Adaptive blind source separation for virtually any source probability density function

Blind source separation (BSS) aims to recover a set of statistically independent source signals from a set of linear mixtures of the same sources. In the noiseless real-mixture two-source two-sensor scenario, once the observations are whitened (decorrelated and normalized), only a Givens rotation matrix remains to be identified in order to achieve the source separation. In this paper, an adaptive estimator of the angle that characterizes such a rotation is derived. It is shown to converge to a stable valid separation solution with the only condition that the sum of source kurtosis be distinct from zero. An asymptotic performance analysis is carried out, resulting in a closed-form expression for the asymptotic probability density function of the proposed estimator. It is shown how the estimator can be incorporated into a complete adaptive source separation system by combining it with an adaptive prewhitening strategy and how it can be useful in a general BSS scenario of more than two signals by means of a pairwise approach. A variety of simulations assess the accuracy of the asymptotic results, display the properties of the estimator (such as its robust fast convergence), and compare this on-line BSS implementation with other adaptive BSS procedures.