Blind Estimation Using Higher-Order Statistics

A myriad of applications require the extraction of a set of signals which are not directly accessible. Instead, this extraction must be carried out from another set of measurements which were generated as mixtures of the initial set. Since usually neither the original signals — called sources — nor the mixing transformation are known, this is certainly a challenging problem of multichannel blind estimation. One of the most typical examples is the socalled “ cocktail party” problem. In this situation, any person attending the party can hear the speech of the speaker they want to listen to, together with surrounding sounds coming from other ’ competing’ speakers, music, background noises, etc. Everybody has experienced how the human brain is able to separate all these incoming sound signals and to ’ switch’ to the desired one. Similar results can be achieved by adequately processing the output signals of an array of microphones, as long as the signals to be extracted fulfil certain conditions [62, 63] . Wireless communications is another usual application field of signal separation techniques. In a CDMA (Code Division Multiple Access) environment several users share the same radio channel by transmitting their signal after modifying it according to an appropriate code. Traditionally, the extraction of the desired signal at the receiving end requires the knowledge of the corresponding code.