A Fundamental Relation Between Blind and Supervised Adaptive Filtering Illustrated for Blind Source Separation and Acoustic Echo Cancellation

In recent years broadband signal aquisition by sensor arrays, e.g., for speech and audio signals in a hands-free scenario, has become a popular research field in order to separate certain desired source signals from competing or interfering source signals ((blind) source separation or interference cancellation) and to possibly dereverberate them (blind deconvolution). In various practical scenarios, some or even all interfering source signals may be directly accessible and/or some side information on the propagation path is known. In these cases we can tackle the separation problem by supervised adaptation algorithms, e.g., the popular LMS- or RLS-type algorithms, rather than the more involved blind adaptation algorithms. In contrast, for blind estimation, such as in the blind source separation (BSS) scenario where both the propagation paths and the original source signals are unknown, the method of independent component analysis (ICA) is typically applied. Traditionally, the ICA method and supervised adaptation algorithms have been treated as different research areas. In this paper, we establish a conceptually simple, yet fundamental relation between these two worlds. This is made possible using the previously introduced generic broadband adaptive filtering framework, called TRINICON. As we will demonstrate, not only both the well-known blind and supervised adaptive filtering algorithms turn out as special cases of this generic framework, but we also gain various new insights and synergy effects for the development of new and improved adaptation algorithms.