Bayesian equilibria in slow fading OFDM systems with partial channel state information

We consider a slow frequency selective fading multiple access channel (MAC) where 2 independent transmitters are simultaneously communicating with a receiver using orthogonal frequency division multiplexing (OFDM) over N subcarriers. Each transmitter has partial knowledge of the channel state. In such a context, the system is inherently impaired by a nonzero outage probability. We propose a low complexity distributed algorithm for joint rate and power allocation aiming at maximizing the individual throughput, defined as the successfully-received-information rate, under a power constraint. As well known, the problem at hand is non-convex with exponential complexity in the number of transmitters and subcarriers. Inspired by effective almost optimum recent results using the duality principle, we propose a low complexity distributed algorithm based on Bayesian games and duality. We show that the Bayesian game boils down to a two-level game, referred to as per-subcarrier game and global game. The per-subcarrier game reduces to the solution of linear system of equations while the global game boils down to the solution of several constrained submodular games. The provided algorithm determines all the possible Nash equilibria of the game, if they exist.