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Preface; Contents; Notations and Symbols; Abbreviations; 1 Introduction; 1.1 Motivation; 1.2 Formulating Resource Allocation Problems; 1.3 Mathematical Background; 1.3.1 Stochastic Robust Optimization; 1.3.2 Worst-Case Robust Optimization; 1.3.2.1 General Norm; 1.3.2.2 Polyhedron Model; 1.3.3 Hybrid Approach: Bounded Uncertainty and Probabilistic Constraints; 1.3.3.1 Chance-Constrained Approach; 1.3.3.2 D-Norm Approach; 1.4 Generic System Model; 1.4.1 System Model for Wireless Networks with Homogeneous Users; 1.4.2 System Model for Wireless Networks with Heterogeneous Users.

1.4.2.1 Underlay Cognitive Radio Network1.4.2.2 Wireless Networks with Heterogeneous Users in Unlicensed Bands; 1.4.3 Physical Layer Security in Wireless Channels; 1.5 Cost of Robustness; 1.6 Organization of This Book; References; 2 Robust Cooperative Resource Allocation; 2.1 Introduction; 2.2 Single-Channel Cellular Cognitive Radio Networks; 2.2.1 Robust Problem; 2.2.1.1 Iterative Algorithm for Solving Nominal and Robust Problems; 2.2.1.2 Reduced Throughput in Robust Solution; 2.2.1.3 Distributed Robust Solutions and Extra Message Passing; 2.2.1.4 Infrequent Message Passing.

2.3 Multi-channel Cognitive Radio Networks2.3.1 Robust Problems; 2.3.1.1 Social Utility of Robust Solutions Versus Uncertainty Levels; 2.3.2 Trade-Off Algorithms; 2.3.2.1 Trade-Off in D-Norm Approach; 2.3.2.2 Trade-off in Chance-Constrained Approach; 2.4 Overview of Other Works on Robust Cooperative Resource Allocation; 2.5 Concluding Remarks; Appendices; Appendix 1: Proof of Proposition 2.2; Appendix 2: Convexity of (9); Appendix 3: Proof of Proposition 2.3; Appendix 4: Proof of Lemma 2.1; Appendix 5: Proof of Proposition 2.4; Appendix 6: Proof of Lemma 2.2; Appendix 7: Proof of Lemma 2.3.

3.3.1.2 Social Utility (Sum Rate)3.3.1.3 Distributed Algorithms; 3.3.1.4 Overview of Other Works on Robust Noncooperative Games with Homogeneous Users; 3.3.2 Robust Power Control in Noncooperative CRNs; 3.3.2.1 Existence and Uniqueness of RNE; 3.3.2.2 Social Utility (Sum Rate); 3.3.2.3 Distributed Algorithms; 3.3.2.4 Overview of Other Works on Robust Noncooperative CRNs; 3.3.3 Robust Power Control for Noncooperative Heterogeneous Users; 3.3.3.1 Robust Stackelberg Games; 3.3.3.2 Single-Leader/Single-Follower Robust Stackelberg Games; 3.3.3.3 Multi-user Stackelberg Games.

Appendix 8: Proof of Proposition 2.5References; 3 Robust Noncooperative Resource Allocation; 3.1 Introduction; 3.2 Overview of Nominal Noncooperative Strategic Games; 3.2.1 Existence and Uniqueness of NE; 3.2.1.1 Existence of NE; 3.2.1.2 Uniqueness of NE; 3.2.1.3 Existence and Uniqueness of NE in Nominal Noncooperative Power Control Games with Homogeneous Users; 3.2.2 Social Utility (Sum Rate) at NE; 3.2.3 Distributed Algorithms; 3.3 Worst-Case Robust Power Control in Noncooperative Games; 3.3.1 Robust Power Control for Noncooperative Homogeneous Users; 3.3.1.1 Existence and Uniqueness of RNE.

This book presents state-of-the-art research on robust resource allocation in current and future wireless networks. The authors describe the nominal resource allocation problems in wireless networks and explain why introducing robustness in such networks is desirable. Then, depending on the objectives of the problem, namely maximizing the social utility or the per-user utility, cooperative or competitive approaches are explained and their corresponding robust problems are considered in detail. For each approach, the costs and benefits of robust schemes are discussed and the algorithms for reducing their costs and improving their benefits are presented. Considering the fact that such problems are inherently non-convex and intractable, a taxonomy of different relaxation techniques is presented, and applications of such techniques are shown via several examples throughout the book. Finally, the authors argue that resource allocation continues to be an important issue in future wireless networks, and propose specific problems for future research.