ABSTRACT
Contents 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
8.1.1 Noncooperative Game Theoretical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 8.2 Power Allocation Games in Multiple Access Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
8.2.1 Static Multiple Access Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 8.2.1.1 Single Input Single Output Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 8.2.1.2 Multiple Output Multiple Input Links. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
8.2.2 Fast Fading Single Input Single Output Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 8.2.3 Fast Fading Multiple Input Multiple Output Channels . . . . . . . . . . . . . . . . . . . . . . . . . . 170
8.2.3.1 Single User Decoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 8.2.3.2 Successive Interference Cancelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
8.3 Power Allocation Games in Interference Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 8.3.1 Static Frequency Selective SISO Interference Channels . . . . . . . . . . . . . . . . . . . . . . . . . . 176 8.3.2 Static Parallel Interference Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 8.3.3 Static MIMO Interference Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
8.4 Power Allocation Games beyond the MAC and IC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 8.4.1 Static Parallel Interference Relay Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 8.4.2 Static MIMO Cognitive Radio Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
8.5 Conclusion and Open Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
This chapter is dedicated to the study of distributed resource allocation problems in wireless communication networks. Noncooperative game theory proves to be a useful tool to investigate this type of problems. The players, the transmitter nodes, choose their power allocation (PA) policies in order to maximize their own information theoretical payoffs, namely, their individual achievable Shannon transmission rates. Our attention is mainly focused on two basic multiuser channel models: the multiple access channel (MAC) and the interference channel (IC). However, more complex channels such as the interference relay channel (IRC) and the cognitive radio channel (CRC) are also discussed. We provide an updated overview of the existing results with respect to the noncooperative solution of the game, the Nash equilibrium (NE): its existence, uniqueness, and convergence of distributed algorithms. Furthermore, we evaluate the performance gap between the NE point and the centralized solution where the network authority dictates the allocation policy of the overall network resources. We also discuss several methods that can improve the performance at the NE while introducing a supplementary cost in terms of signaling. We conclude with a critical discussion about the drawbacks and possible improvements of the game theoretical approach to solve resource allocation problems in general.
