This paper is focused on the cross-layer design problem of joint multiuser detection and power control for energy-efficiency optimization in wireless data networks through a game-theoretic approach. Unlike previous studies in this area, which have considered the application of game theory to achieve energy-efficiency in idealized synchronous code division multiple access systems, more realistic assumptions including system asynchronism, the use of band-limited chip-pulses, and the multipath distortion induced by the wireless channel are explicitly incorporated in the development of this paper. Several noncooperative games are proposed wherein each user may vary its transmit power and uplink receiver in order to maximize its utility, which is defined here as the ratio of data throughput to transmit power. In particular, the case in which a linear multiuser detector is adopted at the receiver is considered first, and then, the more challenging case in which a nonlinear decision feedback multiuser detector is employed is considered. Via large system analysis (LSA), a decentralized implementation of the power allocation game requiring very little prior information on the interference background is proposed. LSA is also used to compare the energy efficiency of several linear multiuser detectors, and to obtain the optimal (i.e., utility-maximizing) length of the training sequence of each data frame. Numerical results show the effectiveness of the proposed solutions, as well as a very satisfactory agreement of the LSA-based analysis with simulation results obtained for systems with finite (and not so large) numbers of users.
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