Game theory for precoding in a multi-user system: Bargaining for overall benefits

A precoding strategy for multi-user spectrum sharing over an interference channel is proposed and analyzed from a game-theoretic perspective. The proposed strategy is based on finding the Nash bargaining solution for precoding matrices in a cooperative scenario over frequency selective channels under a spectrum mask constraint. An in-time update of the precoding matrices is enabled by using time slots to guarantee the effectiveness of the bargaining solution when the number of users varies. A dual decomposition approach is exploited to construct a distributed structure for solving the bargaining problem. The proposed distributed algorithm realizes the physical process of bargaining, which is not present in the Nash bargaining theory.