Large System Analysis of Zero-Forcing Precoding in MISO Broadcast Channels with Limited Feedback

Abstract—In this paper we analyze the sum rate of zero-forcing (ZF) precoding in MISO broadcast channels with limited feed-back, transmit correlation and path loss. Our analysis assumes that the number of transmit antennasM and the number of users K are large, while their ratio remains bounded. By applying re-cent results from random matrix theory we derive a deterministic equivalent of the signal-to-interference plus noise ratio (SINR) and compute the sum rate maximizing number of users as well as the limiting sum rate for high signal-to-noise ratios (SNR), as a function of the channel errors and the channel correlation pattern. Simulations show that theoretical and numerical results match well, even for small system dimensions. I