Analysis of Uplink Achievable Rate in Multi-Cell Multi-User Distributed Massive MIMO System with Time-varying Channels

By jointly considering the time-varying characteristic in mobile channel scenario, the pilot contamination phenomenon, and the channel estimation error, we analyze the impacts of the involved three factors for the achievable rate performance in the multi-cell multi-user distributed massive multiple-input multiple-output (MIMO) uplink system. We employ the Gauss-Markov process to model the time-varying channel, which includes the temporal correlation coefficient as an important parameter to describe how the channel coefficient varies as the time flows. Using Jensen’s inequality, the random matrix theory, and the moments of random variable with Gamma distribution, we derive the analytical expression of the uplink achievable rate including pilot contamination, channel estimation error, and the temporal correlation coefficient, when the maximum ratio combining (MRC) receiver is utilized at the base station. Based on this, we conclude that the temporal correlation coefficient only influences the absolute value of the achievable rate without affecting the transmit power scaling law. What’s more, without considering the power scaling, the achievable rate is only determined by the pilot contamination as the total number of the antennas becomes large, while the effect of the time-varying channel asymptotically vanishes, which indicates that the involved system is robust to the time-varying channel. Finally, Monte Carlo simulations validate the correctness and effectiveness of the deduced conclusions.