D.O.A.. estimation with singular noise correlation matrix [audio signal processing applications]

In this paper, a new method of direction of arrival (D.O.A.) estimation with environmental noise, whose spatial correlation matrix is singular, is proposed. In D.O.A. estimation, identification of signal and noise subspaces plays a very important role. The identification process can be achieved by (generalized) eigenvalue decomposition of the spatial correlation matrix of observations (with respect to that of noise), if these spatial correlation matrices are non-singular. However, these mathematical tools cannot be applied to the problems in which the spatial correlation matrices are singular. The main idea of this work deeply depends on identification of proper and improper eigenvectors of the spatial correlation matrix of noise with respect to that of observations. The results of computer simulations are also presented to verify the efficacy of the proposed method.