Uplink Spectral Efficiency Analysis of Distributed Massive MIMO With Channel Impairments

In this paper, considering the practical channel impairments known as pilot contamination and channel aging induced by both Doppler shift and phase noise, we analyze the uplink spectral efficiency of multi-cell multi-user distributed massive multi-input multi-output (MIMO) systems with linear receivers. A joint channel model is first provided, which allows studying the impacts of these impairments on the achievable rate performance of distributed massive MIMO systems simultaneously. Based on this model, using the properties of Gamma distributions together with the approximate methods for non-isotropic vectors, we derive tractable but accurate closed-form expressions for the uplink achievable rate with maximum ratio combining (MRC) and zero-forcing (ZF) receivers in distributed massive MIMO systems. User ultimate achievable rate is also given when the ratio of total number of transmit antennas to the number of users is very large. It is shown that MRC and ZF receivers achieve the same ultimate achievable rate in the presence of the practical channel impairments. Numerical results show that channel aging has a greater impact on ZF receiver and the impact of the Doppler shift is more detrimental than that of the phase noise.