Max-Min Beamforming for Multi-User Massive MIMO Systems: An Alternating Projection-Based Approach

Abstract

We consider the problem of maximizing the minimum user achievable rate for downlink massive MIMO multi-user systems. The max-min formulation promotes fairness such that all users enjoy a similar quality of wireless service. Nevertheless, solving the max-min beamforming problem is challenging due to the max-min form of the objective function. A commonly used method to handle problems of this kind is the bisection method, which transforms the max-min problem into a sequence of feasibility-checking problems. Existing methods for solving the feasibility-checking problem do not scale well since they are usually involved with computing the inversion of a large matrix whose size scales quadratically with the number of users. To efficiently solve the feasibility-checking problem, we propose to reformulate the problem into a two-set feasibility checking problem, which can be efficiently solved via an averaged alternating reflection algorithm (AARA). The proposed AARA method has a fast convergence speed. Moreover, its computational complexity scales linearly with the number of users. Simulation results show that our proposed method significantly outperforms existing methods in terms of computational complexity.