In this paper, a game-theoretic model for studying power control for wireless data networks in frequency-selective multipath environments is analyzed. The uplink of an impulse-radio ultrawideband system is considered. The effects of self-interference and multiple-access interference on the performance of generic Rake receivers are investigated for synchronous systems. Focusing on energy efficiency, a noncooperative game is proposed in which users in the network are allowed to choose their transmit powers to maximize their own utilities, and the Nash equilibrium for the proposed game is derived. It is shown that, due to the frequency selective multipath, the noncooperative solution is achieved at different signal-to-interference-plus-noise ratios, depending on the channel realization and the type of Rake receiver employed. A large-system analysis is performed to derive explicit expressions for the achieved utilities. The Pareto-optimal (cooperative) solution is also discussed and compared with the noncooperative approach.
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