  We investigate a general channel estimation problem in the massive
multiple-input multiple-output (MIMO) 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 CSI 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.
