Structured Channel Covariance Estimation from Limited Samples for Large Antenna Arrays

In massive MIMO systems, the knowledge of channel covariance matrix is crucial for MMSE channel estimation in the uplink and plays an important role in several downlink multiuser beamforming schemes. Due to the large number of base station antennas in massive MIMO, accurate covariance estimation is challenging especially in the case where the number of samples is limited and thus comparable to the channel vector dimension. As a result, the standard sample covariance estimator yields high estimation error which may yield significant system performance degradation with respect to the ideal channel knowledge case. To address such covariance estimation problem, we propose a method based on a parametric representation of the channel angular scattering function. The proposed parametric representation includes a discrete specular component which is addressed using the well-known MUltiple SIgnal Classification (MUSIC) method, and a diffuse scattering component, which is modeled as the superposition of suitable dictionary functions. To obtain the representation parameters we propose two methods, where the first solves a non-negative least-squares problem and the second maximizes the likelihood function using expectation-maximization. Our simulation results show that the proposed methods outperform the state of the art with respect to various estimation quality metrics and different sample sizes.