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：量化常量封套(QCE)预编码(QCE)是允许每个天线只使用离散的 QCE 传输信号的新传输计划,由于能够减少硬件成本和大量多投入多输出(MIMO)系统的能源消耗,因此引起了越来越多的研究兴趣。然而,QCE的离散性质传递信号,使预编码设计变得非常复杂。在本文件中,我们认为,一个大规模正在逐步转换键盘(PSK)的IMO系统预编码问题,并制定了一种有效的方法来解决建设性干扰(CI)问题。我们的方法基于一种定制的(连续)惩罚模式,该模式与最初的离散多输出(MIMO)系统相当。具体地说,惩罚模式减轻了离散的 QCE 限制,并在目标中以负值$_2美元-诺姆术语惩罚它。这导致了一个非湿度的非凝固值非凝固度优化问题。为了解决这个问题,我们采用最近提出的更替优化(AO)算法。我们表明,AO的算算算法可以有效地在每一种情况下采用封闭式方法来更新我们提出的升级。