Deterministic Equivalent for the SINR of Regularized Zero-Forcing Precoding in Correlated MISO Broadcast Channels with Imperfect CSIT

This paper considers the MISO broadcast channel with different spatial correlations of the user vector channels. The base station implements regularized zero-forcing (RZF) precoding based on an imperfect channel estimation. We derive a deterministic equivalent of the signal-to-interference plus noise ratio (SINR) by applying novel results from the field of large dimensional random matrices. Based on this deterministic equivalent, we compute the sum rate maximizing RZF precoder which is given in closed form for independent and identically distributed channels. Simulations show that the accuracy of the approximated SINR extends well into finite dimensions.