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This paper addresses the computational challenges of matrix inversion in long-term beamforming (LTBF) for massive MU-MIMO systems, showing that dominant interferers worsen the condition number of the LTBF covariance matrix and degrade performance, especially in finite-precision implementations. They propose a subspace nulling method that projects the received signal onto the orthogonal complement of the dominant interference subspace, thereby reducing the eigenvalue spread and improving numerical stability. Simulations in a 5G scenario demonstrate that this approach significantly reduces the number of conjugate gradient iterations needed for near-optimal performance in both floating-point and fixed-point implementations.
By intelligently nulling interference *before* matrix inversion, massive MIMO systems can achieve near-optimal beamforming with significantly reduced computational complexity, even in finite-precision hardware.
Long-term beamforming (LTBF) is a widely-used scalable alternative to instantaneous multi-user MIMO processing that leverages slowly varying spatial channel statistics. VLSI implementations require matrix inversion that become computationally challenging for massive MIMO systems with large number of antennas. In this work, we show that dominant interferers significantly degrade the numerical conditioning of the LTBF covariance matrix, leading to severe performance loss in finite-precision implementations of polynomial and conjugate gradient (CG) based inversion methods. To address this issue, we propose a subspace nulling approach that operates solely on long-term channel statistics and acts as an implicit preconditioning step for LTBF. By projecting the received signal onto the orthogonal complement of the dominant interference subspace, the proposed method reduces the eigenvalue spread of the covariance matrix and improves numerical stability. Through ray-tracing simulations in a realistic 5G scenario, we demonstrate that the proposed method substantially reduces the number of CG iterations required to achieve near-optimal performance across floating-point and fixed-point implementations while preserving the low-overhead nature of LTBF.