Shift invariant sparse arrays and their optimal signal and noise subspaces

Abstract

Many signal processing algorithms utilize singular vectors of the data received by a sensor array or eigenvectors of the sample covariance matrix. The performance of such subspace-based algorithms can be substantially improved by using the optimal signal or noise subspace estimate instead of using the subspaces spanned by the eigenvectors or the singular vectors. The optimal signal and noise subspaces are estimated by exploiting the shift-invariant structure of the sensor array. We develop a methodology to find the optimal subspaces in sparse arrays that possess shift-invariant structure and interpolate the optimal subspaces to match the subspaces of the fully populated arrays with an equal aperture. These shift-invariant sparse arrays’ direction of arrival estimation performance is superior compared to the methods that use eigenvectors or singular vectors directly. Our method also encompasses any symmetric array that is not shift-invariant, thus broadening the class of sparse arrays where our method can be applied.