A cumulant-based approach for direction finding in the presence of mutual coupling

To estimate the direction-of-arrivals (DOAs) of non-Gaussian signals impinging on a uniform linear array (ULA) with unknown mutual coupling, a fourth-order cumulants (FOC)-based approach is presented. A series of FOC matrices are constructed by taking advantage of the banded symmetric Toeplitz structure of the mutual coupling matrix (MCM). It is shown that the DOAs can be estimated in a closed form based on these matrices. Compared with the conventional FOC-based method which only uses the middle subarray, the proposed approach makes use of the whole array and it is able to achieve better performance. Moreover, in the proposed approach the DOAs are determined by the eigenvalue decomposition instead of the exhaustive grid search and hence, it is computationally efficient. Finally, compared with the middle subarray method, the proposed one is applicable to scenarios with stronger mutual coupling. A number of numerical examples are provided to validate essential performance improvements achieved by means of the proposed approach.