This paper considers the one-bit precoding problem for the multiuser downlink massive 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-bit constraint makes the problem generally hard to solve. In this paper, we propose an efficient negative $\ell_1$ penalty approach for finding a high-quality solution of the considered problem. Specifically, we first propose a novel negative $\ell_1$ penalty model, which penalizes the one-bit constraint into the objective with a negative $\ell_1$-norm term, and show the equivalence between (global and local) solutions of the original problem and the penalty problem when the penalty parameter is sufficiently large. We further transform the penalty model into an equivalent min-max problem and propose an efficient alternating optimization (AO) algorithm for solving it. The AO algorithm enjoys low per-iteration complexity and is guaranteed to converge to the stationary point of the min-max problem. Numerical results show that, compared against the state-of-the-art CI-based algorithms, the proposed algorithm generally achieves better bit-error-rate (BER) performance with lower computational cost.

翻译：本文考虑了多用户下行大量多投入多产出(MIMO)系统(MIMO)的单位预编码问题,即分阶段转换键调制(PSK),并侧重于已知的建设性干扰(CI)问题配方。离散一位限制的存在使问题普遍难以解决。在本文中,我们提出一个高效的负值 $ ell_1美元的惩罚方法,以找到一个高质量的问题解决方案。具体地说,我们首先提出一个新的负值 $ ell_1美元的惩罚模式,以负值 $1美元-诺姆术语处罚目标中的一位限制,并显示(全球和地方)最初问题的解决办法与刑罚参数足够大时的处罚问题之间的等值。我们进一步将刑罚模式转换成等值的微轴问题,并提议一种高效的交替优化(AO)算法来解决所考虑的问题。AO算法具有低的渗透性复杂度,并且保证与微负值问题的固定点一致。Numericalal 结果表明,相对于州-CAL-Cal-Cal-Cal-Cal-Cal-Calgal-Cal-Cal-Cal-Cal-Cal-Cal-Calislevol-Cal-Cal-Calations)。