DOA estimation for coherent sources with spatial smoothing without eigendecomposition under unknown noise field

In this paper, we employ the propagator method (PM) to find the direction of arrival angles (DOAs) from the incident sources without any eigendecomposition. This can reduce complexity when compared to eigensubspace methods such as forward/backward spatial smoothing, which requires eigenvalue decomposition (EVD). Also, we apply our proposed algorithm in the situation when the incident sources are coherent. Our proposed algorithm can be applied for more practical situations when the unknown covariance noise matrix is in a complex symmetric Toeplitz form, whereas in Prasad´s model the unknown noise is in a real symmetric Toeplitz form. Moreover, the proposed algorithm, when compared with Prasad´s model does, has three advantages: (1) it does not require any EVD to find the DOAs, whereas Prasad´s model does, (2) our proposed algorithm requires the number of sensors M to be larger than the number of sources K, i.e., M>K, but Prasad´s method requires M>2K, and (3) the proposed method can be applied in the situation when the sources are coherent, but Prasad´s method cannot. Our proposed method is based on a covariance matrix difference between the forward/backward spatial smoothing for covariance matrices of the received data and the Hermition of the backward spatial smoothing only. This difference is introduced to eliminate noise components from the array structure. The numerical results verify that the proposed method gives better performance and less computation than forward/backward spatial smoothing