The rectangular Pisarenko method

Most high-resolution (HR) direction of arrival estimation schemes require the extraction of a low dimensional subspace, a task generally accomplished via a standard eigen-decomposition (ED) that requires at least O(N³) flops for an order N matrix. Different techniques have been proposed to reduce this computational load to O(N²P) flops where P is the number of sources. The method we propose is a HR technique that requires O(P³) flops. The price to be paid for this drastic computational saving is an increase of the variance of the direction estimates which is of the order T^-1 N^-2 for the proposed procedure while it is of order T ^-1N^-3 (T the number of snapshots) for efficient procedures. The idea behind the method is to apply a Pisarenko (1973) like method to a rectangular matrix extracted from the Toeplitz estimated covariance matrix