Self-Calibration DOA Estimation for Moving Dilated Arrays with Gain and Phase Errors

Abstract

Moving dilated arrays (MDAs) can increase the uniform degrees of freedom (uDOFs) while alleviating mutual coupling, but their performance is susceptible to unknown gain and phase errors (GPEs). To deal with this problem, we investigate self-calibration direction-of-arrival (DOA) estimation for MDAs with unknown GPEs. First, multi-position observations are phase aligned to construct an equivalent virtual array with an enlarged aperture. Next, the motion-induced relationships among the GPEs are exploited to establish explicit calibration constraints. By leveraging the orthogonality between the steering vectors and the noise subspace, the joint estimation of the DOAs and GPEs is formulated as a constrained optimization problem. To solve this problem, a two-stage alternating optimization (AO) algorithm is developed. In the first stage, the GPEs are estimated in closed form with the DOAs fixed. In the second stage, the estimated GPEs are used to calibrate the covariance matrix, after which the DOAs are refined using the multiple signal classification (MUSIC) algorithm. To obtain reliable initial estimates, a rotational invariance-like (RIL) initialization method is further developed by exploiting two translated virtual subarrays with identical GPEs. Furthermore, the Cramer-Rao bound (CRB) is derived to characterize the theoretical performance limit of the considered system. Simulation results demonstrate that the proposed method converges reliably and achieves accurate DOA estimation under different array apertures, numbers of snapshots, GPE levels, and numbers of sources.