Expanded coprime array for DOA estimation: augmented consecutive co-array and reduced mutual coupling

Generalized coprime structure decomposes the interleaved subarrays in the conventional coprime array by introducing a displacement and the resulting CADiS, i.e. coprime array with displaced subarrays, configuration can enlarge the minimum adjacent spacing between elements to multiples of half-wavelength, which is considerably attractive in alleviating mutual coupling effect. However, the difference co-array that CADiS yields is fractured, which greatly deteriorates direction of arrival (DOA) estimation performance and achievable degrees of freedom of the algorithms based on consecutive co-array, e.g. spatial smoothing technique and Toeplitz matrix method. In this paper, from the mutual coupling effect and difference co-array perspective, we propose an expanded coprime array (ECA) structure by two steps. The first step is to further augment the displacement between the subarrays of CADiS to suppress the mutual coupling effect. The second step is to relocate a proper number of rightmost elements to concatenate the dominant consecutive co-array generated by CADiS to enhance the consecutive difference co-array. Specifically, we provide the closed-form expressions of resulting consecutive difference co-array, the number of relocated elements and their positions. Furthermore, different from the spatial smoothing based methods, we employ Toeplitz matrix property to directly construct the full-rank covariance matrix of the received data from the consecutive co-array with a lower computational cost and present the Toeplitz-MUSIC algorithm to testify the effectiveness and superiority of the proposed ECA structure.