Joint access point selection and linear precoding game for MIMO multiple-access channels

In this paper, the problem of joint access point (AP) selection and linear precoding for multiple-input multiple-output orthogonal frequency division multiplexing systems is studied in the framework of a non-cooperative game. This game is shown to be a potential game with the potential function being the sum rate achieved by successive interference cancellation. Due to the mixed-integer nature of the optimization variables, it is difficult, if not impossible, to directly characterize the maxima of the potential function, which are closely related to the Nash equilibrium (NE) of the game. Instead, we establish the existence and achievability of the maximum through non-decreasing and upper-bounded properties of the potential function as a direct result of the proposed update scheme. A distributed algorithm is designed where each player selfishly optimizes its AP selection and linear precoding strategy in a sequential manner. Convergence is a byproduct of the established properties of the potential function which are materialized by an iterative water-filling algorithm. Numerical results show that the algorithm is able to reach fast convergence, scale linearly with the number of users in terms of complexity, and provides a practical system sum rate at the NE nearing that of the optimal centralized solution.