  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.
