Enhanced Second-Order Off-Grid DOA Estimation Method via Sparse Reconstruction Based on Extended Coprime Array Under Impulsive Noise

The extended coprime array (ECA) can detect a significantly larger number of targets compared to the actual number of sensor elements. Considering the presence of impulse noise in real environments, the phased fractional low-order moment (PFLOM) is introduced to construct an equivalent covariance matrix. In this article, we propose a multiple measurement vector (MMV) model based on ECA, inspired by the spatial smoothing (SS) technique. The MMV model, when compared to the single measurement vector (SMV) model, enables sparse reconstruction algorithms to achieve higher accuracy in direction-of-arrival (DOA) estimation. The traditional iterative sparse projection (ISP) DOA estimation method lacks an extrapolation step, which provides an opportunity for improvement. Hence, we propose the improved ISP (Imp-ISP) algorithm for DOA estimation, equipped with an extrapolation step to enhance performance. Moreover, we propose a second-order Taylor expansion off-grid model, in contrast to the first-order Taylor interpolation off-grid model, to achieve higher DOA estimation accuracy at a low generalized signal-to-noise ratio (GSNR). To validate the performance of the proposed algorithm, we conducted computer simulations and field experiments, and the results demonstrate its superiority over existing methods.