DOA and Phase Error Estimation for a Partly Calibrated Array With Arbitrary Geometry

Abstract

This paper presents a novel strategy to simultaneously estimate the direction of arrival (DOA) of a source signal and the phase error of a partly calibrated array with arbitrary geometry. We add up the snapshot data of two different sensors, and then extract a knowledge associated with the DOA and phase errors of these two elements by using singular value decomposition. In such a manner, we can establish a series of linear equations with respect to the unknown DOA and phase error, by simply conducting the procedure on any two sensor elements. On this basis, it can be shown that the problem of jointly estimating DOA and phase error is equivalent to a least square (LS) problem with a quadratic equality constraint. To solve this LS problem (so that the DOA and phase error can be obtained), an effective convex-concave procedure is employed. Different from the conventional algorithms that are limited to specific array geometries, the proposed one is suitable for arrays with arbitrary geometries. More importantly, the devised method only requires one extra calibrated sensor, which is not necessarily adjacently located with the reference one. Several simulations are carried out in this paper and the effectiveness of the devised method can be clearly observed.