Blind source separation

Until the mid-1980s, most antenna filtering techniques exploited only the 2nd-order statistics of received signals. In addition, they are described as "informed" in that they require knowledge of antenna responses, and therefore prior calibration [1], or knowledge of "a priori" information on expected signals [2]. Discriminants used to separate the useful signal from interference or noise include :

• direction of arrival, as in radar, sonar or space telecommunications;

• waveform (digital communications) ;

• time (frequency hopping systems) ;

• spectrum (narrowband links in the presence of broadband interference) ;

• power (weak signals disturbed by strong interference) ;

• code (spread spectrum transmissions).

On the other hand, so-called blind or self-taught methods are designed to extract useful signals or parameters of interest without recourse to in-depth knowledge of the latter. This type of approach offers advantages in a number of contexts, notably in passive listening, when none of the above-mentioned discriminating characteristics can be exploited. This is also the case, for example, for towed streamers in sonar when antennas are distorted, in VUHF (very ultra high frequency) or radar when there is coupling between sensors and calibration is too costly. As an indication, we now know that goniometry methods normally offering good resolution, which are very sensitive to the quality of the antenna variety, give very disappointing results in the presence of an approximate calibration.

The most promising blind techniques are based on the assumption of statistically independent, non-Gaussian sources (very common in practice and ubiquitous in radio communications). In addition to information at order 2, they often exploit information contained in statistics of order greater than 2 of the observations. They are therefore referred to as higher-order blind methods.

The aim of this article is essentially to present the philosophy behind these methods, to describe the most promising algorithms at present, and to summarize their performance in different application contexts.