Distributed power allocation game for uplink OFDM systems

In this paper, we consider the uplink of a single cell network with K users simultaneously communicating with a base station using OFDM modulation over N carriers. In such a scenario, users can decide their power allocation based on three possible Channel State Information(CSI) levels, which are called complete, partial and statistical. The optimal solutions for maximizing the average capacity with complete and statistical knowledge are known to be the water-filling game and the uniform power allocation respectively. We study the problem in the partial knowledge case. We formulate it as a strategy game, where each player (user) selfishly maximizes his own average capacity. The information structure that we consider is such that each player, at each time instant, knows his own channel state, but does not know the states of other players. We study the existence and uniqueness of Nash equilibrium. We find the optimal solution for the symmetric case considering two positive channel states, and we show the optimization problem for any L states.