An Enhanced DOA Estimation Method for Coherent Sources via Toeplitz Matrix Reconstruction and Khatri–Rao Subspace

The Toeplitz matrix reconstruction methods are capable of resolving coherent signals, playing a crucial role in the direction-of-arrival (DOA) estimation of acoustic sources. However, the decoherence processing sacrifices the array aperture and further results in a reduced resolution capability for the number of identifiable sources. To solve this issue, we propose an enhanced method using the Khatri–Rao subspace to resolve more coherent sources than that of the existing Toeplitz matrix reconstruction methods. Firstly, a full set of Toeplitz matrices with full rank is obtained. Then, the virtual array aperture can be obtained using the Khatri–Rao product of the array response, and the degree of freedom provided inherently in the virtual array structure is about twice the size of that of the existing Toeplitz methods. Next, linear processing is further used to achieve complexity reduction without losing the effective degree of freedom. Finally, the DOA estimation for more coherent sources can be achieved by combining it with conventional methods. Numerical simulations verify the superiority of the proposed method.