DOA estimation with co-prime array by a combined BNC-PFLOM method in presence of impulsive noise

Direction of arrival (DOA) estimation with co-prime array is well studied in the field of array signal processing, but most research assumes noise to be Gaussian white noise. In practical scenarios, there might be impulsive noise, which has neither second-order statistics nor high-order cumulant, therefore cannot be processed directly in co-prime array configurations. In addition, the signals received by the co-prime virtual array are of single snapshot, which can be considered as coherent virtual signals coming from the same source and therefore performance degradation in DOA estimation. To solve the above mentioned problems, a combined bounded non-linear covariance (BNC) and phase fractional low-order moments (PFLOM), called BNC-PFLOM, is proposed in this brief. The proposed BNC-PFLOM combines the merits of both BNC and PFLOM by constructing equivalent data covariance matrices of the received signal to lower the impact of impulsive noise. Moreover, the proposed BNC-PFLOM can build multiple pseudo snapshots of virtual signals from the co-prime array by using different orders of the proposed method. With the increase of pseudo snapshots, the proposed method is more robust in DOA estimation. Besides, the pseudo snapshots are developed from different methods, which implies different virtual signals coming from different sources. Therefore, the correlation between the virtual co-array signals can be reduced; and the proposed method direct estimates the DOAs of signals without spatial smoothing when the number of incoming signals is small. The proposed method generates multiple pseudo snapshots, which improves the resolution and accuracy in DOA estimation with co-prime array, and can be used for radar, sonar, communication systems, etc . Simulation results demonstrate the effectiveness of the proposed method, which outperforms the conventional BNC, FLOM, and PFLOM with smaller root means square error (RMSE) in terms of the generalized signal to noise ratio (GSNR) and factor of impulsive noise.