Blind separation of circularly distributed sources by neural extended APEX algorithm

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The aim of this work is to present a generalized Hebbian learning theory for complex-weighted linear feed-forward network endowed with lateral inhibitory connections, and to show how it can be applied to blind separation from complex-valued mixtures. We start by stating an optimization principle for Kung–Diamantaras’ network which leads to a generalized APEX-like learning theory relying on some non-linear functions, whose choice determines network's ability. Then we recall the Sudjianto–Hassoun interpretation of Hebbian learning and show that it drives us to the choice of the right set of non-linear functions allowing the network to achieve blind separation. The proposed approach is finally assessed by numerical simulations.