A matrix-pencil approach to blind separation of colored signals

Abstract

The problem of blind source separation in additive noise is an important problem in speech, array, and acoustic signal processing. In general, this problem requires the use of higher order statistics of the received signals. Nonetheless, for many signal sources such as speed with distinct, nonwhite power spectral densities, second-order statistics of the received signal mixture can be exploited for signal separation. While previous approaches often assume that additive noise is absent or that the noise correlation matrix is known, we propose a simple yet effective signal extraction method for signal source separation under unknown temporally white noise. This new and unbiased signal extractor is derived from the matrix pencil formed between output auto-correlation matrices at different delays. Based on the matrix pencil, an ESPRIT-type algorithm is derived to get an optimal solution in the least square sense. Our method performs better than other second-order statistics-based algorithms when sensor noises are correlated. Simulation examples are presented. © 1998 IEEE.