Fast Computation of Zero-Forcing Precoding for Massive MIMO-OFDM Systems

As a simple and popular transmission scheme, zero-forcing (ZF) precoding can effectively reap the great benefits of a multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) wireless system. But as the wireless technology evolves to massive MIMO-OFDM, even the ZF precoding may incur too cumbersome computational complexity. In this paper, we first derive the ZF precoder in the time domain. By exploiting the block-Toeplitzness of the time-domain channel matrix, we propose a novel approximate solution to the original time-domain ZF precoding problem for fast computation. We then provide an approximation analysis to show the convergence to the exact solution. To compute the approximate scheme efficiently, we propose two novel low-complexity algorithms: a fast Fourier transform (FFT) based conjugate gradient algorithm, which can obtain the MIMO-OFDM ZF precoder as a time-domain MIMO finite impulse response (FIR) filter, and a flexible block Toeplitz QR decomposition algorithm exploiting the special structure of the time-domain channel matrix. We also extend the proposed approximate scheme and two low-complexity algorithms to the regularized ZF precoding scenario. Simulation results and complexity analysis show that our methods can achieve favorable performance but with significantly lower computational complexity compared with the state-of-the-art methods.