Eigenstructure-based azimuth and elevation estimation in sparse uniform rectangular arrays

A new method for 2D direction of arrival (DOA) estimation in uniform rectangular arrays (URAs) is proposed. Unlike previous methods, which usually require fully loaded arrays, the proposed method can also be applied in the case of sparse URAs. The algorithm is based on an new formulation of the rank reduction estimator (RARE) which originally was derived for 1D DOA estimation in partly calibrated arrays. Automatically paired estimates of the azimuth and elevation angles are obtained from the roots of matrix polynomials at a low computational cost. Alternative implementations of the RARE matrix polynomial allow this cost to be further reduced. Moreover, a straight-forward extension of the URA-RARE algorithm can also be applied to the multi-dimensional harmonic retrieval problem which is of great importance for numerous applications. Simulation results show that the URA-RARE algorithm applied to URAs provides significantly improved DOA estimation, both asymptotically and in the threshold domain, as compared to the popular 2D unitary ESPRIT algorithm.