Self-Calibration Algorithm with Gain-Phase Errors Array for Robust DOA Estimation

The performance of direction-of-arrival (DOA) estimation algorithms degrades when a partly calibrated array is adopted due to the existing unknown gain-phase uncertainties. In addition, the spatial discretized searching grid also limits the performance improvement and effectiveness of subspacebased DOA estimation algorithms, especially when the true angles do not lie on the grid points which is referred to the off -grid problem alike. In this paper, a self-calibration DOA estimation algorithm is proposed which solves the array calibration and off -grid problems simultaneously. Firstly, the signal model for a partly calibrated array with gain-phase uncertainties is established. To suppress the offgrid errors, an optimization problem for joint parameters estimation is constructed by substituting the approximation of the steering vector into a newly constructed objective function. The alternative minimization (AM) algorithm is employed to calculate the joint DOA and gain-phase uncertainty estimations. Within each iteration step of the optimization problem, a closed-form solution is derived that guarantees the convergence of the proposed algorithm. Furthermore, the Cram & eacute;r-Rao bound (CRB) for the partly calibrated arrays with unknown gain-phase uncertainties is also derived and analyzed in the paper. Simulation results demonstrate the effectiveness of the proposed algorithm.