Pseudo-beam-Forming for Direction-of-Arrival Estimation with Difference Co-array of Co-prime Array

Abstract

This paper focuses on direction finding using a co-prime array from the view of a difference co-array. According to the corresponding relationship between the correlation lag and virtual element position of the difference co-array, from the correlation matrix of the co-prime array, the desired correlation units are extracted as single-snapshot data of the virtual co-array elements of the co-prime array and are then coherently accumulated into a pseudo-beam pattern. Because the difference co-array of a co-prime array consists of a group of contiguous virtual elements and multiple non-uniform virtual elements, this paper considers pseudo-beam-forming using only contiguous virtual elements, as in existing studies, and all of the virtual elements. Compared with the existing sub-beam multiplication method, pseudo-beam-forming reduces the negative effect from grating lobes and resolves more uncorrelated sources than the number of physical elements. Moreover, application of non-uniform virtual elements improves the resolvable source number, angle resolution and noise immunity, which are analyzed quantitatively based on the proposed distribution characteristic of virtual elements. Finally, to suppress side-lobe interference caused by the non-uniform virtual elements, we introduce and evaluate three coherence weighting factors, namely coherence factor (CF), phase coherence factor (PCF) and sign coherence factor (SCF), where CF is proved to be ineffective and SCF is optimal in suppression and computation performance.