Direct exploitation of non-Gaussianity as a discriminant

The main purpose of this paper is to provide some additional insight into the several methods of cochannel blind signal separation that are based on the established concept of Independent Component Analysis (ICA). We compare published versions with a robust algorithm that has been devised and developed by the author. Most ICA algorithms are based on maximising the magnitudes of auto-cumulants and/or minimising various cross-cumulants of orthonormal principal components. In an alternative approach, the objective of independence between multiple signals is obtained by applying unitary rotations estimated from the rotational symmetry observed in joint probability distribution functions (jpdf). We show that the pairwise rotation-sensitive statistic, as used in the latter method, involves bivariate higher order statistical (HOS) terms common to other methods of ICA (but with differing relative weights). With this insight, we observe that, for optimum separation in non-Gaussian noise, the relative weighting applied to individual samples can also be modified. Another difficulty is that of measuring the performance achieved by different blind algorithms. This arises because the weighting of cumulants selected in a test of independence of the output waveforms can unfairly favour the algorithm that uses a similar weighting as it's objective function.