Angle estimation with propagator method for correlated sources under unknown symmetric Toeplitz noise

In this paper, we employ the propagator method (PM) to find the direction of arrival angles (DOAs) from the incident sources without any eigen decomposition. This can reduce the complexity when compared to eigen subspace method such as MUSIC algorithm. Also, we apply our proposed algorithm in the situation when the incident sources are uncorrelated or coherent in pairs. In our proposed algorithm, we assume that the unknown covariance noise matrix is to be a symmetric Toeplitz as the Prasad´s noise model. But our proposed algorithm when compared Prasad´s method, has two main advantages: (1) it does not require any eigen decomposition to find the DOAs whereas Prasad´s requires, and (2) our proposed algorithm requires the number of sensors M to be larger than the number of sources L, i.e., M > L, but the Prasad´s method requires M > 2L. So, our proposed method can take a general situation of M > L where Prasad´s method fails for L < M < 2L case. Our proposed method is based on the covariance matrix difference between the average of the forward-backward covariance matrices of the received data and the Hermition of the backward. This difference is introduced to eliminate the noise components from the array structure. The numerical results verify that the proposed method gives better performance and less computation than the conventional MUSIC