Transform Covariance Differencing Method for Correlated Sources under Unknown Symmetric Toeplitz Noise

Abstract

This paper proposes a method to find the direction of arrival angles (DOAs) from correlated sources under an unknown noise environment. This paper assumes a symmetric Toeplitz covariance matrix for the unknown noise. The proposed method has three advantages over the Prasad's method in S. Prasad et al. (1988). First, the numbers of sensors M in our method is just larger than the number of sources L , i.e., M > L, but the method in S. Prasad et al. (1988) requires M > 2L . Second, the number of peaks Np in the spectrum is equal to the number of sources L, i.e., L = Np, whereas the number of peaks of the method in S. Prasad et al. (1988) is 2Np , which requires a special selection algorithm to determine the true DOAs. Third, the proposed method can be applied for correlated sources but the method in S. Prasad et al. (1988) for only uncorrelated sources. The proposed method employs the covariance matrix difference between a transformed forward-backward average covariance matrix of the received signal and the transpose of the backward covariance matrix to completely eliminate the unknown noise. The numerical results verify that the proposed method gives a better performance with less computation than the method in S. Prasad et al. (1988)