Rectangular Pisarenko method applied to source localization

Most high-resolution (HR) direction-of-arrival (DOA) estimation schemes require the extraction of a low-dimensional subspace: a task that takes O(N³) flops for an order S matrix. Different techniques have been recently proposed to reduce this computational load. For those working on blocks of data, the number of flops required is generally O(N²P), where P, which is the dimension of the subspace (the number of sources), is often quite small as compared with N, which is the number of sensors. The method we propose is a HR technique that requires O(NP²)+O(P³) flops, i.e., that is linear in the number of sensors. The price to be paid for this drastic computational saving is a reduction in performance. Although the Cramer-Rao lower bound (CRLB) on the variance of the direction estimates is of the order T^-1 N^-3 (with T the number of snapshots), this variance is of order T^-1 N^-2 for the proposed procedure. The idea behind the method is to apply a Pisarenko method to a rectangular matrix extracted from the Toeplerized estimated covariance matrix, and it is this Toeplerization that allows preservation of the O(T^-1 N^-2) level of performance