In this paper, we consider the one-bit precoding problem for the multiuser downlink massive multiple-input multiple-output (MIMO) system with phase shift keying (PSK) modulation and focus on the celebrated constructive interference (CI)-based problem formulation. We first establish the NP-hardness of the problem (even in the single-user case), which reveals the intrinsic difficulty of globally solving the problem. Then, we propose a novel negative $\ell_1$ penalty model for the considered problem, 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 a.lternating optimization (AO) algorithm for solving it. The AO algorithm enjoys low per-iteration complexity and is guaranteed to converge to a stationary point of the min-max problem and a local minimizer of the penalty problem. To further reduce the computational cost, we also propose a low-complexity implementation of the AO algorithm, where the values of the variables will be fixed in later iterations once they satisfy the one-bit constraint. Numerical results show that, compared against the state-of-the-art CI-based algorithms, both of the proposed algorithms generally achieve better bit-error-rate (BER) performance with lower computational cost.

翻译：本文研究了采用相移键控（PSK）调制的多用户下行大规模多输入多输出（MIMO）系统中的单比特预编码问题，并聚焦于经典的基于建设性干扰（CI）的问题建模。我们首先证明了该问题的NP难性（即使在单用户情况下），揭示了全局求解该问题的内在难度。接着，我们针对所研究问题提出了一种新颖的负$\ell_1$惩罚模型，该模型通过引入负$\ell_1$范数项将单比特约束惩罚至目标函数中，并证明了当惩罚参数足够大时，原问题与惩罚问题（全局及局部）解之间的等价性。我们进一步将惩罚模型转化为等价的最小-最大问题，并提出了一种高效的交替优化（AO）算法进行求解。该算法每轮迭代计算复杂度低，且保证收敛至最小-最大问题的稳定点以及惩罚问题的局部最优解。为降低计算开销，我们还提出了一种低复杂度的AO算法实现，其中一旦变量满足单比特约束，其值将在后续迭代中固定。数值结果表明，与现有最先进的基于CI的算法相比，所提两种算法通常能以更低计算成本获得更优的误比特率（BER）性能。