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.

翻译：长时波束赋形（LTBF）是一种广泛使用的可扩展替代方案，用于替代瞬时多用户MIMO处理，它利用缓慢变化的信道空间统计特性。超大规模集成电路（VLSI）实现需要矩阵求逆，这对于天线数量众多的大规模MIMO系统而言计算难度极大。本文证明，主导性干扰会显著恶化LTBF协方差矩阵的数值条件，导致基于多项式和共轭梯度（CG）求逆方法的有限精度实现出现严重的性能损失。为解决该问题，我们提出一种子空间置零方法，该方法仅基于长时信道统计特性操作，并作为LTBF的隐式预处理步骤。通过将接收信号投影到主导性干扰子空间的正交补空间上，所提方法降低了协方差矩阵的特征值扩展范围，提高了数值稳定性。通过在真实5G场景中的射线追踪仿真，我们证明该方法在浮点与定点实现中，为达到接近最优的性能所需CG迭代次数显著减少，同时保留了LTBF的低开销特性。