Aperture varying autoregressive covariance modeling for 2D oversampled receive arrays

Recently it has been proposed that two-dimensional (2D) oversampled received arrays could be used to provide signal-to-external noise ratio (SENR) gains for over-the-horizon radar applications which are strongly externally noise limited. These array configurations can be used to exploit superdirective adaptive beamforming techniques. A key element of the superdirective adaptive beamforming process is the estimation of the array spatial noise covariance matrix. In this paper we propose a parametric covariance modeling technique called aperture varying autoregressive (AVAR) covariance modeling that captures the 2D spatial correlation structure of high-frequency (HF) background noise sampled by an oversampled 2D receive array. The use of this covariance modeling technique can significantly reduce the computational requirements for the inversion of large spatial covariance matrices. Additional gains are achieved via reduced sample support requirements for an N-element 2D receive array. In this paper we introduce 2D aperture varying autoregressive models AVAR(m,l) that are spatially non-stationary generalizations of traditional autoregressive AR(m) or AR (m,l) techniques. While traditional AR techniques model covariance structure as toeplitz or toeplitz-block-toeplitz, these new AVAR models enforce a banded or doubly banded inverse covariance structure which is more general. The introduced AVAR methods are closely coupled to the oversampled array architecture which in the presence of nearly homogeneous external noise exhibits spatial correlation most strongly amongst closely spaced elements. Therefore the use of these AVAR methods effectively restricts the adaptive beamforming to gains achievable through superdirective beamforming.