A Game-Theoretical Approach for Energy Efficiency in Multiuser MIMO System.

The game-theoretic analysis of Energy Efficiency (EE) game is known to be difficult due to the non-convexity of EE-utility, especially for tracing the Nash Equilibrium in MIMO system. In this paper, The existence and the uniqueness of the Nash Equilibrium (NE) is affirmed for a MIMO multiple access channel (MAC) communication system and a bisection search algorithm is designed to find this unique NE. Despite being sub-optimal for deploying approximate best response, the policy found by the proposed algorithm is shown to be more efficient than the classical allocation techniques. Simulation shows that even the policy found by proposed algorithm might not be the exact NE of the game, the deviation w.r.t. to the exact NE is small and the resulted policy actually Pareto-dominates the unique NE of the game.