Robust blind extraction of a signal with the best match to a prescribed autocorrelation

Abstract

Several blind extraction algorithms have been proposed that extract some signal of interest from a mixture of signals. We propose a novel blind extraction algorithm that extracts the signal that has an autocorrelation closest to a prescribed autocorrelation that serves as a mold. Based on the mold we perform a linear transformation of sensor correlation matrices. This transformation allows for the construction of a matrix with a specific eigenstructure. Each eigenvalue is related to the Euclidean distance between the mold and the actual autocorrelation of one of the source signals. The extraction filter that extracts the source signal with an autocorrelation closest to the mold is identified as the eigenvector that corresponds to the smallest eigenvalue. We show that this approach is more robust to noise than methods from literature, while it exploits comparable a priori information. The results are validated by means of simulations.