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 alternating 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, especially when the problem is difficult (e.g., high-order modulations, large number of antennas, or high user-antenna ratio).
翻译:在本文中,我们考虑了多用户下行连接大规模多投入多输出量(MIMO)系统的单位预码问题,即分阶段转换键值(PSK)调制,并侧重于已知的建设性干扰(CI)问题配方。我们首先将问题(即使在单一用户案件中)的NP-硬性确定为问题(即使在单一用户案件中),这揭示了在全球范围内解决问题的内在困难。然后,我们提出了一个新颖的负值 $ ell_1美元 罚款模型,该模型用负值 $\ell_1美元-诺姆术语来惩罚目标中的一比特限制,并显示(全球和当地)原问题的计算和刑罚问题之间的等值。我们首先将刑罚模式进一步转换成一个等效的微量问题,并提出一个高效的交替优化方法来解决问题。AO算法具有低度的复杂度,并且保证与基于最小值的最小值(负值问题和最小值的当地最小值)趋同点。为了进一步降低计算成本成本,我们还提议一个更低的算法,一旦达到一个固定值的数值值,就会比较的硬值。