  In this paper, we analyze the ergodic sum-rate of a multi-cell downlink
system with base station (BS) cooperation using regularized zero-forcing (RZF)
precoding. Our model assumes that the channels between BSs and users have
independent spatial correlations and imperfect channel state information at the
transmitter (CSIT) is available. Our derivations are based on large dimensional
random matrix theory (RMT) under the assumption that the numbers of antennas at
the BS and users approach to infinity with some fixed ratios. In particular, a
deterministic equivalent expression of the ergodic sum-rate is obtained and is
instrumental in getting insight about the joint operations of BSs, which leads
to an efficient method to find the asymptotic-optimal regularization parameter
for the RZF. In another application, we use the deterministic channel rate to
study the optimal feedback bit allocation among the BSs for maximizing the
ergodic sum-rate, subject to a total number of feedback bits constraint. By
inspecting the properties of the allocation, we further propose a scheme to
greatly reduce the search space for optimization. Simulation results
demonstrate that the ergodic sum-rates achievable by a subspace search provides
comparable results to those by an exhaustive search under various typical
settings.
