LSE Precoders for Massive MIMO with Hardware Constraints: Fundamental Limits

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 dB can track the performance of the Regularized Zero Forcing (RZF) precoder closely. As the peakto-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.