Robust DOA Estimation With Distorted Sensors

The distorted sensors in an array system will degrade the signal-to-interference-plus-noise ratio of received signal, resulting in performance deterioration. Without knowing the number of source signals, this article focuses on direction-of-arrival (DOA) estimation for a uniform linear array, in whicha small fraction of sensors are distorted. Meanwhile, source enumeration and detection of distorted sensors are realized. We model the array system with distorted sensors by introducing unknown gain and phase errors to the output signals, where the observations corresponding to the distorted sensors are treated as outliers. In this way, we tackle the DOA estimation task under the framework of low-rank and row-sparse matrix decomposition. We directly adopt the rank function and l(2,0)-norm to obtain the low-rank and row-sparse matrices, respectively, instead of utilizing their surrogates as in the conventional methods. Therefore, the approximation bias is avoided. In detail, rank and l(2,0)-norm optimization is converted to l(0)-norm minimization. To solve it, we propose a shifted median absolute deviation-based strategy, achieving adaptive hard-thresholding control. The resultant optimization problem is then handled by proximal block coordinate descent, and the convergences of the objective function value and the solution sequence are proved. Extensive simulation results demonstrate the superior performance of the proposed algorithm in terms of DOA estimation, source number estimation, and distorted sensor detection.