Hole-Free DCA for Augmented Co-Prime Array

Abstract

This paper focuses on developing a hole-filling technique for difference co-array (DCA) of the co-prime array and its variants. In existing methods, obtaining DCA uses vectorization of the covariance matrix obtained from received signals employing Khatri–Rao product. For the co-prime array (CA) family, the DCA so obtained consists of a set of virtual contiguous elements and multiple non-uniform virtual elements. Till now, the DOA estimation from the CA family considers only virtual contiguous elements of the DCA, leaving out “holes” and other virtual non-uniform elements. This existence of holes results in a substantial decrease in consecutive degrees of freedom than expected. To address the issue of holes (in the DCA of CA family), this paper extends the original DCA of augmented CA to obtain a new virtual DCA called $ACA^{EDCA}$. The $ACA^{EDCA}$ is virtually hole-free. Compared to DCA of the existing CA family, the resulting $ACA^{EDCA}$ has a larger effective DOF. Therefore, the aperture length compared to other existing variants of the co-prime array is also larger. Simulations compare performances of 9 element ACA using $ACA^{EDCA}$ with few other arrays of the CA family. With and without using $ACA^{EDCA}$, the ACA respectively resolves 43 and 14 sources. Sliding extended CA and relocating extended CA respectively determine 22 and 25 sources. Similarly, the root-mean-square error performance of ACA using $ACA^{EDCA}$ is better compared to others.