Energy-Efficient MIMO Multiuser Systems: Nash Equilibrium Analysis

TL;DR

This paper analyzes energy efficiency in MIMO multiuser systems, proving the existence and uniqueness of Nash Equilibrium, and proposes an efficient, easy-to-implement algorithm that outperforms classical methods in certain scenarios.

Contribution

It introduces a bisection search algorithm for finding the unique NE in energy-efficient MIMO MAC systems, with demonstrated advantages over traditional fractional programming approaches.

Findings

The NE exists and is unique in the considered game.

The proposed algorithm is more efficient and easier to implement than classical methods.

The policy found, even if not the NE, Pareto-dominates the NE in 2-user cases.

Abstract

In this paper, an energy efficiency (EE) game in a MIMO multiple access channel (MAC) communication system is considered. The existence and the uniqueness of the Nash Equilibrium (NE) is affirmed. A bisection search algorithm is designed to find this unique NE. Despite being sub-optimal for deploying the $\varepsilon$-approximate NE of the game when the number of antennas in transmitter is unequal to receiver's, the policy found by the proposed algorithm is shown to be more efficient than the classical allocation techniques. Moreover, compared to the general algorithm based on fractional programming technique, our proposed algorithm is easier to implement. Simulation shows that even the policy found by proposed algorithm is not the 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 at least for 2-user situation.