Improved Covariance Matrix Estimation using Riemannian Geometry for Beamforming Applications

Abstract

The estimation of interference plus noise covariance (INC) matrix for beamforming applications is considered from a Riemannian space perspective. A new INC estimation technique based on regularized Burg algorithm (RBA), Riemannian mean and Riemannian distance is proposed to maintain a stable performance in presence of angle of arrival mismatch and small sample size with high and low signal to interference plus noise ratio (SINR). The RBA is exploited to generate Toeplitz Hermitian positive definite (THPD) covariance matrices from the estimates of the reflection coefficients for each radar snapshot. The estimated INC is formulated as a linear combination of THPD covariance matrices of the interference plus noise excluding potential target snapshots. The weights of the linear combination operation are based on the Riemannian distance between the Riemannian mean and each THPD covariance matrix. The largest distance (potential target) will have zero weight and the smallest distance will have maximum weight. Simulation results demonstrate the performance of the proposed technique in comparison with sample covariance and Riemannian mean covariance under steering vector mismatch and small sample size in presence of high and low SINR.