E {Y p (k)Y∗p (k)} = gl (k)P(k)g∗l (k),  (3.3)  where E (·) represents the expectation operation and P(k) = E {X(k)X∗ (k)}. The transmit symbol vector X(k) is formed as  ˜ X(k) = S(k)X(k),  (3.4)  ˜ where S(k) is the transmit beamforming vector (which is an M × 1 vector) and X(k) is a modulated symbol. All modulated symbols in the transmission stream are assumed to be independent of each-other and are drawn from unit variance constellation. This implies that P(k) = S(k)S∗ (k) is an M × M matrix and its mth diagonal element represents the power in mth transmit antenna. This further implies that the transmit power of SU in subcarrier k is given by tr(P(k)). Then, the total SU transmit power in all subcarriers is given by K  Ptot =  ∑ tr(P(k)).  (3.5)  k=1  From (3.3), the total interference power at lth PU due to SU transmission in all subcar-  81  riers is given by K  Il,tot =  ∑ Il (k) =  k=1  K  ∑ gl (k)P(k)g∗l (k).  (3.6)  k=1  The received signal and noise power at SU for kth subcarrier is given by PSU,r (k) = E {Ys (k)Y∗s (k)} = H(k)P(k)H∗ (k)  (3.7)  2 2 2 σn,k IN = σ p,k IN + σs,k IN ,  (3.8)  and  2 is variance of interference in subcarrier k at SU due to PU transrespectively, where σ p,k 2 is variance of total noise in subcarrier k at SU due to thermal noise and SU mitters, and σs,k  transmission in other subcarriers (frequency bands). Since there are several primary and secondary transmitters in the same geographical area, the total noise in subcarrier k at SU receiver can be assumed to have zero-mean Gaussian distribution.  3.3 Power Allocation Scheme for CR Capacity Optimization The MIMO CR channel capacity of kth subcarrier is a function of P(k) and is given by [92]  Ck (P(k)) = log det IN + = log det IM +  82  1 H(k)P(k)H∗ (k) 2 σn,k 1 P(k)H∗ (k)H(k) . 2 σn,k  (3.9)  Therefore, the total capacity for CR system under consideration is given by K  Ctot (P) =  ∑ log det  IM +  k=1  1 P(k)H∗ (k)H(k) , 2 σn,k  (3.10)  where P = {P(1), P(2), . . ., P(K)}. We are interested in maximizing the total CR channel capacity given by (3.10) subject to the PU interference constraint and total CR transmit power constraint, Pmax . Since maximizing a function is equivalent to minimizing its negative, the optimization problem can be formulated as follows: K  minimize P  f (P) = − ∑ log det IM + k=1  1 P(k)H∗ (k)H(k) 2 σn,k  (3.11)  K  subject to  ∑ gl (k)P(k)g∗l (k) ≤ Il,th  k=1 K  ∀l = 1, . . ., L  ∑ tr(P(k)) ≤ Pmax  (3.12) (3.13)  k=1  pi (k) ≥ 0  ∀i = 1, . . . , M,  ∀k = 1, . . . , K,  (3.14)  where Il,th is the interference threshold for the lth PU, i.e., the maximum allowable total interference to PU l from transmissions in all SU subcarriers, and pi (k) is the ith diagonal element of P(k), i.e., the transmit power of ith SU antenna for kth subcarrier. The inequality constraint (3.14) represents the non-negativity of transmission power for all antennas and subcarriers. It can be easily shown that the optimization problem (3.11)–(3.14) is convex. Therefore, numerical solution for the unknown P up to a desired precision can be obtained using convex optimization techniques [83].  83  3.4 Performance Analysis and Results In this section, we analyze the performance of the considered multicarrier MIMO based CR in terms of channel capacity and transmission power with support of some numerical results. We briefly introduce some of the power allocation schemes existing in the literature and compare the performance of proposed scheme with those schemes. We use interior point method to solve the optimization problem in (3.11)–(3.14). We assume that perfect channel state information (CSI) is available at SU transmitter by the use of feedback channels. We also assume that SU estimates the channel between the SU and PU with help of pilot signal transmitted by PU or using blind channel estimation methods [e.g., 95]. Supposing that interference temperature is same for all PUs, without loss of generality, we can assume that only one PU is present in the system which has interference threshold of Ith . Therefore, we remove the superscript l and represent the channel gain between SU and PU for subcarrier k as g(k).  3.4.1 Simulation Setup The elements of MIMO channel matrix, H(k) ∀k = 1, . . ., K, are modelled as zero-mean unit-variance independent and identically distributed (i.i.d.) Rayleigh variables. Without loss of generality, we do not consider the path losses and normalize the average power gain of H(k) to 0 dB. Channel gain g(k) is modelled as zero mean Rayleigh distributed variable. The average interference power to PU depends on various factors such as spectral and spatial distance between the PU and SU bands, the pulse shape at transmitter and performance of low pass filter at the receiver. In the worst case, assuming that the PU and SU are in adjacent bands and that raised cosine pulse at the transmitter is used with suitable rolloff factor, we can achieve 30 dB attenuation in the main sidelobe of transmit pulse  84  Table 3.1: Simulation parameters for power allocation for multicarrier CR with MIMO antennas. Parameter Number of transmit antennas Number of receive antennas Received noise variance at SU Interference threshold Number of subcarriers CR maximum transmit power  Value Range Default  Notation M N 2 σn,k Ith K Pmax  1–4  0.001 – 0.011 4 – 16 1–100  2 2 1 0.005 8 50  [12] which is SU power spilling over to PU band. This is modelled in our simulations by taking variance of elements of g(k) as σg2 = 10−3 which translates to average channel gain of −30 dB. Other simulation parameters are given in Table 3.1. Default parameter values as indicated in Table 3.1 are used unless stated otherwise. Since the channel gains are randomly generated, an average over 10,000 independent channel realizations is considered for each data point in the resulting graphs.  3.4.2 Comparison With Existing Schemes We compare the system capacity and maximum allowable transmit power using our scheme for CR with the following schemes existing in the literature. 1. Uniform power allocation (UPA): In UPA, the transmitted signal power is simply distributed equally over the transmitting antennas [96]. UPA is asymptotically optimal for high signal to noise ratio (SNR) [97] and has been shown to be optimal in a gametheoretic sense [98]. For multicarrier MIMO scenario, the available power is equally divided among all the antennas and subcarriers in UPA. Moreover, for the CR scenario, we need to introduce the interference threshold constraint in conventional UPA scheme. 85  Since all antennas will transmit equal power in all subcarriers in UPA, it is easy to see that the CR capacity will be maximized when the interference constraint is tight, i.e., K ∗ ∑K k=1 g(k)P(k)g (k) = Ith or the total power constraint is tight, i.e., ∑k=1 tr(P(k)) = Pmax .  Therefore, the total transmit power for such scenario can be obtained as  PU,tot  where  ·  2      = min     M K Ith K  ∑  k=1  g(k)      , Pmax  ,  2  (3.15)  is the Euclidean norm. Furthermore, each diagonal element of P(k), ∀k  will be equal to  PU,tot MK .  2. Multi-stage power allocation (MSPA): In [94], authors have proposed a multi-stage power allocation scheme for MIMO-OFDM based CR networks. In their method, the total CR transmit power is first divided among the available subcarriers, followed by allocation of the subcarrier’s transmit power to respective antennas. We describe this method in brief below. When the knowledge of channel gain for kth subcarrier H(k) is available, applying singular value decomposition (SVD), the channel can be represented as Λ(k)V∗ (k), H(k) = U(k)Λ  (3.16)  where U(k) ∈ CN×N and V(k) ∈ CM×M are unitary matrices, and Λ(k) ∈ RN×M is a rectangular matrix with off-diagonal elements equal to zero and diagonal elements consisting of λ1 (k) ≥ λ2 (k) ≥ . . . ≥ λNmin (k) which are the non-zero singular values of H(k), where Nmin = min(M, N) [99]. Now, the CR channel capacity optimization problem can 86  be written as K Nmin  maximize C(MSPA) =  ∑∑  log 1 +  q j (k) λ j2 (k)  k=1 j=1  2 σn,k  subject to Itot ≤ Ith  (3.17) (3.18)  K Nmin  ∑ ∑ q j (k) ≤ Pmax  (3.19)  k=1 j=1  q j (k) ≥ 0,  ∀ j = 1, . . . , Nmin ,  ∀k = 1, . . ., K,  (3.20)  where Itot is the total interference to the PU and q j (k) is the power assigned to the jth non-zero eigenchannel of the kth subcarrier [92, 99]. Since V(k) is the pre-processing matrix used in such representation, the actual transmit powers of the antennas is given by M × 1 vector p(k) formed by the diagonal elements of V(k)Q(k)V∗ (k) where Q(k) is the diagonal matrix with initial Nmin diagonal elements equal to q j (k) and all other elements equal to zero. The following two stages are proposed to solve the above problem in [94]: Stage 1: Sub-carriers power allocation In this stage, total power allocated to each subcarrier is determined according to the interference constraint by solving the following optimization problem: K  maximize CStage1 (MSPA) =  ∑ log  k=1  subject to I˜tot ≤ Ith  1+  q(k) λ 2 (k) 2 σn,k  (3.21) (3.22)  K  ∑ q(k) ≤ Pmax  k=1  87  (3.23)  q(k) ≥ 0,  ∀k = 1, . . ., K,  (3.24)  where q(k) is the total transmit power on kth subcarrier and λ (k) is defined as the Frobenius norm of H(k) [94]. Since the transmit power of each antenna is not known at this stage, it is not possible to calculate the exact interference to the PU. Therefore, the approximated interference is represented by I˜tot above and is given by K  I˜tot =  ∑ q(k)||g(k)||2/M.  (3.25)  k=1  It will be clear later that this approximation is reasonable in limiting the long-term average interference to the PUs. Stage 2: Antennas power allocation In this stage, the per subcarrier transmit power allocated in stage 1 above is divided among different antennas. This is done by solving the following optimization problem for each k = 1, . . ., K: Nmin  maximize CStage2 (MSPA) =  ∑ log  1+  q j (k) λ j2 (k)  j=1  2 σn,k  (3.26)  Nmin  subject to  ∑ q j (k) ≤ q∗ (k)  (3.27)  j=1  q j (k) ≥ 0,  ∀ j = 1, . . ., Nmin ,  where q∗ (k) is the value of q(k) obtained by solving (3.21)–(3.24) in stage 1.  88  (3.28)  3.4.3 Results and Discussion In Fig. 3.3, we plot the capacity of CR versus interference introduced to PU for K = 8 and Pmax = 50 with different number of transmit antennas (M). We assume that each subcarrier has a unit bandwidth. We compare the performance of the proposed scheme with the existing schemes (namely, MSPA and UPA with interference constraint) as described in Section 3.4.2. We observe that increase in Ith results in increased CR system capacity for all of these power allocation schemes. However, it can be observed that for the same interference threshold, the CR capacity provided by the proposed power allocation is significantly higher in general than that provided by the existing schemes. For example, the capacity for M = 4 is found to range from double to four times higher for proposed power allocation scheme compared to UPA for the considered range of interference threshold. The performance of MSPA is better than UPA but mediocre compared to the proposed scheme. Note that for M = 1, both MSPA and proposed scheme have same performance since both are equivalent for this case. When the number of transmit antenna increases (i.e., M > 1), a significant performance gap between MSPA and the proposed scheme exists. The main reason for this significantly high CR capacity of the proposed scheme is that the proposed power allocation allows transmitting higher amount of power by CR without exceeding the limit of interference to PUs. This is clear from Fig. 3.4 where we plot the permissible total transmit power of CR for different interference thresholds. Fig. 3.4 shows that, with the proposed power allocation scheme, the total power transmittable by the CR is significantly higher in general than UPA and MSPA. In addition, the transmittable power limit increases significantly with increase in number of transmit antennas in the proposed scheme. This is due to the fact that channel gains between the transmit antennas and PU are varying and the proposed power allocation scheme assigns more power to those antennas 89  30 M=1 M=2 25  Proposed Scheme  M=3  CR Capacity (bit/s/Hz)  M=4 K =8 Pmax = 50  20  15  10  UPA Scheme  5 MSPA Scheme 0  1  2  3  4  5 6 7 Interference to PU  8  9  10  11 −3  x 10  Figure 3.3: Variation of MIMO channel capacity of CR versus interference temperature threshold.  