Asymptotic Characterisation of Regularised Zero-Forcing Receiver for Imperfect and Correlated Massive MIMO Systems with Optimal Power Allocation

In this paper, we present asymptotic high dimensional analysis of the regularised zero-forcing (RZF) 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 (MIMO) communication system. We assume that the channel matrix is spatially correlated and not perfectly known. We 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, we derive 1) the optimal regularisation factor for RZF; 2) the optimal power allocation scheme. Numerical simulations show a close match to the derived asymptotic results even for a few dozens of the problem dimensions.