  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 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, respectively of the channel
realization. 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.
