  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.
