Two-dimensional equirotational stack subspace fitting with an application to uniform rectangular arrays and ESPRIT

A two-dimensional (2-D) multiple invariance technique for computing signal subspaces for uniform rectangular arrays (URAs) of size M*N sensors is introduced. The method is based on a multiple maximum overlap configuration of the sensors in the array with m*n subarrays of (M-m+1)*(N-n+1) sensors each. We exploit the fact that the stacked subspace of the subarray sensor output signals admits a two-level equirotational stack parametrization. We introduce a TLS-type algorithm for estimating the parameters of this equirotational stack subspace model. Based on this method of equirotational stack subspace fitting, the overall array signal subspace can be estimated with a much higher accuracy than with conventional unstructured SVD and TLS techniques. Detailed experiments validate the theoretical results. We propose a variant of 2-D ESPRIT based on equirotational stack subspace fitting. This 2-D equirotational stack ESPRIT (2-D ES-ESPRIT) algorithm clearly outperforms conventional unstructured variants of 2-D ESPRIT. A detailed comparison with 2-D unitary ESPRIT is presented