Efficient Constant Envelope Precoding With Quantized Phases for Massive MU-MIMO Downlink Systems

This study considers a generalized constant envelope-based precoding design problem in massive multiuser multiple-input multiple-output systems, in which the output signals of digital-to-analog converters are restricted to M-ary phase-shift keying signaling to facilitate the use of low-cost and power-efficient power amplifiers at a base station. We aim to jointly optimize the precoding vector and the precoding factor to minimize the mean-squared error between the transmitted and the estimated symbols. However, the considered precoding problem is nonconvex and challenging to solve because the precoding vector and the precoding factor are coupled together. To address this problem, we apply the alternating minimization (AltMin) framework to decouple the considered problem into two problems: the precoding factor design problem and the precoding vector design problem. The former has an analytical solution, while the latter requires solving a difficult combinatorial problem, which we address by proposing a simple yet efficient gradient projection (GP)-based algorithm to find an approximate precoding vector. Simulation results demonstrate that the proposed GP-based AltMin algorithm achieves the same or higher BER performance than state-of-the-art algorithms while requiring lower complexity. In addition, when higher order modulations are employed, the error floor experienced by the existing algorithms can be substantially mitigated by the proposed GP-AltMin algorithm through increasing the number of phase bits.