  Spatial channel covariance information can replace full instantaneous channel
state information for the analog precoder design in hybrid analog/digital
architectures. Obtaining spatial channel covariance estimation, however, is
challenging in the hybrid structure due to the use of fewer radio frequency
(RF) chains than the number of antennas. In this paper, we propose a spatial
channel covariance estimation method based on higher-order tensor decomposition
for spatially sparse time-varying frequency-selective channels. The proposed
method leverages the fact that the channel can be represented as a low-rank
higher-order tensor. We also derive the Cram\'er-Rao lower bound on the
estimation accuracy of the proposed method. Numerical results and theoretical
analysis show that the proposed tensor-based approach achieves higher
estimation accuracy in comparison with prior compressive-sensing-based
approaches or conventional angle-of-arrival estimation approaches. Simulation
results reveal that the proposed approach becomes more beneficial at low
signal-to-noise (SNR) region.
