  In this contribution, the performance of a multi-user system is analyzed in
the context of frequency selective fading channels. Using game theoretic tools,
a useful framework is provided in order to determine the optimal power
allocation when users know only their own channel (while perfect channel state
information is assumed at the base station). We consider the realistic case of
frequency selective channels for uplink CDMA. This scenario illustrates the
case of decentralized schemes, where limited information on the network is
available at the terminal. Various receivers are considered, namely the Matched
filter, the MMSE filter and the optimum filter. The goal of this paper is to
derive simple expressions for the non-cooperative Nash equilibrium as the
number of mobiles becomes large and the spreading length increases. To that end
two asymptotic methodologies are combined. The first is asymptotic random
matrix theory which allows us to obtain explicit expressions of the impact of
all other mobiles on any given tagged mobile. The second is the theory of
non-atomic games which computes good approximations of the Nash equilibrium as
the number of mobiles grows.
