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We investigate a general channel estimation problem in the massive multiple-input multiple-output system which employs the hybrid analog/digital precoding structure with limited radio-frequency (RF) chains. By properly designing RF combiners and performing multiple trainings, the proposed channel estimation can approach the performance of fully-digital estimations depending on the degree of channel spatial correlation and the number of RF chains. Dealing with the hybrid channel estimation, the optimal combiner is theoretically derived by relaxing the constant-magnitude constraint in a specific single-training scenario, which is then extended to the design of combiners for multiple trainings by sequential and alternating methods. Further, we develop a technique to generate the phase-only RF combiners based on the corresponding unconstrained ones to satisfy the constant-magnitude constraints. The performance of the proposed hybrid channel estimation scheme is examined by simulations under both nonparametric and spatial channel models. The simulation results demonstrate that the estimated channel state information can approach the performance of fully-digital estimations in terms of both mean square error and spectral efficiency. Moreover, a practical spatial channel covariance estimation method is proposed and its effectiveness in hybrid channel estimation is verified by simulations.

Framework of Channel Estimation for Hybrid Analog-and-Digital Processing Enabled Massive MIMO Communications