90  50 M=1 45  M=2 M=3  40  M=4 SU Transmit Power  35 30  K =8 Pmax = 50  25  Proposed Scheme  20 MSPA Scheme 15 10 5 0  UPA Scheme 1  2  3  4  5 6 7 Interference to PU  8  9  10  11 −3  x 10  Figure 3.4: Variation of maximum permissible power transmission of CR versus interference temperature threshold.  91  which produces less instantaneous interference to PU. It is also observed that for high interference threshold, the transmit power starts saturating due to the total transmit power constraint (3.13) of the CR transmitter. In contrary, the total transmittable power doesn’t increase for UPA and MSPA with increase in number of transmit antennas. In fact, the transmittable power decreases slightly for UPA with more antennas because addition of transmit antenna tend to increase interference to PU in absence of dynamic power allocation which adapts to channel conditions. As expected, the total transmit power of UPA is observed to increase linearly with increase in interference constraint as long as total power constraint is satisfied. This is also intuitive from (3.15). The implications of this is directly seen in the achieved capacity in Fig. 3.3, which shows that CR capacity doesn’t increase much with M when we use UPA. When the number of transmit antennas is increased in MSPA (i.e., M > 1), the optimization problem in stage 1 does not have information about the exact transmit powers of each antennas (which are assigned in stage 2). Therefore, the channel conditions are not dynamically exploited in the calculation of interference constraint. As a result, the power allocated in MSPA decreases with increase in number of transmit antennas. In Fig. 3.5, we plot the cumulative distribution function (CDF) of interference introduced to PU by different power allocation schemes. Although Fig. 3.3 (above) shows that average interference to the PU by MSPA is within interference threshold, instantaneous interference to PU by using MSPA may not be within limit at all times as depicted in Fig. 3.5. This is because MSPA stage 1 does not have information about the exact power allocated to each antenna, and thus cannot limit the interference. However, the long-term statistical average of the interference is within the threshold, which is also intuitive from (3.25). Fig. 3.5 also shows the effect of transmit power budget constraint on the interference intro-  92  1 Ith = 10−3  Ith = 5 × 10−3  0.9  Cumulative Distribution Function  0.8 Ith = 11 × 10−3  0.7 0.6 0.5  K =8 Pmax = 10 M =2  0.4 0.3 0.2  Proposed Scheme MSPA Scheme UPA Scheme  0.1 0  0  0.005  0.01  0.015  Interference to PU  Figure 3.5: Cumulative distribution function of instantaneous interference caused to PU.  93  duced by different schemes. When Ith is low, the limiting factor is interference constraint (instead of the power budget); that is why both the proposed scheme and UPA show sharp rise in CDF of interference to PU at the value corresponding to Ith . For higher value of Ith , the power budget constraint also starts acting as limiting factor resulting in lower than threshold interference in some cases. That is the reason for a smoother rise of interference CDF for higher Ith for all the schemes. However, it should be noted that, contrary to MSPA, at no time do the proposed scheme and UPA allow interference more than the threshold to the PU. Therefore, it can be concluded that MSPA is not applicable in the scenarios where instantaneous interference threshold constraint needs to be imposed. Therefore, using the proposed scheme, we can achieve significant increase in capacity with increase in number of transmit antennas while satisfying the given interference threshold at all times. Furthermore, the gaps between transmittable power limits of proposed power allocation and the existing schemes in Fig. 3.4 also demonstrate that if similar amount of power is transmitted by all the considered methods, the interference to PUs will be unacceptably higher with UPA and MSPA. In the previous Figs. 3.3 and 3.4, we have observed that when interference temperature limit is increased, the proposed scheme offers possibility of transmitting more power, thus increasing CR capacity. To study the relationship of the permissible transmit power and CR capacity using proposed power allocation scheme more clearly, we plot Fig. 3.6. Note that we obtain the increase in average CR transmit power by increasing corresponding Ith in Fig. 3.6. We observe in Fig. 3.6 that the CR capacity initially increases almost linearly with the average transmit power. When the average transmit power starts satuarating due to total transmit power constraint (Pmax ), the capacity curve goes up since there is no more leeway for the transmit power to increase. In this transmit power region, CR’s total power  94  30  CR Capacity (bit/s/Hz)  25  Ith Ith Ith Ith Ith Ith  = 1 × 10−3 = 3 × 10−3 = 5 × 10−3 = 7 × 10−3 = 9 × 10−3 = 11 × 10−3  20  15  K =8 Pmax = 50  10  5  0 10  M=1 M=2 M=3 M=4 15  20  25 30 35 Average CR Transmit Power  40  45  50  Figure 3.6: CR capacity versus total transmit power using proposed power allocation scheme.  95  constraint starts becoming the limiting factor instead of the interference constraint. Fig. 3.6 also shows that although the gain in CR capacity for a particular total transmit power may not be huge by increasing number of transmit antennas, addition of transmit antennas indeed allows total transmit power to go up without violating interference constraint. Thus, for the proposed power allocation scheme, addition of transmit antenna has the potential to increase the achievable CR capacity significantly without violating regulatory constraints. Figs. 3.7 and 3.8 show the CDF of total transmit power of CR for different Ith and M, respectively. As we are allowing the CR transmitter to transmit as high power as it can within its power budget limit without interfering PU unacceptably, the total power transmission for a given value of Ith is not a constant, but has a distribution based on the values of Ith and Pmax . As seen in Fig. 3.7, when Ith is increased, the CDF of transmit power moves towards higher transmit power region which signifies that the mean transmit power increases. However, because of the maximum transmit power constraint, the distribution is truncated above the value of Pmax . In addition, the slope of CDF curves decreases as interference threshold increases, which means that the variability of transmit power could be higher for higher Ith . However, the distribution quickly reaches Pmax for higher Ith and the transmit power is limited by power budget. Similar results are observed in Fig. 3.8; CDF of CR transmit power shifts towards higher transmit power region when number of transmit antennas is increased for proposed power allocation scheme. These observations further confirm the results shown in Fig. 3.4. Now, we compare the performance of the considered schemes with variation in CR transmit power budget (Pmax ). Fig. 3.9 depicts the CR channel capacity versus total power budget of CR transmitter. It is observed that the capacity first increased rapidly with increase in Pmax and saturates soon. The saturation of capacity is because the system operates  96  1 Ith = 1 × 10 −3  0.9  Ith = 3 × 10 −3 Ith = 5 × 10 −3  Cumulative Distribution Function  0.8  Ith = 7 × 10 −3  0.7  Ith = 9 × 10 −3 Ith = 11 × 10 −3  0.6 0.5 0.4 0.3 0.2  K =8 M =2 Pmax = 50  0.1 0  0  10  20 30 Total Transmit Power of CR  40  50  Figure 3.7: CDF of total transmit power of SUs using proposed power allocation scheme for different interference temperature thresholds.  97  1 M =1 0.9  M =2 M =3  Cumulative Distribution Function  0.8  M =4 0.7 0.6 0.5 0.4 0.3 0.2  K =8 Ith = 5 × 10−3 Pmax = 50  0.1 0  0  10  20 30 Total Transmit Power of CR  40  50  Figure 3.8: CDF of total transmit power of SUs using proposed power allocation scheme for different number of transmit antennas.  98  25 M=1  Proposed Scheme  M=2 M=3  CR Capacity (bit/s/Hz)  20  M=4  15  10 MSPA Scheme  5 UPA Scheme  0  0  Ith = 5 × 10−3 K =8  25 50 75 Maximum CR Transmit Power (Pmax)  Figure 3.9: Capacity of CR versus total transmit power budget (Pmax ).  99  100  in scenario which is limited by interference to PU for high power budget, and therefore cannot transmit more power even if it is available. However, until this situation is reached, any increased amount of power budget directly results in increased capacity, as shown for low power budget region. Fig. 3.9 also confirms that the saturation occurs at significantly high transmit power for proposed power allocation compared to the existing MSPA and UPA, resulting in significantly higher CR capacity for the proposed power allocation scheme. Fig. 3.10 depicts the relationship between the CR channel capacity and the number of subcarriers, K. Note that by increasing K, we assume that CR gets more bandwidth. It should not be confused with the case when the same bandwidth is divided into smaller parts to form more subcarriers. Therefore, for a traditional scenario without interference constraint, one would expect a linear increase in capacity with increase in K . We observe in Fig. 3.10 that, for all the considered power allocation schemes, the slope of CR capacity curve decreases with increase in K. This signifies that the CR capacity will saturate at some value of K. This is because of the two constraints: i) interference constraint, and ii) power budget constraint. With increased K, there is more likelihood of increased interference to the PU from SU transmissions in wider frequency band. This results in decreased total transmittable power of SUs, which in turn prevents the CR capacity from increasing linearly with K. On the other hand, with higher value of K and M, the total power budget of CR transmitter starts being active, as discussed earlier. Comparison of the proposed scheme with the existing schemes in Fig. 3.10 also depicts that with higher K and M, the performance gap increases between MSPA and the proposed scheme. The proposed power allocation scheme can gain higher performance for larger CR bandwidth owing to its ability to optimally allocate transmit powers to all subcarriers and antennas according to channel conditions. In contrary, for UPA scheme, the CR capacity  100  30 M=1  Proposed Scheme  M=2 25  M=3  CR Capacity (bit/s/Hz)  M=4 20  Ith = 5 × 10−3 Pmax = 50  15  MSPA Scheme  10  5 UPA Scheme 0  4  6  8 10 12 Number of Subcarriers (K)  14  16  Figure 3.10: Capacity of CR versus number of subcarriers using proposed power allocation scheme.  