Low-rank Preconditioning in Beamspace Domain For Massive MU-MIMO Long-Term Beamforming

TL;DR

This paper introduces a low-rank preconditioning method using randomized eigenvalue decomposition to improve the efficiency of long-term beamforming in massive MU-MIMO systems, reducing computational complexity and energy consumption.

Contribution

It proposes a hardware-friendly preconditioning framework based on top eigenpairs and a randomized eigenvalue decomposition, enhancing beamforming efficiency.

Findings

Reduces CG iteration count by 2-3 times in simulations.

Maintains SINR performance comparable to exact inversion.

Transforms the system to be more sparse and easier to compute.

Abstract

Long-term beamforming substantially reduces the channel estimation and inversion overhead of conventional massive MU-MIMO receivers; yet, its construction still hinges on the inversion of a large Hermitian matrix, whose condition number deteriorates with the per-user SNR dynamic range. When this inversion is approximated in hardware via the conjugate gradient (CG) algorithm, the deterioration directly inflates the iteration count and, consequently, the energy and latency budget. We propose a hardware-friendly low-rank preconditioning framework that targets exactly this bottleneck. The preconditioner is constructed from the top eigenpairs of the long-term covariance matrix through a randomized complex eigenvalue decomposition (RC-EVD), whose inner QR factorizations are realized via a Cholesky-based scheme (QRC), confining the dominant cost to generalized matrix multiplication (GEMM) and small triangular solves that map naturally onto systolic arrays. We further show that performing the preconditioned CG inversion in the beamspace domain induces sparsification of the system matrix and provides additional convergence acceleration at negligible transformation cost. Ray-tracing simulations confirm that the joint scheme reduces the required CG iteration count by two to three while matching the post-equalization SINR of the exact inversion.