A Two-Stage Majorization-Minimization Based Beamforming for Downlink Massive MIMO

In this paper, we investigate the transmit beamforming design for weighted sum-rate maximization in massive multiple-input multiple-output (MIMO) downlink systems. Currently, the most popular algorithm for this scenario is the weighted minimum mean square error (WMMSE) algorithm. We propose a two-stage majorization-minimization (MM) based beamforming (dubbed TMMBF) which transforms the weighted sum-rate maximization problem into a quadratic convex problem by utilizing the MM method twice. The proposed algorithm converges to a stationary point of the weighted sum-rate maximization problem. Interestingly, we find that the WMMSE algorithm is a special case of the TMMBF algorithm, thus unifying the WMMSE algorithm into the MM framework for the first time. In addition, the surrogate function of TMMBF is tighter than that of WMMSE, resulting in faster convergence of the TMMBF algorithm. The simulation results on 3GPP channel models generated from Quadriga show that the TMMBF algorithm has better performance and faster numerical convergence compared to the WMMSE algorithm.