Joint estimation of DOA and mutual coupling via imposing an annihilation constraint

Abstract

The mutual coupling between elements degrades the direction-of-arrival (DOA) estimation performance. This paper considers jointly estimating the DOA and mutual coupling. Firstly, based on the fact that the noiseless array output without mutual coupling consists of complex exponential sums, an annihilation relation is obtained. Then, an optimization problem is proposed by combining a cost function derived from the maximum likelihood principle and a constraint formed by the annihilation relation. The optimization problem is solved by the sequential quadratic programming (SQP) method, where the Jacobian matrix is derived via exploiting the symmetric Toeplitz structure of the mutual coupling matrix. At last, a post-processing method is proposed for further improving the accuracy of mutual coupling estimation. The new method can handle single snapshot estimation, and it is gridless while utilizing the whole aperture. It is also insensitive to overestimation of the degree of mutual coupling. The method has been verified by simulations and compared with representative methods regarding accuracy and efficiency.