Optimum adaptive blind source separation algorithms

Adaptive blind source separation algorithms are conventionally composed of two parts. The first, using second order statistics, is responsible for whitening the measured signals, whereas the second, based on nonlinear statistics, imposes independence and achieves the final separation. In this work we show that this two-part scheme is in fact not necessary. By proposing a general nonlinear adaptation model, we find conditions that lead to source separation and guarantee an overall desirable symmetric behavior of the algorithm. Furthermore, using a local performance measure, we optimize the general adaptation scheme and obtain algorithms that have optimum convergence rate. Finally we show that the proposed optimum schemes, except for trivial cases, cannot be put under the two-part classical scheme of the literature, suggesting that the latter is suboptimum.