Abstract: Aiming at the current matrix reconstruction algorithm for decoherence by losing the array aperture, i.e., sacrificing the degree of freedom, this thesis proposes a new DOA estimation algorithm for coherent signals based on virtual array expansion and Toeplitz matrices reconstruction (VAE-TOEP). Firstly, the nature of the forth-order cumulant is utilized to expand the array virtually to enlarge the array aperture, however, the obtained fourth-order cumulant matrix contains a lot of redundant entries, and how to remove these redundant entries in order to get the covariance matrix corresponding to the orientation vectors of the virtually extended array is the key to the success of the virtual expansion of the original array. In this thesis, the algorithm is derived rigorously: remove the rows and columns in the fourth-order cumulant matrix that do not correspond to the orientation vectors of the virtual expanded array, retain the rows and columns that correspond to the orientation vectors of the virtual expanded array, and then reconstruct the covariance matrix by combining with the Forward and Backward Partial Toeplitz square Matrices Reconstruction algorithm. Finally, the DOA estimation of incident signal direction is performed based on the reconstructed covariance matrix. The simulation experimental results show that, because of the virtual expansion of the original array aperture and the effective removal of the redundant entries, even if the covariance matrix is reconstructed using the Forward and Backward Partial Toeplitz square Matrices Reconstruction algorithm, the dimensionality of the covariance matrix will not be reduced, i.e., the degree of freedom of the array are not sacrificed, so the algorithm proposed in this thesis is able to efficiently estimate the direction of arrival of more coherent signals with higher DOA estimation accuracy than the existing matrix reconstruction algorithms without sacrificing the degrees of freedom.