A special coprime array configuration for increased degrees of freedom

Abstract

In this work, we propose a novel coprime array configuration that will increase the degrees of freedom (DOF) and reduce the mutual coupling than those of the prototype coprime array (PCA). The novel array will be called as special coprime array (SCA). Here we utilize both the temporal and spatial information to get the sum difference coarray (SDCA). There will be a significant improvement of the consecutive DOF of SCA than that of the PCA. In fact, we will prove that only the difference coarray of SCA achieves a consecutive DOF of O(MN), which is only O(M+N) in the case of PCA. We give detailed explanations of the properties of difference coarray, sum coarray, and SDCA of SCA. If M and N (M<N) denote the number of sensors in the two subarrays of SCA, we carry out the analysis of the structure by taking three different cases (a) N is even (b) N is odd and M≠2 and (c) N is odd and M=2. As one of the subarrays of the SCA is shifted, the mutual coupling of the SCA will be much less than that of the PCA. To reduce the mutual coupling further, we will flip one of the subarrays of SCA to get the special unfolded coprime array (SUCA). We also optimize the array for a fixed number of sensors. We then carry out all the required simulations in both the array configurations to prove the superiority of SCA and SUCA over other existing coprime arrays.