Recursive estimator for separation of arbitrarily kurtotic sources

Blind source separation has many important applications in communications and array signal processing. Many widely used methods require prior knowledge on the sign of the kurtosis of the sources and may fail if the mixtures contain both sub- and super-Gaussian signals. In this paper we present an adaptive algorithm for separating arbitrarily kurtotic sources. The blind separation problem is modeled using a state-space formulation. The resulting separation algorithm uses a subspace tracker and a predictor-corrector filter structure related to the well-known Kalman filter. It lends itself easily to real-time implementation. The zero-memory nonlinearities needed for finding independent sources are selected online by monitoring the statistics of each estimated source signal. Consequently, separation may be achieved even if a change in the sign of the kurtosis occurs. Simulation examples illustrating the ability to adapt to time-varying mixing systems and source distributions of unknown kurtosis are presented using communications and biomedical signals. In the biomedical example, the sources are two positive kurtotic ECG signals representing maternal and fetal heart beats at frequencies about 1 Hz and 3 Hz respectively and an interfering sinusoid of 50 Hz (negative kurtotic).