An enhanced expanding and shift sparse array based on the coprime array and nested array

In recent years, sparse arrays based on the fourth-order difference coarray (FODCA) have received increased research attention due to their small number of array elements and large consecutive virtual arrays. The expanding and shift structure based on the nested array (NA) and coprime array (CPA) (EAS-NA-CPA) is the representative one. The EAS-NA-CPA comprises two sparse subarrays, wherein the NA is expanded and shifted according to the second-order difference coarray of the CPA. Although the number of consecutive elements is large, there are many redundant elements in the FODCA of the EAS-NA-CPA. To decrease the number of redundant elements and increase the number of consecutive elements in the FODCA, the authors proposed the enhanced EAS-NA-CPA (EEAS-NA-CPA). Compared with the original EAS-NA-CPA, the EEAS-NA-CPA increases the adjacent physical sensor spacing further by using more fourth-order cross-correlation coarrays in the FODCA, which are not considered in the original EAS-NA-CPA. By performing a theoretical analysis of the FODCA provided by the proposed EEAS-NA-CPA, the sensor spacing in the expanded NA was further increased to obtain a larger number of consecutive elements compared with the original EAS-NA-CPA. Furthermore, the relationship between the number of physical sensors and corresponding number of consecutive elements provided by the FODCA was explicitly expressed. Experimental simulations were conducted to verify the effectiveness of the proposed sparse array for the fourth-order cumulant-based direction of arrival estimation.