Blind Unitary Prewhitening with a Real-Valued Eigendecomposition

Abstract

Prewhitening is a standard step for the processing of noisy signals. Typically, eigenvalue decomposition (EVD) of the sample data covariance matrix is used to calculate the whitening matrix. From a computational point of view, an important problem here is to reduce the complexity of the EVD of the complex-valued sample data covariance matrix. In this paper, we show that the computational complexity of the prewhitening step for complex-valued signals can be reduced approximately by a factor of four when the real-valued EVD is used instead of the complex-valued one. Such complexity reduction can be achieved for any axis-symmetric array. The performance of the proposed procedure is studied in application to a blind source separation (BSS) problem. For this application, the performance of the proposed prewhitening scheme is illustrated by means of simulations, and compared with the conventional prewhitening scheme. Among a number of BSS methods which use prewhitening, the second-order blind identification procedure has been adopted in this paper.