A Stochastic Proximal WMMSE for Ergodic Sum Rate Maximization

We consider ergodic weighted sum rate (WSR) maximization in a massive multi-user multiple-input multiple-output system. Existing solutions iteratively minimize the average WSR based on all the historical information, and use bisection search to satisfy the power constraint at each iteration, resulting in both high storage burden and high computational complexity. In contrast, we propose an efficient stochastic proximal weighted minimum mean-square error (SPWMMSE) algorithm, which updates the precoder only based on the current single channel realization, without checking the power constraint at each iteration. Furthermore, we propose a novel proximal term to incorporate all the previous channel and surrogate function information in precoder updates. Our analysis shows that SPWMMSE converges to the stationary point of the original ergodic WSR maximization problem almost surely. Simulation results demonstrate the effectiveness of SPWMMSE over the current best alternatives.