# Efficient Constant Envelope Precoding for Massive MU-MIMO Downlink via Majorization-Minimization Method

## TL;DR

This paper introduces an efficient algorithm for constant envelope precoding in massive MU-MIMO systems to improve energy efficiency and reduce power consumption.

## Contribution

A novel CE precoding algorithm using AltMin, MM, and FISTA methods for massive MU-MIMO systems is proposed.

## Key findings

- The proposed algorithm achieves a 1dB BER performance gain over existing CE precoding methods.
- The algorithm maintains acceptable computational complexity for practical implementation.
- Performance improvements are also observed in the discrete constant envelope (DCE) precoding case.

## Abstract

The practical implementation of massive multi-user multi-input–multi-output (MU-MIMO) downlink communication systems power amplifiers that are energy efficient; otherwise, the power consumption of the base station (BS) will be prohibitive. Constant envelope (CE) precoding is gaining increasing interest for its capability to utilize low-cost, high-efficiency nonlinear radio frequency amplifiers. Our work focuses on the topic of CE precoding in massive MU-MIMO systems and presents an efficient CE precoding algorithm. This algorithm uses an alternating minimization (AltMin) framework to optimize the CE precoded signal and precoding factor, aiming to minimize the difference between the received signal and the transmit symbol. For the optimization of the CE precoded signal, we provide a powerful approach that integrates the majorization-minimization (MM) method and the fast iterative shrinkage-thresholding (FISTA) method. This algorithm combines the characteristics of the massive MU-MIMO channel with the second-order Taylor expansion to construct the surrogate function in the MM method, in which minimizing this surrogate function is the worst-case of the system. Specifically, we expand the suggested CE precoding algorithm to involve the discrete constant envelope (DCE) precoding case. In addition, we thoroughly examine the exact property, convergence, and computational complexity of the proposed algorithm. Simulation results demonstrate that the proposed CE precoding algorithm can achievean uncoded biterror rate (BER) performance gain of roughly 1dB compared to the existing CE precoding algorithm and has an acceptable computational complexity. This performance advantage also exists when it comes to DCE precoding.