Impact of Angular Spread in Correlated MIMO Channels under Pilot Contamination

Pilot contamination is known to be one of the main bottlenecks for massive multi-input multi-output (MIMO) networks. For moderately large antenna arrays (of importance to recent/emerging deployments) and correlated MIMO, pilot contamination may not be the dominant factor in certain scenarios. To the best of our knowledge, a rigorous characterization of the achievable rates and their explicit dependence on the angular spread (AS) is not available in the existing literature for moderately large antenna array regime. In this paper, considering an eigen-beamforming (EBF) precoding, we derive an exact analytical expression for achievable rates in multi-cell MIMO systems under pilot contamination, and characterize the relation between the AS, array size, and respective user rates. Our analytical and simulation results reveal that the achievable rates for both the EBF and the regularized zero-forcing (RZF) precoders follow a non-monotonic behavior for increasing AS when the antenna array size is moderate. We argue that knowledge of this non-monotonic behavior can be exploited to develop effective user scheduling techniques. Index Terms Eigen-beamforming (EBF), large scale multi-input multi-output (MIMO), pilot contamination, regularized zero-forcing (RZF), uniform linear array (ULA).