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In massive multiple-input multiple-output (MIMO) systems, the knowledge ofthe users' channel covariance matrix is crucial for minimum mean square error(MMSE) channel estimation in the uplink as well as it plays an important rolein several multiuser beamforming schemes in the downlink. Due to the largenumber of base station antennas in massive MIMO, accurate covariance estimationis challenging especially in the case where the number of samples is limitedand thus comparable to the channel vector dimension. As a result, the standardsample covariance estimator may yield a too large estimation error which inturn may yield significant system performance degradation with respect to theideal channel covariance knowledge case. To address such problem, we propose amethod based on a parametric representation of the channel angular scatteringfunction. The proposed parametric representation includes a discrete specularcomponent which is addressed using the well-known MUltiple SIgnalClassification (MUSIC) method, and a diffuse scattering component, which ismodeled as the superposition of suitable dictionary functions. To obtain therepresentation parameters we propose two methods, where the first solves anon-negative least-squares problem and the second maximizes the likelihoodfunction using expectation-maximization. Our simulation results show that theproposed methods outperform the state of the art with respect to variousestimation quality metrics and different sample sizes.

Structured Channel Covariance Estimation from Limited Samples for Large Antenna Arrays