# A New Class of Nonlinear Precoders for Hardware Efficient Massive MIMO Systems

## TL;DR

This paper introduces a new class of nonlinear precoders for massive MIMO systems, analyzing their performance using advanced statistical mechanics methods and demonstrating their effectiveness in reducing peak power without significant loss.

## Contribution

It develops a comprehensive analysis of nonlinear LSE precoders with various constraints using the replica method, including novel insights into peak power reduction and performance under different assumptions.

## Key findings

- LSE precoders can reduce peak to average power ratio to 3dB.
- RS assumption fails for PSK, 1-RSB provides more accurate predictions.
- Nonlinear precoders improve hardware efficiency in massive MIMO.

## Abstract

A general class of nonlinear Least Square Error (LSE) precoders in multi-user multiple-input multiple-output systems is analyzed using the replica method from statistical mechanics. A single cell downlink channel with $N$ transmit antennas at the base station and $K$ single-antenna users is considered. The data symbols are assumed to be iid Gaussian and the precoded symbols on each transmit antenna are restricted to be chosen from a predefined set $\mathbb{X}$. The set $\mathbb{X}$ encloses several well-known constraints in wireless communications including signals with peak power, constant envelope signals and finite constellations such as Phase Shift Keying (PSK). We determine the asymptotic distortion of the LSE precoder under both the Replica Symmetry (RS) and the one step Replica Symmetry Breaking (1-RSB) assumptions. For the case of peak power constraint on each transmit antenna, our analyses under the RS assumption show that the LSE precoder can reduce the peak to average power ratio to 3dB without any significant performance loss. For PSK constellations, as $N/K$ grows, the RS assumption fails to predict the performance accurately and therefore, investigations under the 1-RSB assumption are further considered. The results show that the 1-RSB assumption is more accurate.