Multiple-Toeplitz Matrices Reconstruction Algorithm for DOA Estimation of Coherent Signals

In this paper, a new direction-of-arrival (DOA) estimation method based on multiple Toeplitz matrices reconstruction is proposed for coherent narrowband signals with a uniform linear array (ULA). First, the received signals impinging on the ULA are rearranged in a Toeplitz matrix, and a full set of correlation matrices are computed by the Toeplitz-based matrix and the observed data of each sensor. Then, a weighted summation by squaring these correlation matrices is obtained to form the full rank equivalent data covariance matrix. Furthermore, a forward-and-backward scheme is presented to improve the estimation accuracy of the covariance matrix. Based on the joint diagonalization structure of the covariance matrix with noise contributions as a scalar matrix, the angle estimation problem can be resolved by combining it with subspace-based methods. In comparison with currently known matrix reconstruction methods, the proposed algorithm applies all information contained in the correlation matrices adequately without de-noising processing in advance. Even in the case of a low signal-to-noise ratio and low snapshot number with half the array aperture reduced, the new method provides good performance on estimation and resolution. Finally, simulation results are demonstrated to verify the theoretical prediction.