101  quickly saturates and increases minimally even with increased CR bandwidth.  3.5 Conclusion In this chapter, we proposed an optimal power allocation scheme for a multicarrier CR network employing MIMO antennas. We considered interference to PU and maximum transmit power of SU transmitter as constraints for CR capacity optimization. We concluded that conventional power allocation algorithms cannot be used directly to CR scenario because of the interference constraint. We compared the performance of the proposed scheme with the existing power allocation schemes for MIMO-based CR available in the literature, namely multi-stage power allocation (MSPA) and uniform power allocation (UPA). With simulations, we showed that in the presence of interference constraint, the proposed power allocation scheme outperforms the existing UPA and MSPA in terms of CR channel capacity. This gain in capacity is due to the proposed scheme’s ability to allow higher transmit power to CR transmitter without violating regulatory constraints. It was also shown that increasing number of transmit antennas may not provide any gain in UPA scheme. However, significant diversity gain can be achieved by the proposed power allocation scheme in increasing achievable CR channel capacity with the increase in number of transmit antennas. We observed that increasing power budget for CR transmitter increases the achievable capacity initially; however, the CR capacity saturates for higher power budget due to interference limit constraint. Although an increased CR bandwidth results in higher CR capacity, the capacity gain was not found to be linear because of the increased interference to PU from SU transmissions in wider frequency band.  102  Chapter 4 Resource Allocation to Enable Green Communication in Wireless Networks1 4.1 Introduction In the past, energy efficiency of wireless communication systems and their impact to the environment have been largely ignored during the design and implementation of existing wireless networks. Designers of these networks had mainly focused on the spectral efficiency. Increasing energy consumption in these networks has been recently identified as a global problem due to its adverse effects on the environment and increasing cost of operation [29, 30, 31, 32, 33, 34]. Cellular system constitutes a major part of wireless communication and its use in daily  1 The results of the research work presented in this chapter has been published as: U. Phuyal, S. C. Jha, and V. K. Bhargava, “Resource allocation for green communication in relay-based cellular networks,” in Green Radio Communication Networks, E. Hossain, V. K. Bhargava, and G. Fettweis, Eds. Cambridge: UK, 2012, pp. 331–356 [100]; and U. Phuyal, S. C. Jha, and V. K. Bhargava, “Green resource allocation with QoS provisioning for cooperative cellular network,” in Proc. IEEE CWIT 2011, May 2011, pp. 206–210 [101].  103  life is increasing more than ever [39]. It is speculated that web data traffic increases by a factor of more than ten in five years; mobile devices are expected to surpass the personal computers as the main web accessing devices in the near future [1, 15]. Therefore, mobile communications can contribute up to 15–20% of the overall energy consumption in information and communication technologies (ICT) [15], which can no longer be disregarded. The total energy consumption of ICT itself is difficult to estimate because studies vary depending on the definition of ICT, the methodology used to generate the estimates and the proportion of a device’s energy consumption that is attributed to ICT [36, 102]. Several studies have suggested that the fraction of overall electricity consumption due to ICT infrastructure corresponded to around 7.8% in the European Union in 2005 [35], which is expected to rise to 10.9% by 2020. Around 3% of the world’s electricity consumption is attributed to ICT – contributing to about 2% of worldwide CO2 emissions [29, 36, 37, 38]. Therefore, it is apparent that there is an urgent need to design a sustainable wireless communication system by developing energy-efficient (green) technologies. The concept of green communication has attracted attention of a huge research community recently. Green communication is a vast research area that covers energy saving at all layers in the protocol stack of wireless access networks as well as that in design of wireless architecture and techniques of next generation communication systems [16]. In this chapter, we mainly focus on reducing the transmit energy consumption in wireless networks. A number of approaches that may reduce the energy consumption and thus enable green communication in wireless networks have been under discussion. For example, discontinuous transmission by base station (BS) and discontinuous reception (DRX) [103] by mobile station (MS) where some of the hardware components are switched off, multi-hop  104  transmission approach, and coordinated multi-point (CoMP) [18] architectures are being discussed as energy saving measures [15]. One of the most popular approaches is relaybased cooperative transmission which can reduce the overall energy consumption without requiring much changes in existing infrastructure of cellular systems [46, 47]. Therefore, our focus in this chapter is on enabling green communication in next generation wireless communication systems by employing relay-based cooperative transmission. Since energy consumption in wireless networks is closely related to their radio resource management schemes, designing energy-aware resource management techniques is crucial in realizing green communication.  4.1.1 Outline The main focus of this chapter is to explore the energy-efficient resource allocation strategies in a cellular system using relay-based dual-hop transmission approach. Various approaches to achieve green communication in a cellular network are first discussed. Our approach in this chapter is on an algorithmic and protocol design level instead of energyefficient circuitry design for communication devices. Therefore, the advantages of and implementation issues for relay-based cooperative transmission approach are analyzed in the context of its potential to enable green communication. Some performance metrics that can provide a quantitative measure of the green performance of wireless communication network are also discussed. A novel resource allocation scheme is then introduced in order to address some of the shortcomings of the existing schemes identified in Section 1.4.1 and to optimize the energy efficiency or “green performance” of cooperative communication network (CCN). Performance of different schemes is evaluated and analyzed. Since the improvement of green performance comes at the cost of degraded overall system throughput  105  in general, a trade-off between system throughput and green performance is also analyzed using multi-objective optimization approach.  4.2 Enabling Green Communication in Wireless Communication Networks Energy saving can be achieved at various levels in wireless communication networks. These levels can be broadly classified in three categories: component level, equipment level and network level. We discuss about each of these levels in brief below.  4.2.1 Component Level Each piece of equipment in a wireless communication system, e.g., BS and MS, consists of several components such as antenna(s), power amplifier, baseband processor, power supply, and other supporting components. The energy efficiency of these components have huge impact on overall energy efficiency of the system [30, 15]. Various green performance metrics can be used to measure the energy efficiency of these components2. For example, the ratio of radiated power to input power can be used as a green metric for antennas while the ratio of effective output power to input power can be used as a green metric for power amplifiers and power supply units [15]. A significant fraction of energy is wasted as heat in the very essential components such as power amplifiers. It goes without saying that green components form the basis for achieving green communication.  2A  brief introduction of green performance metrics is given in Section 4.3.3 later.  106  4.2.2 Equipment Level BSs and MSs are the most used equipments in a cellular wireless communication system. It is estimated that about 80% of the total energy consumed by ICT infrastructure can be attributed to the BSs alone, which amounts in approximately 5–10 million KWh per annum [29, 37, 38]. This further underscores the criticality of energy efficiency of BSs in achieving green communication. Generally, power-consumption per unit effective system throughput is the green metric used to calculate energy efficiency of equipment such as BS. Here, the effective throughput generally includes the frame overhead from the physical and link layers. Similarly, power consumption should also take into account the energy consumption in any auxiliary devices such as cooling unit needed to operate the equipment.  4.2.3 Network Level Energy efficiency at the network level depends on various factors such as deployment topology, network layout, transmission management, and resource management strategies. Since most of the existing cellular networks are optimized for high load, their performance in terms of energy efficiency is poor at low load. Network-level performance parameters may include total system throughput, total coverage area, coverage area per BS, number of subscribers served per BS, etc. Therefore, green metrics used for network-level energy efficiency can be, for example, coverage area per unit power consumption, number of subscribers served per unit power consumption, and useful throughput (excluding frame overhead) per unit power consumption. Coverage area per unit power consumption may be a green metric better suited for networks in rural area, while number of subscribers served per unit power consumption may be better suited for urban-area network.  107  4.2.4 Computation Complexity Versus Transmit-power-saving When energy-efficient algorithms to save transmit power are implemented at the equipment level such as in the BS and MS, the computational complexity introduced by the algorithm may demand for increased energy requirement for signal processing as well as encoding and decoding, resulting in a decreased network-level energy efficiency. Therefore, tradeoff analysis of computational complexity versus saving in transmit-power requirement is an important issue. Emphasis should be given to designing low-complexity schemes resulting in easy implementation while providing a reasonable gain in overall network-level energy efficiency.  4.3 Relay-based Green Cooperative Communication Network As discussed earlier, relay-based cooperative transmission is popular among the number of approaches at network level that may enable green communication in wireless networks since it can reduce the overall energy consumption without requiring much changes in existing cellular infrastructure [46, 47]. In a traditional cellular network shown in Fig. 4.1(a), each BS serves a number of MSs within its service area. On the other hand, in a relaybased CCN shown in Fig. 4.1(b), one or more relay stations (RSs) provide alternative path to transmit data from BS to MS. In such network, BS and RSs cooperate to serve MSs within their service area as illustrated in Fig. 4.1(b). As discussed in Section 1.1.1, relay-based cooperative transmission offers several advantages in modern wireless communication systems such as increased service reliability and coverage. In addition, this approach seems to be cost effective and more practical to enable green communication in cellular networks compared to other approaches such as  108  BS  RS  MS  (a)  Desired Signal Interference  (b)  Figure 4.1: Cellular networks with ideal hexagonal cells: (a) traditional, and (b) relay-based CCN. While relays offer alternative communication paths, they also cause more inter-cell interference to near-cell-edge users.  