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

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.

I. Introduction

Array signal processing has been extensively applied in the fields like radar, navigation, wireless communication, and so forth. One of the most important topics in array processing is direction-of-arrival (DOA) estimation [1]–[6], in which the DOAs of plane waves impinging on a sensor array need to be determined. Many high-resolution eigendecomposition methods such as multiple signal classification (MUSIC) [7], estimation of signal parameter via rotational invariance technique (ESPRIT) [8], and maximum likelihood (ML) [9] have been devised to tackle the problem of DOA estimation. However, it has been generally accepted that the performance of these methods is critically dependent on the knowledge of the array manifold. Unfortunately, the array perturbations are inevitable in practical applications, and hence the estimators performance would degrade substantially when errors exist and the assumed observation model deviates from real situation.