Exploiting non-Gaussianity for signal separation

The purpose of this paper is to contrast, in terms of standard criteria for statistical independence, cumulant-based methods of independent component analysis (ICA) with a potentially more robust blind signal separation technique called BLISS. This is able to separate independent non-Gaussian co-channel signals from multisensor data using only the joint probability distributions of instantaneous linear mixtures of those signals. BLISS is also able, without prior array calibrations or training waveforms, to estimate individual steering vectors including unknown mutual coupling and multipath. We point out fundamental reasons for the difficulty of comparing the performance of different ICA algorithms on finite duration practical data. We also propose a novel method for applying real-valued ICA to complex-valued data. By separately estimating in-phase and quadrature un-mixing parameters, we avoid the difficulty of selecting a subset of real and complex-valued cumulants. To justify our approach, we extend the definition of independence to the complex-valued case.