Unified ESPRIT spatial spectrum for Direction-of-Arrival estimation with an arbitrary sparse array

Classic Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) is limited to an arbitrary array for the Direction-of-Arrival (DoA) estimation because shift invariance is a prerequisite. In this paper, an extended ESPRIT algorithm is newly proposed for such an array with an additional compensation angle input. First, an angle-dependent unitary transformation is applied to the received snap shot, and the extended ESPRIT will output one angle estimate together with its corresponding eigenvalue only. Then a novel unified ESPRIT spatial spectrum is defined based on the extended ESPRIT method. It is shown that the spectral peaks only appear where the true DoAs are located, and thus all the DoA estimates can be obtained by searching for the unambiguous needle-like spectral peaks. Simulations are carried out to reveal that the performance of the proposed algorithm is quite satisfactory. Therefore, the classic ESPRIT is extended to be an alternative method to the DoA estimation with an arbitrary array except the Multiple Signal Classification (MUSIC).