LSE Precoders for Massive MIMO with Signal Constraints: Fundamental Limits

TL;DR

This paper introduces nonlinear LSE precoders for multiuser MIMO channels with signal constraints, analyzing their performance and fundamental limits using the replica method, and demonstrating their effectiveness compared to traditional precoders.

Contribution

It develops a closed-form asymptotic distortion expression for LSE precoders under various constraints and compares their performance to RZF precoders, including improvements via replica symmetry breaking.

Findings

LSE precoders with 3 dB PAPR closely match RZF performance.

Constant envelope precoders achieve RZF performance with 20% more antennas.

Lower-bound on distortion for M-PSK is tight for moderate antenna-to-user ratios.

Abstract

This paper proposes the nonlinear Least Square Error (LSE) precoders for multiuser MIMO broadcast channels. The output signals of LSE Precoders are limited to be chosen from a predefined set which let these precoders address several constraints such as peak power limitation, constant envelope transmission and discrete constellations. We study the large-system performance of these precoders via the replica method from statistical physics, and derive a closed-form expression for the asymptotic distortion. Our results demonstrate that an LSE precoder with the output peak-to-average power ratio of $3~{\rm dB}$ can track the performance of the Regularized Zero Forcing (RZF) precoder closely. As the peak-to-average power ratio reduces to one, the constant envelope precoder is recovered. The investigations depict that the performance of the RZF precoder is achieved by the constant envelope precoder with $20\%$ of more transmit antennas. For $M$-PSK constellations, our analysis gives a lower-bound on the asymptotic distortion which is tight for moderate antenna-to-user ratios and deviates as the ratio grows. We improve this bound by deriving the replica solution under one-step of replica symmetry breaking. Our numerical investigations for this case show that the bound is tight for antenna-to-user ratios less than $5$.