109  micro-cell, pico-cell, or femto-cell and cell zooming (CZ). Micro-, pico-, and femto-cells require the installation of new BSs and reliable wired backhaul connection. Femto-cells provide an efficient way to improve performance for indoor users; however, they may not improve the performance if only outdoor BSs are deployed because the major bottleneck is the path-loss from outdoor BSs to indoor MSs [104]. On the other hand, CZ suffers from several implementation issues in practice [105]. Firstly, CZ is possible only with a very close coordination among neighboring cells which usually requires an extra entity called CZ server connected to all these cells. Secondly, the effectiveness of CZ entirely depends on the knowledge of traffic load fluctuation in the network, which is difficult to trace and feed back to the CZ server concisely and timely in practice. Thirdly, it can also cause problems like increased inter-cell interference and coverage holes.  4.3.1 Implementation Issues and Challenges In this section, we discuss some of the major implementation issues and research challenges in enabling green communication by cooperative relay–based transmission approach. 1. Relay Deployment Cost Versus Green Performance Enhancement: There is always the question: will using relay(s) increase performance for current scenario? The answer depends on various factors. There may be cases when the channels between BS–MS, BS–RS, and RS–MS are of similar quality. It is obvious that relay does not help much in such scenario. Relays are useful only when they can offer better channel conditions compared to direct (BS–MS) path. Enabling relaying in a cellular network also requires software (and possibly hardware) upgrade at BS and MSs. Moreover, while relay-based cooperative transmission offers several advantages, deployment of RSs, on the other hand, causes more inter-cell inter110  ference to near-cell-edge users as illustrated in Fig. 4.1. It is necessary for the operator that performance enhancement due to relaying be worthwhile relative to the investment in relays. Therefore, efficient use of relaying is necessary to improve performance of system in terms of green performance metrics,3 network coverage, and system capacity in order to justify the investment. 2. Choice of Relaying Protocol: When the answer to the question above is “yes”, the next question is about the choice of relaying protocol – whether to use dumb relays which simply amplify and forward (AF) the received signal; smart ones which decode the received signal and retransmits after re-encoding and re-modulating (i.e., decode and forward (DF)); or something in between these two, which demodulates the received signal, removes the noise and retransmits after re-modulating without decoding (Regenerate and Forward). It is understandable that relays with higher degree of signal processing need more computational power and thus consume more energy. Since AF relays are transparent to source/destination coding and modulation schemes and have lower complexity, AF relaying seems to be more practical compared to the other protocols [67, 68]. 3. Relay Mobility: As previously discussed in Section 2.1, cooperation among the nodes in a CCN can be realized in various ways such as by installing fixed RSs at predefined locations, by enabling relay functionality in MSs, or by doing both. Because of power supply constraint (battery life) and other hardware limitations of MS, it may be difficult to enable relay functionality in MS. Moreover, MSs need to have sufficient incentive to  3 Some  green performance metrics will be briefly discussed in Section 4.3.3 later.  111  cooperate, for example, prioritized resource allocation in upcoming time-slots. In the lack of such incentive, there is a risk of MSs reporting false channel state or battery-life to avoid relaying. In contrast, fixed relays deployed by the wireless operator do not typically have these constraints. Network planning and routing design also become easier with such relays [106]. While installing such fixed relays, their positions can be selected to optimize the system performance. Moreover, installation of fixed RSs is a trade-off point between the following two options: i) very costly hardware changes by installing new BSs and using more spectrum, and ii) low cost but not very reliable ad hoc relaying by the MSs. Therefore, in this chapter, we mainly focus on CCN with pre-installed fixed AF relays to achieve green communication in a more realistic way. 4. Relay Positioning and Selection: Performance of relay-based CCN depends on the location of relays. Therefore, for a fixed relay–based system, relays should be installed such that the system performance is optimized. If the source decides to use relay-based transmission when there are multiple potential RSs present, then smart relay selection to optimize system performance is a crucial step. Efficient relay positioning and selection strategies are necessary to harness the potential benefits of cooperative transmission in order to enhance energy efficiency of CCN such as by improving frequency- and/or code-reuse. To illustrate this, let us take an example network scenario shown in Fig. 4.2. MS1 is outside the BS transmission range. When RS1 and RS2 are positioned such that they are not within transmission range of each other, BS can transmit data to RS2 using same frequency band (or codeword) used in RS1 –MS1 transmission. Note, however, that in the above example if the data from BS  112  is intended for MS2 via RS2 , then MS2 should not be inside the transmission range of RS1 and BS at the same time. Some relay selection strategies in a multi-relay CCNs were discussed in Sections 2.3.2 and 2.3.3. Detailed description of various relay selection strategies in relay-based CCNs can be found in [82] and references therein. 5. Resource Distribution Among Source and Relays: Since the total transmit power is limited in a wireless communication system due to regulatory constraints, it must be smartly distributed among the source and the relays. Therefore, the design of efficient resource allocation scheme can be one of the major ways to enable green communication in a CCN. At low traffic demand, temporarily switching off network elements is a state-of-theart solution to save energy [15]. However, it may not be effective in modern cellular networks where traffic load remains consistently higher. Energy-efficient resource allocation is a potential alternative to save energy in such networks. Most of the work in the literature focus on optimizing the spectral efficiency and transmission reliability. Developing a resource allocation strategy to maximize green performance of CCN is an open research challenge which demands more research. 6. End-user Node (MS) Complexity: From the above discussions, it is clear that, the implementation of relay-based cooperative approach increases the complexity of BS and/or MS nodes as they need to decide whether to transmit via relay or not. If they decide to use relaying, they need to be able to smartly select relay(s). If MSs are also allowed to function as relays, they need to be upgraded with such a capability. Finally, at the receiver end, MS needs to be able to make good use of multiple copies of data obtained 113  via direct and/or relay paths and effectively combine them in a useful manner. Because of limited computational capacity and energy resources available at end-user MSs, these requirements may significantly increase MS node’s complexity. Therefore, it is essential to take this factor into account while designing energy-efficient communication system.  4.3.2 Advantages of Fixed Relay–based CCN As discussed earlier in Chapter 2, the main advantage of fixed relay-based approach is that it requires minimum to no hardware modification in the existing cellular architecture. Hence it is more practical because only software upgrades at BS and MSs may be sufficient. In addition, deployment of fixed relays is cheaper and includes less planning than installing new BSs. Therefore, cooperative approach is more economical and feasible compared to micro-, pico- and femto-cell approaches to implement a green cellular system [30]. Moreover, the cooperative technique is an easier way to implement CZ [105]. As discussed earlier, frequency- and/or code-reuse can be improved by using relaybased communication. Other inherent benefits of fixed relay–based cooperative transmission include increase in system throughput, transmission reliability, and network coverage [61]. In addition, relay-based approach shortens the propagation distance between the nodes and reduces the required transmission power, hence providing potential to save energy. In addition, RS installation does not need expensive back-haul links which are necessary for BSs. Due to these attractive advantages of fixed relay–based cooperative technique, it has been recently envisioned as one of the potential candidates for future generation green cellular networks.  114  4.3.3 Green Performance Metrics for Resource Allocation In the context of green performance of cellular networks, the energy efficiency metrics can be defined at component, device and system/network levels [30]. The metrics at component and device levels indicate the energy efficiency performance of individual component and device, and have been well established [15]. In this chapter, we are interested in energy efficiency metrics for resource allocation at system/network level. System performance per unit energy or power consumption is a vital green metric at network level. For example, power consumption per unit coverage area of a cell (W/m2 ), power consumed per unit achieved system throughput (J/bit), and the fraction of total power saved by energy-aware scheme are examples of green metrics at network level. A detailed discussion on green metrics can be found in [15, 30], and the references therein. We consider power consumption required for unit system throughput (J/bit) as a basis for optimizing the resource allocation. Minimizing J/bit enhances green performance; however, it may result in overall poor system throughput. Therefore, this green metric combined with a quality of service (QoS) metric which guarantees a predefined minimum data rate or signal to noise ratio (SNR) to each MS seems to be more practical basis for resource allocation.  