Asymptotic characterisation of regularised zero‐forcing receiver for imperfect and correlated massive multiple‐input multiple‐output systems

Abstract

In this work, the authors present an asymptotic high-dimensional analysis of the regularised zero-forcing receiver in terms of its mean-squared error (MSE) and bit error rate (BER) when used for the recovery of binary phase-shift keying (BPSK) modulated signals in a massive multiple-input multiple-output communication system. The asymptotic analysis is carried out when the system dimensions grow simultaneously large at a fixed ratio. The authors assume that the channel matrix is spatially correlated and not perfectly known. The authors use the linear minimum mean-squared error (LMMSE) method to estimate the channel matrix. The asymptotic approximations of the MSE and BER enable us to solve various practical optimisation problems. Under MSE/BER minimisation, the authors derive (1) the optimal regularisation factor for RZF; (2) the optimal power allocation scheme. The numerical simulations match the derived asymptotic expressions, even when the problem dimensions are small.