An Accelerated Mixed Weighted-Unweighted MMSE Approach for MU-MIMO Beamforming

TL;DR

This paper introduces A-MMMSE, a GPU-friendly, fast-converging algorithm for MU-MIMO beamforming that maintains optimal performance while significantly reducing computational complexity.

Contribution

It proposes a novel block coordinate gradient descent algorithm with warm-start strategy, eliminating matrix inversions for efficient MU-MIMO precoding.

Findings

Achieves WSR performance comparable to WMMSE and reduced-WMMSE.

Reduces computational time significantly across various system setups.

Converges to a stationary point efficiently.

Abstract

Precoding design based on weighted sum-rate (WSR) maximization is a fundamental problem in downlink multi-user multiple-input multiple-output (MU-MIMO) systems. While the weighted minimum mean-square error (WMMSE) algorithm is a standard solution, its high computational complexity--cubic in the number of base station antennas due to matrix inversions--hinders its application in latency-sensitive scenarios. To address this limitation, we propose a highly parallel algorithm based on a block coordinate descent framework. Our key innovation lies in updating the precoding matrix via block coordinate gradient descent, which avoids matrix inversions and relies solely on matrix multiplications, making it exceptionally amenable to GPU acceleration. We prove that the proposed algorithm converges to a stationary point of the WSR maximization problem. Furthermore, we introduce a two-stage warm-start strategy grounded in the sum mean-square error (MSE) minimization problem to accelerate convergence. We refer to our method as the Accelerated Mixed weighted-unweighted sum-MSE minimization (A-MMMSE) algorithm. Simulation results demonstrate that A-MMMSE matches the WSR performance of both conventional WMMSE and its enhanced variant, reduced-WMMSE, while achieving a substantial reduction in computational time across diverse system configurations.