4.4 Design of a Green Power Allocation Scheme In this section, we introduce a novel energy-efficient (green) power allocation scheme for a relay-based CCN. This scheme minimizes the required transmit power per unit achievable throughput (i.e., J/bit) to optimize the green performance of the system and at the same time it guarantees a QoS in terms of end-to-end data rate required by each MS.  115  4.4.1 System Model We consider a CCN where relays help a source node (i.e., BS) in transmitting its data to an intended end-user MS. More specifically, we study a scenario where the BS is fixed and a cell-edge MS is served by a fixed RS deployed by the operator, as shown in Fig. 4.2. Multiple fixed RSs with sectorial antennas may be installed by operator at predetermined locations in order to physically isolate the service areas of individual RSs. As discussed in Chapter 2, there may be multiple RSs which are capable of serving a particular BS– MS communication; however, for less-complex and practical system implementation, we assume that only one RS is selected to assist any MS at a particular time [59]. Since relay selection is not within the main scope of this chapter, we assume that BS chooses such RS that can potentially maximize the achievable end-to-end SNR of the MS. We consider a downlink (DL) transmission of a two-hop two-time-slot-based half duplex system with AF relaying. The complete transmission takes place in two stages: i) Source S (i.e., BS) broadcasts the signal towards relay RS1 and destination D (i.e., MS1 ) in first time-slot using transmit power Ps, and ii) RS1 amplifies the signal received in first time-slot and retransmits it towards D in second time-slot with transmit power Pr . However, we assume that the direct link S–D is in deep fade which necessitates transmission via RS for a QoS guarantee. Following similar approach as in derivation of (2.35) in Section 2.3.1 for a single-relay case (i.e., k = 1), we can represent the SNR at the destination MS1 , in absence of direct link, as  γ=  β1 β2 Ps Pr , β1 Ps + β2 Pr + 1  (4.1)  where β1 = |hsr |2 /σr2 and β2 = |hrd |2 /σd2 are constants whose values depend on S–R and  116  h h h  3  1  1  2  2  Figure 4.2: An ideal hexagonal cell of a relay-based CCN. Shaded region shows the service area (transmission region) of fixed relay RS1 which contains the nodes of our interest.  117  R–D channel conditions (hsr and hrd , respectively) and relay and destination receiver noise variances (σr2 and σd2 , respectively). This means both β1 and β2 are non-negative. In addition, note that for any communication link to be possible between the BS and MS, β1 and β2 cannot be zero. Therefore, both β1 and β2 are positive constants. We assume that RS and MS estimate the channels with help of pilot signal transmitted by BS and RS or using blind channel estimation methods and send this information to the BS by using feedback channel, either directly or via RS. Based on these assumptions, a green power allocation (GPA) scheme is described below.  4.4.2 Green Power Allocation Scheme In order to find energy-efficient power allocation between the BS and RS, we consider a scenario where total transmit power is constrained to Pmax . We are interested in allocating the available power between BS and RS such that minimum power is spent per unit achievable system throughput and the predefined QoS is guaranteed. Therefore, the optimization problem for GPA can be formulated as  minimize {Ps ,Pr }  f (Ps , Pr ) =  Ps + Pr log(1 + γ )  subject to Ps + Pr ≤ Pmax  1 log(1 + γ ) ≥ Rmin 2  Ps > 0,  Pr > 0,  (4.2)         (4.3)         where Rmin > 0 is the minimum end-to-end data rate needed to fulfil QoS requirement of the user. The factor  1 2  in the second constraint accounts for the fact that S–D data transmission  via RS is achieved over two time-slots. Note, however, that this factor is not included in the  118  objective function as it simply scales the value of objective function but does not affect the solution of the optimization problem. When Ps or Pr is zero, from (4.1), γ will be zero. In such case, the second constraint cannot be satisfied. Therefore, it is clear that both Ps and Pr must have positive values as indicated by the last two constraints. Now, let us briefly analyze the characteristics of the objective function f (Ps , Pr ). Determining the convexity (or concavity) of f (Ps , Pr ) doesn’t seem to be straightforward since γ given by (4.1) is neither convex nor concave in (Ps , Pr ). This can be shown by calculating determinant of the Hessian matrix of γ :  |Hγ | =  =  =  ∂ 2γ ∂ Ps2 ∂ 2γ ∂ Pr ∂ Ps  ∂ 2γ ∂ Ps ∂ Pr ∂ 2γ ∂ Pr2  2β 2 β P (β2 Pr +1) 3 1 s 2 Pr +1) β1 β2 (β1 Ps +β2 Pr +2β1 β2 Ps Pr +1) (β1 Ps +β2 Pr +1)3 β12 β22 − , (β1 Ps + β2 Pr + 1)4  − (β1 P2+rβ  β1 β2 (β1 Ps +β2 Pr +2β1 β2 Ps Pr +1) (β1 Ps +β2 Pr +1)3 2β β 2 P (β Ps +1) − (β1 P2+sβ P1 +1) 3 1 s 2 r  (4.4)  which turns out to be negative. However, the Bordered Hessians [107, §3.4] of γ are given by  D1 =  0  ∂γ ∂ Ps  ∂γ ∂ Ps  ∂ 2γ ∂ Ps ∂ Pr  =−  β12 β22 Pr2 (β2 Pr + 1)2 (β1 Ps + β2 Pr + 1)4  119  (4.5)  and  0 D2 =  ∂γ ∂ Ps ∂γ ∂ Pr  ∂γ ∂ Ps  ∂γ ∂ Pr  ∂ 2γ ∂ Ps2 ∂ 2γ ∂ Ps ∂ Pr  ∂ 2γ ∂ Ps ∂ Pr ∂ 2γ ∂ Pr2  =  2β13 β23 PB PR (β1 Ps + 1)(β2 Pr + 1) . (β1 Ps + β2 Pr + 1)5  (4.6)  Since Ps , Pr , β1 , and β2 all can have only positive values, we see that D1 < 0 and D2 > 0. Therefore, γ is quasi-concave in (Ps, Pr ). Since log(·) is a monotonically increasing function for positive argument, the function l(Ps, Pr ) = log(1 + γ ),  (4.7)  where γ is given by (4.1) must be quasi-concave in (Ps, Pr ) [108]. Moreover, as described in Appendix F, it can be proved that l(Ps, Pr ) is strictly concave in (Ps, Pr ) when γ ≥ 0.5. In any practical system, SNR should be generally higher than 0.5 for successful communication. Furthermore, the objective function in (4.2) is positive quasi-convex function and the feasible region defined by (4.3) is a convex set. Standard algorithms exist in the literature to solve such optimization problem efficiently (e.g., [83, §4.2.5]). Note that when the optimization problem (4.2)–(4.3) is infeasible, such event contributes to QoS outage since the QoS guarantee cannot be provided by the available power budget.  4.4.3 Performance Analysis of GPA Scheme Now, we evaluate the performance of the GPA scheme described above and compare it with that of other selected power allocation schemes in the literature. For performance evaluation, we consider following two metrics: i) green performance metric defined as  120  total power required to achieve unit end-to-end data rate (J/bit), and ii) QoS outage defined as the probability that the predefined throughput requirement for QoS guarantee cannot be achieved in a two-time-slot transmission cycle. Obviously, lower values of both of these metrics are desirable to enable green communication and to ensure better QoS. For comparison, we consider the following power allocation schemes: 1. Throughput maximization power allocation (TMPA): In such scheme, the optimal power allocation between BS and RS is generally found by maximizing log(1 + γ ) subject to the same set of constraints (4.3). Therefore, TMPA solution can be found by solving a convex optimization problem. 2. Uniform power allocation (UPA): This is one of the easy-to-implement schemes widely used to calibrate performance of other schemes. It is also known as equal power allocation because all the transmitting nodes and/or frequency channels are provided with equal transmit power in such scheme.For our scenario, this means that both BS and RS transmit powers will be Pmax /2. 3. GPA with no QoS provisioning (GPANQ): We also consider the GPA without QoS guarantee for comparison. The optimization problem for this case will be similar to (4.2)– (4.3) but without the data rate constraint, i.e.,  minimize {Ps ,Pr }  f (Ps, Pr ) =  Ps + Pr log(1 + γ )  subject to Ps + Pr ≤ Pmax Ps > 0,  Pr > 0.  (4.8)     (4.9)     Since a constraint is relaxed in GPANQ compared to GPA, it is easy to see that, without 121  further modifications, the energy efficiency obtained by GPANQ serves as a bound for energy efficiency of GPA scheme. In other words, J/bit for GPA in general will be equal to or higher than J/bit for GPANQ. However, adapting to channel conditions and dynamically deciding whether to relay or not can result in better energy efficiency as described below. Adaptive Interrupted Transmission Since GPA, TMPA, and UPA possess QoS constraint in terms of minimum guaranteed throughput, it seems reasonable for these schemes to interrupt and suspend the transmission in situations when QoS requirement cannot be guaranteed. By doing so, these schemes can further improve their energy efficiency without introducing added outage. Therefore, we assume that GPA, TMPA, and UPA dynamically decide whether or not to carry-out relaybased transmission based on their instantaneous channel conditions. It will soon be clear that adapting the dynamic transmission interruption, these power allocation schemes can provide better energy efficiency compared to GPANQ.  4.4.4 Results and Discussion Now, we present some simulation results demonstrating the performance of different power allocation schemes discussed above. The channel gains hsr and hrd are modeled as zero mean independent and identically distributed (i.i.d.) Rayleigh variables assumed to be constant over the period of two time-slots. The effect of log-distance-based path loss [109, §4.9.1] is taken into account by changing variance of channel gains. The list of various simulation parameters and their corresponding values is given in Table 4.1. The numerical solutions of the power allocation optimization problems are obtained using interior point method. First, we study the effect of the position of RS on performance of the considered power 122  Table 4.1: Simulation parameters for relay-based green CCN. Parameter Cell radius (BS to cell-edge MS distance) BS–RS distance Free space path loss exponent Carrier frequency Channel bandwidth Receiver noise figure QoS data-rate requirement Total transmit power constraint  Notation  Value Range  250 – 750 m  Rmin Pmax  0.75 – 2.0 bit/s/Hz 4.5 – 7.5 W  Default 1000 m 500 m 3.0 2 GHz 5 MHz 5 dB 1.5 bit/s/Hz 6.0 W  allocation schemes. For this purpose, we simulate scenarios for different BS–RS distances keeping BS–MS distance fixed at 1000 m. We move the RS along the path from BS to MS and plot the corresponding results in Figs. 4.3–4.5. It is observed in Fig. 4.3 that, in terms of the green performance metric (i.e., transmit power per unit throughput)4, GPA outperforms other considered power allocation schemes whereas UPA exhibits the worst performance. It can also be observed in Fig. 4.3 that, compared to UPA, the sensitivity of the green performance metric to the change in relay position is less for GPA, TMPA, and GPANQ. In contrast, this metric for UPA significantly depends on the relay position, and is better when RS is near the middle of BS and MS. This is because GPA, TMPA, and GPANQ possess the ability to adapt their power allocation to the channel gains of BS–RS and RS–MS links. This ability is lacking in UPA because UPA assigns a static transmit power regardless of the channel conditions. Note that the green  4 Note  that in all the simulation results in this chapter, throughput is normalized by bandwidth. Therefore, the unit of this metric is J/(bit/Hz).  123  Power Per Unit Throughput (J/(bit/Hz))  3 2.8 2.6 2.4  Pmax = 6 W Rmin = 1.5 bit/s/Hz  GPA TMPA UPA  2.2  GPANQ  2 1.8 1.6 250  300  350  400  450  500  550  600  650  700  750  BS-RS Distance (m)  Figure 4.3: Variation of energy efficiency with respect to relay position for QoS satisfied users.  