Toeplitz Matrix Completion for Direction Finding Using a Modified Nested Linear Array

A modified nested linear array (MNLA) has been reported recently for a greater potential in increasing the degree-of-freedom. However, there exist some "holes" in the difference co-array, which results in missing "lags" and limited performance of direction-of-arrival (DOA) estimation. In order to tackle this problem, this paper applies a Toeplitz matrix completion technique to MNLA, and investigates the performance of DOA estimation on this basis. Particularly, a semidefinite program with trace minimization is derived to obtain the covariance matrix with Hermitian and Toeplitz structure. The recovered Toeplitz covariance matrix is then utilized to perform DOA estimation. Various numerical examples are provided to verify the effectiveness and superiority of the proposed method.