Enhanced DOA Estimation With Co-Prime Array in the Scenario of Impulsive Noise: A Pseudo Snapshot Augmentation Perspective

Co-prime array configuration is popular in the recent development of array signal processing. However, the assumption of Gaussian noise in most co-prime array processing research leads to model mismatch in practical scenarios of impulsive noise, therefore has an adverse impact on the estimation of direction of arrival (DOA) of the incoming sources. Moreover, co-prime array builds an enlarged virtual array by vectorizing the covariance matrix of the received signals, where the equivalent received signals of the virtual array have only a single snapshot. In this article, we propose an enhanced fractional low-order method (EFLOM) for co-prime array configuration in the scenarios of impulsive noise, from the perspective of pseudo snapshot augmentation. Since impulsive noise does not have finite second-order statistics or high-order cumulant, we construct a series of equivalent covariance matrices by using phased fractional low-order moments with different orders of the received signals. Then, the vectorization of the multiple equivalent covariance matrices can be considered as the equivalent received signals of virtual array with multiple pseudo snapshots. As multiple pseudo snapshots are constructed from the same sources, additional spatial smoothing preprocessing operations are still needed for enforced decorrelation. In this article, we propose an improved spatial smoothing (ISS) technique by applying the information of both autocorrelation and cross subarray correlation in the covariance matrix. Afterwards, the classical multiple signal classification (MUSIC) is applied for the estimation of DOAs. In addition, the proposed method can also be extended to the other sparse array geometrics. The performance of the proposed method is theoretically verified and simulations are provided to show its effectiveness in terms of the generalized signal to noise ratio (GSNR), parameter of impulsive noise, and angle separation. Simulation results show that the proposed method can greatly improve the resolution, accuracy, and degrees of freedom (DOFs) in DOA estimation in presence of impulsive noise.