124  performance metric for GPA is even better than that of GPANQ thanks to the adaptive interrupted transmission method described in Section 4.4.3. For the similar reason, it is obvious that QoS outage would be higher for UPA, which is verified by Fig. 4.4. The QoS outage for UPA rises sharply when the RS is moved away in either direction from the middle of BS and MS. In contrast, GPA and TMPA are robust against the change in RS position and the outage does not change much for a wider range of relay positions. Note that system outages for GPA is observed to be equal to that of TMPA. This is because as long as TMPA can provide QoS guarantee within the prescribed power budget, GPA can also do it. GPA raises its transmit power to provide QoS guarantee even at the cost of energy efficiency if it is possible to do so without violating the power budget constraint. Note also that QoS outage for GPANQ is not shown in the plot. This is because there is no QoS guarantee in GPANQ and therefore QoS outage is not defined for this scheme. From above results, energy efficiency is observed to be much better for GPA compared to other schemes for all relay positions without added penalty in QoS outage. As discussed earlier, due to the absence of QoS constraint, better energy efficiency may be achieved by GPANQ in absence of adaptive interruption in transmission. However, GPANQ suffers from decreased system throughput as illustrated by Fig. 4.5 where variation of average system throughput provided by different power allocation schemes is plotted. It is clear that other schemes perform much better than GPANQ in providing system throughput. Therefore, GPANQ may not be a good choice for commercial systems. In Fig. 4.5, it is also observed that the average system throughput is less sensitive towards the position of relay for the proposed GPA scheme. In addition, it is worthwhile to note that average system throughput may be less than Rmin because of the existence of  125  40 GPA  38  TMPA UPA  QoS Outage (%)  36  Pmax = 6 W Rmin = 1.5 bit/s/Hz  34 32 30 28 26 24 250  300  350  400  450  500  550  600  650  700  BS-RS Distance (m)  Figure 4.4: Variation of QoS outage with respect to relay position.  126  750  1.8 1.6  Throughput (bit/s/Hz)  1.4 1.2 1 GPA  0.8  Pmax = 6 W Rmin = 1.5 bit/s/Hz  TMPA UPA  0.6  GPANQ  0.4 0.2 250  300  350  400  450  500  550  600  650  700  750  BS-RS Distance (m)  Figure 4.5: Variation of average system throughput with respect to relay position.  127  QoS outage events where transmission is suspended and no throughput is achieved as such. Fig. 4.5 further shows that average throughput is better for all power allocation schemes when RS is about the midway between BS and MS. It is also worthwhile to note that, as observed in Figs. 4.3–4.5, for the methods which are more sensitive to relay position, the performance results are almost symmetrical in terms of moving the relay in either direction (towards BS or RS) from the midway. This is because among the BS–RS and RS–MS links, the one for which the propagation distance is larger generally becomes the bottleneck in the end-to-end link. Based on Fig. 4.5, it may be argued that throughput is higher for TMPA and UPA. However, total transmit power consumption is also much higher for those schemes. This is demonstrated in Fig. 4.6 where total power consumption by various power allocation schemes is plotted against various values of power budget, Pmax . Since all of the power allocation schemes perform better when the relay is positioned near the middle of BS and MS, for fair comparison we take BS–RS distance (equal to RS–MS distance) of 500 m for this and subsequent simulations. A linear increase in total power consumption with Pmax is observed in Fig. 4.6 for GPA and TMPA. Although power consumption of GPA also increases almost linearly with Pmax , the rate of increase for UPA and TMPA is almost four times higher compared to GPA. This results in a higher performance gap between GPA and other schemes for higher Pmax . The power consumption of GPANQ is the least among considered schemes and almost invariant with Pmax . Fig. 4.7 shows the variation of energy efficiency metric (J/(bit/Hz)) against Pmax for different power allocation schemes. The figure further confirms that GPA uses less power to deliver unit throughput compared to TMPA and UPA for all values of Pmax . When Pmax is increased, the performance gap between GPA and TMPA increases. On the other hand,  128  6 Power Consumption for QoS Satisfaction (W)  GPA TMPA  5  UPA GPANQ  4 Rmin = 1.5 bit/s/Hz  3 2 1 0 4.5  5  5.5  6  6.5  7  7.5  Maximum Total Transmit Power, Pmax (W)  Figure 4.6: Total transmit power consumption for QoS satisfaction by different power allocation schemes.  129  3.5 Pow Per Unit Throughput (J/(bit/Hz))  GPA TMPA  3  UPA GPANQ  2.5  2  1.5  Rmin = 1.5 bit/s/Hz  1 4.5  5  5.5  6  6.5  7  Maximum Total Transmit Power, Pmax (W)  Figure 4.7: Average power per unit throughput for different Pmax .  130  7.5  the gap between GPA and GPANQ decreases with increase in Pmax . This is because the QoS outage decreases with increase in Pmax resulting in less events of suspended transmission. The decrease of QoS outage with increase in Pmax is depicted in Fig. 4.8. As shown by the plot in Fig. 4.8, outage for GPA is less than that for UPA for all values of Pmax . This reconfirms that GPA provides better energy efficiency without introducing any outage penalty. The variation of the performance parameters with change in the QoS constraint (i.e., the required minimum throughput) for a fixed Pmax is depicted in Figs. 4.9–4.11. As expected, more stringent QoS constraint results in increased outage probability which is confirmed by Fig. 4.9. However, GPA outperforms other schemes even for a significant increase in the throughput requirement. Fig. 4.9 further shows that outage probability increases more rapidly for higher throughput requirement. The results are plotted without making any assumptions on the acceptable outage limit. This figure also presents the trade-off between the two QoS parameters, namely, throughput requirement and acceptable outage probability of the system. Fig. 4.9 can be used to find upper bound on the throughput guarantee that can be satisfied for a certain outage limit and vice-versa for a given Pmax . For example, for Pmax = 6 W and maximum outage probability of 10%, UPA can handle the throughput requirement of up to 0.85 bit/s/Hz, whereas GPA can satisfy the requirements of as much as 1 bit/s/Hz in the considered simulation scenario. For a fixed Pmax , average throughput of UPA and TMPA monotonically decrease with increase in Rmin because of the increase in QoS outage. This is depicted in Fig. 4.10. In contrary, average throughput for GPA first increases with increase in Rmin , attains a peak and starts decreasing. For lower Rmin , throughput offered by GPA is lower in order to offer  131  38 GPA  36  TMPA UPA  QoS Outage (%)  34 32  Rmin = 1.5 bit/s/Hz  30 28 26 24 22 20 4.5  5  5.5  6  6.5  Maximum Total Transmit Power, Pmax (W)  Figure 4.8: QoS outage for different Pmax .  132  7  7.5  60 GPA TMPA  QoS Outage (%)  50  UPA  40 30 20 Pmax = 6 W  10 0 0.75  1  1.25  1.5  1.75  Minimum Guaranteed Throughput, Rmin (bit/s/Hz)  Figure 4.9: Variation of QoS outage for different Rmin .  133  2  Throughput (bit/s/Hz)  2  1.5  GPA TMPA UPA GPANQ  1 Pmax = 6 W  0.5  0 0.75  1  1.25  1.5  1.75  Minimum Guaranteed Throughput, Rmin (bit/s/Hz)  Figure 4.10: Average throughput for different Rmin .  134  2  Power Per Unit Throughput (J/(bit/Hz))  3.2 3 2.8 2.6 GPA  2.4 2.2  TMPA  Pmax = 6 W  UPA GPANQ  2 1.8 1.6 1.4 0.75  1  1.25  1.5  1.75  Minimum Guaranteed Throughput, Rmin (bit/s/Hz)  Figure 4.11: Variation of energy efficiency for different Rmin .  135  2  a significant enhancement in green performance compared to UPA and TMPA. For higher Rmin , average throughput for GPA also decreases because of the outage. Therefore, it is observed in Fig. 4.11 that more power per unit throughput is required by GPA to satisfy more stringent QoS constraint. The performance gap between GPA and TMPA decreases with increase in throughput requirement because energy efficiency of TMPA and UPA improves for increased throughput requirement at the cost of rising outage and falling average throughput. As illustrated by Figs. 4.10 and 4.11, throughput and energy efficiency offered by GPANQ are independent of Rmin . The throughput of GPANQ is lowest among the considered power allocation schemes whereas the energy efficiency is better than TMPA and UPA but mediocre compared to GPA.  4.5 Green Performance Versus System Capacity In Section 4.4, we focused on green performance of relay-based CCN and formulated the problem to minimize J/bit. As discussed and observed in previous sections, minimization of J/bit generally degrades the capacity (throughput) of the network. Due to ever-growing traffic demand, network capacity has been a prime focus for most of the cellular operators. Achieving green communication at the cost of degraded overall system throughput may not be reasonable in practice. As a result, a trade-off between system capacity and energy efficiency is inevitable. In this section, we discuss about multi-objective problem formulation method [110] which can jointly optimize the energy efficiency and system capacity. This can be achieved by minimizing the total transmit power (Ps +Pr ) while maximizing throughput (minimizing its reciprocal) at the same time. Therefore, we can formulate a multi-objective optimization  136  problem as minimize {Ps , Pr }  fm (Ps , Pr ) = α f¯pwr (Ps, Pr ) + (1 − α ) f¯thr (Ps, Pr )  (4.10)  subject to (4.3), where the objective function consists of weighted sum of two separate functions: f¯pwr (Ps, Pr ) accounting for power consumption and f¯thr (Ps, Pr ) accounting for achievable throughput. 0 ≤ α ≤ 1 is a trade-off parameter which decides the relative priorities given to green performance and system throughput. Value of α higher than 0.5 assigns higher priority to green communication. In multi-objective optimization, it is essential to transfer the individual objective functions to a dimensionless entity and normalize their values [110]. Since 0 ≤ (Ps +Pr ) ≤ Pmax , the objective function f¯pwr (Ps , Pr ) can be formed by normalizing (Ps + Pr ) by Pmax . Similarly, due to the QoS constraint, we are interested in the throughput values such that 2 log(1+γ )  ≤  1 Rmin .  Therefore, f¯thr (Ps, Pr ) can be formed by first normalizing  1 2 log(1 + γ )  by Rmin and then taking its reciprocal to get a fair multi-objective optimization. Hence, the multi-objective function can be defined as fm (Ps, Pr ) = α  2Rmin (Ps + Pr ) + (1 − α ) . Pmax log(1 + γ )  (4.11)  As shown in Appendix F, log(1 + γ ) is strictly concave for γ ≥ 0.5. Since reciprocal of a positive concave function is convex, 1/ log(1 + γ ) is a convex function in (Ps , Pr ) for  γ ≥ 0.5. As α , Pmax , and Rmin are positive constants, and γ ≥ 0.5 for practical systems, objective function fm (Ps, Pr ) given by (4.11) is convex in (Ps, Pr ). Therefore, (4.10) is a convex optimization problem. 