Linear Precoding Game for MIMO MAC With Dynamic Access Point Selection

This paper examines a non-cooperative game in precoding design for MIMO multiple-access channels with dynamic access point (AP) selection. This game is first shown to be a potential game, where the potential function is the sum rate achieved by successive interference cancellation. Due to the mixed-integer nature of the optimization variable, it is challenging to directly characterize the maximum 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 upperbounded properties of the potential function as a direct result of our 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 by-product of the established properties of the potential function which are materialized by an iterative waterfilling algorithm. Numerical results show that the algorithm is able to reach fast convergence and provides a system sum rate nearing that of the optimal centralized solution.