Quantized constant envelope (QCE) precoding, a new transmission scheme that only discrete QCE transmit signals are allowed at each antenna, has gained growing research interests due to its ability of reducing the hardware cost and the energy consumption of massive multiple-input multiple-output (MIMO) systems. However, the discrete nature of QCE transmit signals greatly complicates the precoding design. In this paper, we consider the QCE precoding problem for a massive MIMO system with phase shift keying (PSK) modulation and develop an efficient approach for solving the constructive interference (CI) based problem formulation. Our approach is based on a custom-designed (continuous) penalty model that is equivalent to the original discrete problem. Specifically, the penalty model relaxes the discrete QCE constraint and penalizes it in the objective with a negative $\ell_2$-norm term, which leads to a non-smooth non-convex optimization problem. To tackle it, we resort to our recently proposed alternating optimization (AO) algorithm. We show that the AO algorithm admits closed-form updates at each iteration when applied to our problem and thus can be efficiently implemented. Simulation results demonstrate the superiority of the proposed approach over the existing algorithms.

翻译：量化恒包络（QCE）预编码作为一种新型传输方案，仅允许每根天线输出离散的QCE发射信号，因其能够降低大规模多输入多输出（MIMO）系统的硬件成本与能耗而备受关注。然而，QCE发射信号的离散特性极大增加了预编码设计的复杂度。本文考虑采用相移键控（PSK）调制的大规模MIMO系统中的QCE预编码问题，并提出一种高效方法解决基于建设性干扰（CI）的优化模型。该方法基于定制化（连续）惩罚模型，该模型与原离散问题等价。具体而言，惩罚模型通过引入负$\ell_2$范数项松弛离散QCE约束并在目标函数中进行惩罚，从而构成非光滑非凸优化问题。为求解该问题，我们采用近期提出的交替优化（AO）算法，并证明该算法在每次迭代中可得到闭式更新解，因此可高效实现。仿真结果表明，所提方法相较于现有算法具有显著优越性。