Generalized splitting functions for blind separation of complex signals

This paper proposes the blind separation of complex signals using a novel neural network architecture based on an adaptive nonlinear bi-dimensional activation function (AF); the separation is obtained maximizing the output joint entropy. Avoiding the restriction due to the Louiville's theorem, the AF is composed of a couple of bi-dimensional spline functions, one for the real and one for the imaginary part of the signal. The surface of this function is flexible and it is adaptively modified according to the learning process performed by a gradient-based technique. The use of the bi-dimensional spline defines a new class of flexible AFs which are bounded and locally analytic. This paper aims to demonstrate that this novel bi-dimensional complex AF outperforms the separation in every environment in which the real and imaginary parts of the complex signal are not decorrelated. This situation is realistic in a large number of cases.