Nonlinear One-bit Precoding for Massive MIMO Downlink: Minimizing the Maximum Mean Squared Error

Abstract

In this paper, we study the nonlinear one-bit pre-coding in the massive multiple-input multiple-output downlink system. Different from the conventional criterion of minimizing the sum of mean squared error (min-sum MSE) of all users, the criterion of minimizing the maximum MSE (min-max MSE) is considered here which is more suitable for communications in block and slow fading channels. Based on this min-max MSE criterion, two methods are proposed to optimize the precoding vector and precoding factor. In the first semi-definite relaxation (SDR) method, the min-max MSE problem is first formulated as a semi-definite programming problem with non-convex rank-1 constraint, and then SDR is employed to relax this constraint. The output of SDR is further processed by Gaussian randomization procedure, where, for each candidate precoding vector generated according to the output of SDR, the precoding factor is solved by the quadratically-constrained quadratic programming. To reduce the complexity, the second method employing two-stage processing strategy is further proposed. In the two-stage precoding, the initial solution is first acquired by the efficient alternating direction method of multipliers for the min-sum MSE problem, and then refined to achieve better min-max MSE performance by the symbol-flipping (SF). Finally, the proposed methods are demonstrated by computer simulations.