Achievable Downlink Rates of MRC and ZF Precoders in Massive MIMO With Uplink and Downlink Pilot Contamination

Massive multi-input multi-output (MIMO) systems require channel state information (CSI) at base stations. In multicell environments, adjacent cells using the same spectrum cause a pilot contamination problem and degrade CSI quality. Under such practical environments, it is important to assess achievable rate of the system for a proper system design. There exist achievable rate bounds of uplink (UL) systems in the literature, but general closed-form rate bounds for downlink (DL) systems are not available yet. This paper studies a practical massive MIMO DL system with or without pilot-aided coherent detection under the scenario of pilot contamination, and derives closed-form approximate achievable DL rate expressions for both maximum ratio combining (MRC) and zero forcing (ZF) precoders. For the case with DL pilot, a corresponding DL effective channel estimator is also developed. Numerical simulation results corroborate accuracy of the closed-form rate expressions and they also show performance characteristics of pilot-contaminated massive MIMO DL systems with MRC and ZF precoders.