Massive MIMO system yields significant improvements in spectral and energy efficiency for future wireless communication systems. The regularized zero-forcing (RZF) beamforming is able to provide good performance with the capability of achieving numerical stability and robustness to the channel uncertainty. However, in massive MIMO systems, the matrix inversion operation in RZF beamforming becomes computationally expensive. To address this computational issue, we shall propose a novel randomized sketching based RZF beamforming approach with low computational complexity. This is achieved by solving a linear system via randomized sketching based on the preconditioned Richard iteration, which guarantees high quality approximations to the optimal solution. We theoretically prove that the sequence of approximations obtained iteratively converges to the exact RZF beamforming matrix linearly fast as the number of iterations increases. Also, it turns out that the system sum-rate for such sequence of approximations converges to the exact one at a linear convergence rate. Our simulation results verify our theoretical findings.

中文翻译：

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通过随机草图实现大规模 MIMO 的大规模波束成形


大规模 MIMO 系统可显着提高未来无线通信系统的频谱和能源效率。正则化迫零（RZF）波束形成能够提供良好的性能，能够实现数值稳定性和对信道不确定性的鲁棒性。然而，在大规模 MIMO 系统中，RZF 波束成形中的矩阵求逆运算的计算成本变得很高。为了解决这个计算问题，我们将提出一种新颖的基于随机草图的 RZF 波束形成方法，计算复杂度低。这是通过基于预处理理查德迭代的随机草图求解线性系统来实现的，这保证了对最佳解决方案的高质量近似。我们从理论上证明，随着迭代次数的增加，迭代获得的近似序列能够快速线性地收敛到精确的 RZF 波束形成矩阵。此外，事实证明，这种近似序列的系统总和速率以线性收敛速率收敛到精确的总和速率。我们的模拟结果验证了我们的理论发现。