Game theoretic power allocation for fading MIMO multiple access channels with imperfect CSIR

In this paper, we formulate the power allocation (PA) problem for uplink of MIMO fading multiple access channels using a game theoretic framework with channel estimation error at receiver side. We investigate the effect of the error on derived PA policy and on performance of the system. Furthermore, it is assumed that the CSI at transmitter side is imperfect i.e., each transmitter is informed with the statistics of the channels instead of the instantaneous channel states. We use lower bound of mutual information between each user and the base station to derive a utility function for the concave game, regarding the channel estimation error. Following the formulation of problem, existence and uniqueness of the game’s equilibrium are investigated and it is proved that the proposed game has a unique Nash equilibrium (NE). Also a primal-dual subgradient based best-response algorithm is designed to find the NE. The algorithm updates the policy of each player regarding the given policy of other players, at each iteration. Finally, simulation results of the achieved PA policy are illustrated to investigate the effect of channel estimation error. In particular, simulations show that the overall system performance will be improved when channel estimation error in modeling the PA game is considered.