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This paper considers the one-bit precoding problem for the multiuser downlinkmassive multiple-input multiple-output (MIMO) system with phase shift keying(PSK) modulation and focuses on the celebrated constructive interference(CI)-based problem formulation. The existence of the discrete one-bitconstraint makes the problem generally hard to solve. In this paper, we proposean efficient negative $\ell_1$ penalty approach for finding a high-qualitysolution of the considered problem. Specifically, we first propose a novelnegative $\ell_1$ penalty model, which penalizes the one-bit constraint intothe objective with a negative $\ell_1$-norm term, and show the equivalencebetween (global and local) solutions of the original problem and the penaltyproblem when the penalty parameter is sufficiently large. We further transformthe penalty model into an equivalent min-max problem and propose an efficientalternating optimization (AO) algorithm for solving it. The AO algorithm enjoyslow per-iteration complexity and is guaranteed to converge to the stationarypoint of the min-max problem. Numerical results show that, compared against thestate-of-the-art CI-based algorithms, the proposed algorithm generally achievesbetter bit-error-rate (BER) performance with lower computational cost.

A Novel Negative $\ell_1$ Penalty Approach for Multiuser One-Bit Massive MIMO Downlink with PSK Signaling