Abstract
In D.O.A. estimation, identification of the signal and the noise subspaces plays an essential role. This identification process was traditionally achieved by the eigenvalue decomposition (EVD) of the spatial correlation matrix of observations or the generalized eigenvalue decomposition (GEVD) of the spatial correlation matrix of observations with respect to that of an observation noise. The framework based on the GEVD is not always an extension of that based on the EVD, since the GEVD is not applicable to the noise-free case which can be resolved by the framework based on the EVD. Moreover, they are not applicable to the case in which the spatial correlation matrix of the noise is singular. Recently, a quotient-singular-value-decomposition-based framework, that can be applied to problems with singular noise correlation matrices, is introduced for noise reduction. However, this framework also can not treat the noise-free case. Thus, we do not have a unified framework of the identification of these subspaces. In this paper, we show that a unified framework of the identification of these subspaces is realized by the concept of proper and improper eigenspaces of the spatial correlation matrix of the noise with respect to that of observations.
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