Regularized finite-order finite-rank covariance matrix approximation for adaptive beamforming in oversampled 2D HF antenna arrays

This paper proposes a multi-channel adaptive array spatial covariance matrix estimation technique in which the covariance is modeled as consisting of two complementary components. The first component has finite rank and is meant to capture the low-rank components of the external interference environment. The second component has full rank and corresponds to external noise, but is modeled by a low-order parametric model. In isolation both of these covariance models require relatively low training sample support, comparable to the rank or order. The main goal of this paper is to demonstrate that these covariance modeling methods can be applied together as a finite-order finite-rank (FOFR) covariance estimate. This estimate can be used to perform efficient low-loss adaptive beamforming for two-dimensional spatially oversampled high-frequency over-the-horizon radar receive arrays consisting of a large number of sensor elements and limited training sample support.