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We study the problem of semi-blind channel estimation and symbol detection in the uplink of multi-cell massive MIMO (multi-input multi-output) systems with spatially correlated time-varying channels. An algorithm based on expectation propagation (EP) is developed to iteratively approximate the joint a posteriori distribution of the unknown channel matrix and the transmitted data symbols with a distribution from an exponential family. This distribution is then used for direct estimation of the channel matrix and detection of data symbols. A modified version of the popular Kalman filtering algorithm referred to as KF-M is also proposed which emerges from our EP derivations. Performance of the Kalman smoothing algorithm followed by KF-M, referred here as KS-M, is also examined. Simulation results demonstrate that channel estimation error and the symbol error rate (SER) of the semi-blind KF-M, KS-M, and EP-based algorithms improve with the increase in the number of base station antennas and the length of the data symbols in the transmitted frame. In particular, by increasing the number of transmitted data symbols in the frame, the proposed semi-blind algorithms can mitigate the effects of pilot contamination as well as time-varying channels in a multi-cell massive MIMO system with pilot-overhead of around 5&#x0025;.

Semi-Blind Channel Estimation and Data Detection for Multi-Cell Massive MIMO Systems on Time-Varying Channels