137  4.5.1 Performance Analysis We use the same system model and simulation environment as described in Section 4.4 for the performance analysis of the proposed multi-objective optimization based scheme. For such system, Figs. 4.12–4.14 demonstrate how the multi-objective optimization based power allocation results in a trade-off between the two performance parameters, namely, power consumption and achievable throughput, for various values of the trade-off parameter, α . It is observed in Fig. 4.12 that the average power consumption decreases with increase in α . Note that α = 1 corresponds to the power minimization scheme, which is also clear from (4.11). Consequently, the average system throughput decreases with increase in α and is highest for α = 0 which corresponds to the throughput maximization scheme. This is demonstrated in Fig. 4.13. Comparing the two plots in Figs. 4.12 and 4.13, it can be observed that the power consumption curve declines sharply with increase in α and quickly approaches its lower bound whereas the throughput curve declines at a comparatively slower rate. This means that the energy efficiency metric, J/bit, can be expected to decrease for increase in the value of α . However, as observed in Fig. 4.14, this is true for increase in α only up to a limit. Within this limit, enhanced green performance may be achieved at the cost of decreased throughput. In contrary, the energy efficiency does not improve with increase in α beyond this limit. Therefore, only minimizing the total transmit power may not be the ultimate energyefficient solution. Finding a right balance between throughput and power consumption during the power allocation can significantly improve the throughput performance of a relay-based CCN while maintaining the J/bit metric. For example, for Pmax = 6 W and 138  Power Consumption for QoS Satisfaction (W)  4.5 4 Throughput maximization  3.5  Power-throughput trade-off Power minimization  3  Pmax = 6 W Rmin = 1.5 bit/s/Hz  2.5 2 0  0.2  0.4  0.6  0.8  1  Trade-off Parameter (α)  Figure 4.12: Variation of average power consumption with respect to trade-off parameter α .  139  1.7  Throughput (bit/s/Hz)  1.6  1.5  Throughput Maximization Power-throughput Trade-off Power Minimization  1.4  Pmax = 6 W Rmin = 1.5 bit/s/Hz  1.3  1.2  1.1  0  0.1  0.2  0.3  0.4 0.5 0.6 0.7 Trade-off Parameter (α)  0.8  0.9  1  Figure 4.13: Variation of average throughput with respect to trade-off parameter α .  140  Power Per Unit Throughput (J/(bit/Hz))  2.8 2.6 2.4  Throughput maximization Power-throughput trade-off  2.2  Power minimization  Pmax = 6 W Rmin = 1.5 bit/s/Hz  2 1.8 1.6 0  0.2  0.4  0.6  0.8  Trade-off Parameter (α)  Figure 4.14: Variation of energy efficiency with respect to trade-off parameter α .  141  1  Rmin = 1.5 bit/s/Hz, Fig. 4.14 shows that, though only by a small margin, energy efficiency metric is minimum at α = 0.7, meaning that the system is more energy-efficient than power minimization scheme for this choice of α in this particular scenario. The energy efficiency metric does not change much for values of α above 0.6. Compared to α = 1 (power minimization), α = 0.6 provides 4.07% higher throughput (see Fig. 4.13) without any penalty on energy efficiency metric while α = 0.5 provides 12.42% increase in throughput with only 2.92% deterioration in energy efficiency metric. It should be noted that system outage is independent of α . This is because as long as optimization problem (4.10) is feasible, there is no outage. Since the feasibility of the problem is independent of α (which is clear from (4.3)), the trade-off parameter has no effect on the QoS outage.  4.6 Conclusion In this chapter, we argued that implementation of relay-based cooperative transmission in cellular network can be an economical and easier approach to enable green communication which requires minimal modification in existing cellular infrastructure. Transmit power required per unit achievable throughput was considered as the main green performance metric. We investigated the potential of resource allocation in enhancing green performance and studied an energy-efficient resource allocation scheme for downlink transmission in fixed relay–based CCN. The proposed GPA scheme minimizes the power per unit throughput while fulfilling the QoS in terms of minimum throughput guarantee. Simulation results showed that GPA outperforms other schemes such as throughput maximization and uniform power allocation, and helps in enabling green communication with QoS guarantee. It was also observed that maximizing green performance generally degrades the over-  142  all system throughput. Since higher system capacity is a crucial factor in practical cellular networks, a balance between green performance and system capacity is inevitable. Therefore, trade-off between these two parameters was analyzed by introducing a design parameter (trader-off factor) in a multi-objective optimization–based resource allocation scheme. It was also shown that only minimizing the total transmit power may not be the ultimate energy-efficient solution; finding a right balance between throughput and power consumption can significantly improve the throughput performance of a relay-based CCN while maintaining the J/bit metric. The trade-off factor provides extra flexibility to wireless operators in obtaining this balance based on the requirements.  143  Chapter 5 Conclusions and Directions for Future Work 5.1 Conclusions In this thesis, we have studied various resource allocation mechanisms for next generation wireless communication technologies to improve the efficient utilization of available resources. We have made following four major contributions in this thesis. First, we have developed a novel precoder design method for power allocation between multiple data streams at multi-antenna base station (BS) and relay station (RS). The precoders have been designed by using joint zero-forcing (ZF) strategy in order to avoid multiuser interference (MUI) in the signal received by mobile stations (MSs) via both the direct and relay links. Most of the existing methods in the literature ignore the transmission via direct link while performing power allocation. From our study, it was found that accounting for the direct link transmission during power allocation is very important, especially when the relays are not along the direct path between BS and MS. This is a more practi144  cal scenario for real wireless communication networks. The proposed method is useful in providing quality of service (QoS) guarantee to cell-edge MSs. Second, we have studied optimal power allocation scheme followed by various low complexity suboptimal relay selection strategies to maximize the overall system throughput in a cooperative communication network (CCN) with multiple single-antenna relays. Optimal scheme maximizes the system throughput by selecting higher number of relays and allocating power to relays within the given total relay power constraint. In practice, simultaneously selecting more relays increases the computational and hardware complexity of destination node. Therefore, we have proposed simpler schemes which select less number of relays. The suboptimal schemes can achieve near-optimal system throughput with lower system complexity. Third, we have developed an optimal power allocation scheme for multicarrier cognitive radio (CR) network consisting of multi-antenna secondary users (SUs). CR has been characterized as intelligent wireless system that can adapt to changing network characteristics for spectrum reuse without causing harmful interference. Conventional power allocation algorithms existing in the literature for multiple-input multiple-output (MIMO) systems cannot be used directly to MIMO-CR scenario since those schemes may not contain the interference to primary users (PUs) within regulatory limits. We have shown that introduction of such interference constraint in conventional method such as uniform power allocation degrades the system performance in terms of channel capacity. Compared to the existing schemes, the proposed scheme significantly increases achievable CR channel capacity while satisfying the regulatory constraints on interference to legacy users. Finally, we have developed a power allocation scheme for green communication. The proposed green power allocation (GPA) scheme improves the energy efficiency of the net-  145  work by minimizing transmit power required per unit achievable throughput. We have analyzed the benefits and implementation challenges of relay-based approach to enable green communication. Our approach for green communication in this work has been on an algorithmic and protocol design level instead of energy-efficient design of device-circuitry. We have shown that the method developed in this thesis can be used to satisfy a QoS requirement of the MS in terms of minimum data-rate guarantee while making the system more energy-efficient compared to existing power allocation schemes. We have also developed a multi-objective optimization based model to analyze the tradeoff between the energy and spectral efficiency of the system and introduced a trade-off parameter which can be configured to choose the system operating point on the trade-off curve. This provides flexibility to wireless operator to tune the system performance as per the requirement. Since the research conducted for this thesis is not based on any specific wireless communication standard or protocol, the methods and algorithms developed in this thesis are applicable to broad range of wireless communication systems. For example, relay-based cooperation is already considered as an integral part in modern wireless cellular standards such as 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE) and LTE-Advanced [17, 18, 19], and IEEE 802.16 family of standards (commonly known as WiMAX) [20]. In addition, the requirement to be able to support MS-relaying for emergency responders during disaster rescue and recovery situations has been recently identified by 3GPP [24] as Federal Communications Commission (FCC) has announced LTE to be the communication standard for the United States nationwide public safety network [25, 26]. Since the standards in general allow resource allocation algorithms to be implemented by the operators according to their choice, the new methods and algorithms developed in this thesis for improving spectral as well as energy efficiency of CCN can be applied to these  146  systems. Similarly, since orthogonal frequency division multiplexing (OFDM) has been adopted for the recent CR standard IEEE 802.22 [10] (in addition to the other standards mentioned above), the power allocation method proposed in this thesis for multicarrier CR possesses high potential for its application in real implementation of next generation wireless systems.  5.2 Future Work The results of the research conducted in this thesis not only have important future applications, they have also exposed us to various other interesting challenges for further research. Some possible research directions that can follow from this thesis are briefly described below.  