A Unified Framework and Sparse Bayesian Perspective for Direction-of-Arrival Estimation in the Presence of Array Imperfections

Self-calibration methods play an important role in reducing the negative effects of array imperfections during direction-of-arrival (DOA) estimation. However, the dependence of most such methods on the eigenstructure techniques greatly degrades their adaptation to demanding scenarios, such as low signal-to-noise ratio (SNR) and limited snapshots. This paper aims at formulating a unified framework and sparse Bayesian perspective for array calibration and DOA estimation. A comprehensive model of the array output is presented first when a single type of array imperfection is considered, with mutual coupling, gain/phase uncertainty, and sensor location error treated as typical examples. The spatial sparsity of the incident signals is then exploited, and a Bayesian method is proposed to realize array calibration and source DOA estimation. The array perturbation magnitudes are assumed to be small according to most application scenarios, and the geometries of mutually coupled arrays are assumed to be uniform linear and those of arrays with sensor location errors are assumed to be linear. Cramer-Rao lower bounds (CRLBs) for the array calibration and DOA estimation precisions are also obtained. The sparse Bayesian method is finally extended to deal with the DOA estimation problem when more than one type of array perturbation coexists.