A Novel Mutual Coupling Compensation Method for Underdetermined Direction of Arrival Estimation in Nested Sparse Circular Arrays

A simple mutual coupling (MC) compensation method for nested sparse circular arrays that is capable of underdetermined direction-of-arrival (DOA) estimation is proposed. Sparse signal reconstruction (SSR) has offered a renewed interest to the problem of DOA estimation. In SSR framework, DOA estimation is accomplished by finding the sparse coefficients of the array covariance vectors in an overcomplete basis, which achieves high resolution and is statistically robust even in low signal-to-noise ratio. We use a nested sparse circular array composed of dense and sparse parts, which obtains very low MC. Thus, we propose a banded-like circulant MC matrix (MCM), which has a very few MC coefficients. By incorporating the MCM in the DOA estimation problem, the proposed array’s capability of estimating more sources than sensors is improved. As compared with conventional methods, the proposed technique is cost effective and easy to implement, while achieving better performance. Simulation results show that a better underdetermined DOA estimation performance is achieved. We use two methods: subspace based method—MUSIC and SSR method $\ell _{1}$ -based optimization.