Generalized Reduced-WMMSE Approach for Cell-Free Massive MIMO With Per-AP Power Constraints

TL;DR

This paper addresses the high computational burden of downlink beamforming optimization in cell-free mMIMO with per-AP power constraints. It introduces a generalized reduced-WMMSE (G-R-WMMSE) that partition-beams per AP and leverages block-coordinate descent and Lagrange duality to obtain closed-form subproblem solutions, enabling sequential and parallel implementations. The approach achieves substantial complexity savings (over 99%) while preserving near the same sum-rate performance as the conventional WMMSE method, outperforming simpler schemes like ZF and MRT. The parallel variant further accelerates computation with manageable performance trade-offs, making real-time cooperative beamforming in large-scale CF mMIMO more practical.

Abstract

The optimization of cooperative beamforming vectors in cell-free massive MIMO (mMIMO) systems is presented where multi-antenna access points (APs) support downlink data transmission of multiple users. Albeit the successes of the weighted minimum mean squared error (WMMSE) algorithm and their variants, they lack careful investigations about computational complexity that scales with the number of antennas and APs. We propose a generalized and reduced WMMSE (G-R-WMMSE) approach whose complexity is significantly lower than conventional WMMSE. We partition the set of beamforming coefficients into subvectors, with each subvector corresponding to a specific AP. Such a partitioning approach decomposes the original WMMSE problem across individual APs. By leveraging the Lagrange duality analysis, a closed-form solution can be derived for each subproblem, which substantially reduces the computation burden. Additionally, we present a parallel execution of the proposed G-R-WMMSE with adaptive step sizes, aiming at further reducing the time complexity. Numerical results validate that the proposed G-R-WMMSE schemes achieve over 99% complexity savings compared to the conventional WMMSE scheme while maintaining almost the same performance.

Figures (3)

• Figure 1: Average sum-rate versus the number of APs $M$ ($K=12$, $n_A=2$, $\text{SNR}^{\text{dl}} = 20$ dB, $\text{SNR}^{\text{ul}} = 10$ dB, and $L=10$).
• Figure 2: Average algorithm runtime versus the number of APs $M$ ($K=12$, $n_A=2$, $\text{SNR}^{\text{dl}} = 20$ dB, $\text{SNR}^{\text{ul}} = 10$ dB, $L=10$).
• Figure 3: Average weighted sum-rate versus the downlink SNR ($K=24$, $M=32$, $n_A=2$, $\text{SNR}^{\text{ul}} \in \{0, 10\}$ dB, and $L=20$).

Theorems & Definitions (1)

• Remark 1