5.2.1 Cooperative CR Network As discussed before, relay-based CCN can improve throughput and coverage, improve energy saving performance at the mobile devices, increase reliability in transmission, and decrease overall interference in the network, to name a few of the advantages. On the other hand, CR is promising in providing spectral efficiency by opportunistically utilizing the spectrum holes in licensed bands. Therefore, combination of cooperative communication techniques and CR technology may further improve the spectral efficiency. The latest research in these areas is moving towards implementing cooperation in CR networks. Cooperative spectrum sensing in CR based on game theoretic approaches has been studied in [111]. Cooperation between SUs and PUs is also possible to benefit indirectly by finishing the PU’s transmission task sooner thereby increasing the chances of SUs to get opportunistic spectrum access [112], such as in [113]. Relay-based cooperation  147  is also possible among the SUs only. In such system, the transmission between the SUs may be performed with the help of relay SUs to harvest the advantages of cooperation for themselves directly. This integration of cooperative and cognitive transmission brings various challenges and introduces a variety of research possibilities. For example, consider a multi-carrier based cooperative CR network where the SU relay stations employ multiple antennas. In such scenario, in addition to total transmit power constraints at SU nodes (source node and relays), interference to PU due to source and relay SUs should be considered. One optimization criterion could be to maximize capacity of MIMO channel between SUs. This criterion generally favors the nodes with better channel conditions. To promote cooperation, other criteria may be based on fairness and guaranteed QoS for cooperating nodes.  5.2.2 Effect of Uncertainty in Channel State Information In this thesis, we have assumed that perfect and timely knowledge about the channel state information (CSI) is available during the radio resource allocation procedure. Such assumptions have limited impact in slow mobility scenario and/or slow fading environment. However, this may not be the case in dynamically changing radio environment. Error in channel estimation at the receiver and/or the delay in CSI feedback from the receiver to transmitter can result in imperfect CSI. An exciting future research will be to extend the methods presented in this thesis to incorporate the scenario of imperfect CSI. For example, the imperfectness of the CSI can be modelled as presence of zero-mean Gaussiandistributed uncertainty (additive estimation errors) in the channel coefficients. Relevant bounds of corresponding performance metrics, e.g., lower bounds of the achievable channel capacity and upper bounds of the system outage, can be studied.  148  5.2.3 Green CR Network In Chapter 4, we studied various issues and challenges to enabling green communication in wireless communication systems. We analyzed relay-based cooperation as one of the ways to enable green communication. As further work, enabling green communication in CR networks can be studied. CR technology requires frequent sensing of the radio spectrum and processing of the sensor data which would require additional computational energy. Therefore, it is necessary to design energy-efficient sensing schemes so that improvement in data rate due to opportunistically acquired spectrum can justify the increase in the energy consumption. 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IEEE GLOBECOM’11, Dec. 2011, pp. 1–6. → page(s) 147 [112] Q. Zhang, J. Jia, and J. Zhang, “Cooperative relay to improve diversity in cognitive radio networks,” IEEE Commun. Mag., vol. 47, no. 2, pp. 111–117, Feb. 2009. → page(s) 147 [113] X. Hao, M. H. Cheung, V. Wong, and V. Leung, “A stackelberg game for cooperative transmission and random access in cognitive radio networks,” in Proc. IEEE PIMRC’11, Sep. 2011, pp. 411–416. → page(s) 147  160  Appendix A List of Publications Journal Publications [J1] U. Phuyal, S. C. Jha, and V. K. Bhargava, “Joint zero-forcing based precoder design for QoS-aware power allocation in MIMO cooperative cellular network,” IEEE J. Sel. Areas Commun., vol. 30, no. 2, pp. 350–358, Feb. 2012. [J2] C.-Y. Chiang, U. Phuyal, and V. K. Bhargava, “Power allocation in two-dimensional superposition modulation based cooperative wireless communication system,” IEEE Trans. Commun., vol. early access, pp. 1–9, 2012. [J3] R. Devarajan, S. C. Jha, U. Phuyal, and V. K. Bhargava, “Energy-aware resource allocation for cooperative cellular network using multi-objective optimization approach,” IEEE Trans. Wireless Commun., vol. 11, no. 5, pp. 1797–1807, May 2012. [J4] S. C. Jha, U. Phuyal, M. M. Rashid, and V. K. Bhargava, “Design of OMC-MAC: An opportunistic multi-channel MAC with QoS provisioning for distributed cognitive radio networks,” IEEE Trans. Wireless Commun., vol. 10, no. 10, pp. 3414–3425, 161  Oct. 2011. [J5] Z. Hasan, U. Phuyal, V. Yadav, A. Chaturvedi, and V. K. Bhargava, “ISI-free pulses for high-data-rate ultra-wideband wireless systems,” Canadian J. Elect. Comput. Eng., vol. 32, no. 4, pp. 187–192, Fall 2007.  Book Chapter [B1] U. Phuyal, S. C. Jha, and V. K. Bhargava, “Resource allocation for green communication in relay-based cellular networks,” in Green Radio Communication Networks, E. Hossain, V. K. Bhargava, and G. Fettweis, Eds. Cambridge: UK, 2012, pp. 331– 356.  Conference Proceedings [C1] U. Phuyal, S. C. Jha, and V. K. Bhargava, “QoS guaranteed resource allocation in cooperative cellular network with MIMO-based relays,” in Proc. IEEE ICC’11, June 2011, pp. 1–6. [C2] U. Phuyal, S. C. Jha, and V. K. Bhargava, “Optimal and suboptimal relay selection and power allocation in multi-relay cooperative network,” in Proc. AH-ICI’11, Nov. 2011, pp. 1–6. [C3] U. Phuyal, S. C. Jha, and V. K. Bhargava, “Green resource allocation with QoS provisioning for cooperative cellular network,” in Proc. IEEE CWIT 2011, May 2011, pp. 206–210. [C4] U. Phuyal, A. Punchihewa, V. K. Bhargava, and C. Despins, “Power loading for multicarrier cognitive radio with MIMO antennas,” in Proc. IEEE WCNC’09, Apr. 2009, 162  pp. 1–5. [C5] C.-Y. Chiang, U. Phuyal, and V. K. Bhargava, “Two-dimensional superposition modulation and power allocation for cooperative wireless communication system,” in Proc. IEEE GLOBECOM 2011, Dec. 2011, pp. 1–6. [C6] S. C. Jha, U. Phuyal, and V. K. Bhargava, “Joint power and subcarrier allocation in multi-hop OFDMA network: A cross-layer approach,” in Proc. AH-ICI’11, Nov. 2011, pp. 1–6. [C7] S. C. Jha, U. Phuyal, and V. K. Bhargava, “Cross-layer resource allocation approach for multi-hop distributed cognitive radio network,” in Proc. IEEE CWIT 2011, May 2011, pp. 211–215. [C8] R. Devarajan, S. C. Jha, U. Phuyal, and V. K. Bhargava, “Energy-aware user selection and power allocation for cooperative communication system with guaranteed qualityof-service,” in Proc. IEEE CWIT 2011, May 2011, pp. 216–220. [C9] G. Bansal, M. J. Hossain, P. Kaligineedi, H. Mercier, C. Nicola, U. Phuyal, M. M. Rashid, K. C. Wavegedara, Z. Hasan, M. Khabbazian, and V. K. Bhargava, “Some research issues in cognitive radio networks,” in Proc. AFRICON 2007, Sep. 2007, pp. 1–7.  163  Appendix B Derivation of γk in (2.12) For maximal ratio combining (MRC) at the receiver, total SNR at the kth MS can be expressed as  γk = γBM,k + γRM,k ,  (B.1)  where γBM,k and γRM,k are SNRs due to BS–MS and RS–MS paths respectively. From (2.5) and (2.10), γBM,k = λk , as the receiver noise is assumed to be distributed with unit variance. Similarly, from (2.9) and (2.11),  γRM,k =  λ k qk . qk hTk 2 + 1  Substituting these results on (B.1), we get (2.12).  164  Appendix C Quasi-concavity of γk Given by (2.12) We can prove the quasi-concavity of γk , given by (2.12), by calculating determinants of its bordered Hessians [107, §3.4], which are given by  D1 =  0  ∂ γk ∂ λk  ∂ γk ∂ λk  ∂ 2 γk ∂ λk2  qk + hTk 2 qk + 1 hTk 2 qk + 1  =−  2  (C.1)  and  D2 =  =  0  ∂ γk ∂ λk  ∂ γk ∂ qk  ∂ γk ∂ λk  ∂ 2 γk ∂ λk2  ∂ 2 γk ∂ λk ∂ qk  ∂ γk ∂ qk  ∂ 2 γk ∂ qk ∂ λk  ∂ 2 γk ∂ q2k  2λk ( hTk  hTk 2 qk + 1) , ( hTk 2 qk + 1)4  2 + 1)(q  k+  (C.2)  respectively. We see that D1 < 0 and D2 > 0 as qk ≥ 0 and λk > 0 for non-zero power transmission to kth MS. Therefore, γk is quasi-concave in (λk , qk ) [107, §3.4]. 165  Appendix D Solution of Problem P2 Defined in (2.24)–(2.27) The Lagrangian of P2 defined in (2.24)–(2.27) is given by L (λ U , qU , µ U , ν ) = f (λ U , qU ) + ∑ µi (γi,min − γi ) i∈U  +ν  ∑ λi  i∈U  gBM,i  2  − P˜B,max ,  (D.1)  where µ U and ν are the Lagrange multipliers. Constraint (2.25) is independent for individual users. Since we are interested in minimizing weighted sum of squares of λi and qi , and since γi increases monotonically with λi and qi , we can show that (2.25) becomes tight at the optimal point. Therefore, representing the values of individual variables at the optimal solution of P2 by (·)∗ , we can write the  166  Karush-Kuhn-Tucker (KKT) conditions when α = 0 as  λi∗ +  λi∗ q∗i = γi,min , q∗i hTi 2 + 1  ∀i ∈ U,  (D.2)  2  ≤ P˜B,max ,  (D.3)  q∗U  0,  ν ∗ ≥ 0,  (D.4)  2  − P˜B,max  ∑ λi∗  gBM,i  i∈U  λ ∗U ν∗  ∑ λi∗  0,  gBM,i  i∈U  ∂L ∂ λi  λ =λ∗∗ q=q  = −µi∗ 1 +  q∗i q∗i  + ν ∗ gBM,i  hTi 2 + 1  2  = 0,  = 0,  (D.5)  ∀i ∈ U,  (D.6)  and  ∂L ∂ qi  λ =λ∗∗ q=q  = 2q∗i −  µi∗ λi∗ q∗i hTi  2+1 2  = 0,  ∀i ∈ U.  (D.7)  It is clear from (D.2) that λi∗ ≤ γi,min. Eq. (D.2) can further be written as  λi∗ = γi,min  q∗i hTi 2 + 1 q∗i hTi 2 + q∗i + 1  ,  ∀i ∈ U.  (D.8)  Equating the values of µi∗ from (D.6) and (D.7), and substituting the result of (D.8), we get 2q∗i (q∗i hTi  2  + q∗i + 1)2 = ν ∗ gBM,i 2 γi,min ,  ∀i ∈ U.  (D.9)  We know that when (2.20) does not hold, at least one q∗i will be positive. Also, λi∗ > 0 ∀i ∈ U. This means from (D.9) that ν ∗ = 0. This also implies that q∗i > 0 ∀i ∈ U.  167  Furthermore, from (D.5), (2.26) will also be tight at the optimal point, i.e.,  ∑ λi∗  gBM,i  2  = P˜B,max.  (D.10)  i∈U  The positive real q∗i obtained by solving (D.9) can be substituted to (D.8) to get λi∗ ∀i ∈ U. Finally, the value of ν ∗ can be obtained such that (D.10) is satisfied.  168  Appendix E Convexity of Problem (2.40) First, let us look at the objective function in (2.40). It is equivalent to N  f=  ∑ fk ,  (E.1)  k=1  where fk = −  αk βk Pk , αk Ps + βk Pk + 1  k = 1, . . . , N.  (E.2)  As αk , βk and Ps are all non-negative constants, the only optimization variable in fk is Pk . Differentiating fk twice w.r.t. Pk , we get ′′  fk =  2αk βk2 (αk Ps + 1) (αk Ps + βk Pk + 1)3  .  (E.3)  ′′  Since Pk ≥ 0 (due to second constraint in (2.40)), fk ≥ 0 in the feasible region. This means fk is convex for all k. Therefore, objective function f , which is summation of convex functions, is convex. As the first constraint is linear equality and second constraint represents a set of linear 169  inequalities, the feasible region of problem (2.40) is also convex. Therefore, problem (2.40) is a convex optimization problem.  170  Appendix F Concavity of l(Ps, Pr ) given by (4.7) The Hessian matrix of l(Ps, Pr ) given by (4.7) can be written as    Hl =     =  ∂ 2l ∂ Ps2  ∂ 2l ∂ Ps ∂ Pr  ∂ 2l  ∂ 2l ∂ Pr2  ∂ Pr ∂ Ps      β12 β12 − 2 (β1 Ps +β2 Pr +1) (β1 Ps +1)2 β1 β2 (β1 Ps +β2 Pr +1)2  β1 β2 (β1 Ps +β2 Pr +1)2 β22 β22 − 2 (β1 Ps +β2 Pr +1) (β2 Pr +1)2     .  (F.1)  The first order leading principal minor of the matrix Hl (which is the top-left element) is always negative because both β2 and Pr are positive, which results in first term being smaller than second term. The second order leading principal minor is the determinant of Hl , which can be written as  |Hl | =  β12 β22 (1 − ψ ) , (β1 Ps + 1)2 (β2 Pr + 1)2  171  (F.2)  where  ψ=  (β1 Ps + 1)2 + (β2 Pr + 1)2 . (β1 Ps + β2 Pr + 1)2  (F.3)  Therefore, we need ψ < 1 for |Hl | to be positive, which translates to the condition: 2β1 β2 PB PR > 1. This condition is satisfied when γ ≥ 0.5. In such case, the Hessian becomes negativedefinite [107, §3.2.2], and thus l(Ps , Pr ) will be strictly concave in (Ps, Pr ) [83, §3.1.4].  172  

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