Large System Analysis of Linear Precoding in MISO Broadcast Channels with Limited Feedback

In this paper we study the sum rate of zero-forcing (ZF) as well as regularized ZF (RZF) precoding in large MISO broadcast channels, under the assumptions of imperfect channel state information at the transmitter, channel transmit correlation and different user path losses. Our analysis assumes that the number of transmit antennas $M$ and the number of users $K$ are large and of the same order of magnitude. We apply recent results on the empirical spectral distribution of certain kinds of large dimensional random matrices to derive deterministic equivalents for the signal-to-interference plus noise ratio (SINR) at the receivers. Based on these results and under sum rate maximization, we evaluate for RZF (i) the optimal precoder, for ZF (ii) the optimal number of active users and (iii) the optimal amount of channel training in TDD multi-user systems. Moreover, we study the sum rate under limited feedback and derive an approximation of the necessary feedback rate to maintain a given rate offset relative to perfect CSIT. Numerical simulations suggest that the approximations, almost surely exact as $M,K\to\infty$, are accurate even for small $M,K$.