A generalized ICA algorithm for extraction of super and sub Gaussian source signals from a complex valued mixture

Extraction of unknown independent source signals from a noisy mixture is a fundamental problem in most signal processing applications. The existing independent component analysis (ICA) algorithms have tackled this problem for complex and real valued mixtures for both super and sub Gaussian sources. However in reality super and sub Gaussian sources exist collectively in a mix. It was observed when examining the kurtosis surface behavior for a super-sub Gaussian collective mixture the implications of a positive region implies the existence of at least one super Gaussian source while a statement cannot be made about the existence or non-existence of a sub-Gaussian source. The same observation holds for the reverse case where a negative valued kurtosis surface exists. Thus a modified sign update equation is proposed for source extraction for a super-sub Gaussian mixture in that spirit. The update equation takes into account the existence of a positive/negative region to conclude on the existence of a super/sub Gaussian source and employs an ascent/descent approach accordingly. The technique is analyzed for both real and complex valued mixtures.