A Statistically Efficient Estimator for Co-array Based DoA Estimation

Co-array-based Direction of Arrival (DoA) estimation using Sparse linear arrays (SLAs) has recently gained considerable interest in array processing due to the attractive capability of providing enhanced degrees of freedom. Although a variety of estimators have been suggested in the literature for co-array-based DoA estimation, none of them are statistically efficient. This work introduces a novel Weighted Least Squares (WLS) estimator for the co-array-based DoA estimation employing the covariance fitting method. Then, an optimal weighting is given so that the asymptotic performance of the proposed WLS estimator coincides with the Cram\'{e}r-Rao Bound (CRB), thereby ensuring statistical efficiency of resulting WLS estimator. This implies that the proposed WLS estimator has significantly better performance compared to existing methods in the literature. Numerical simulations are provided to corroborate the asymptotic statistical efficiency and the improved performance of the proposed estimator.