  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.
