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 non-linear bi-dimensional activation function; the separation is obtained maximizing the output joint entropy. Avoiding the restriction due to the Louiville’s theorem, the activation function is composed by 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 activation functions which are bounded and locally analytic. This paper aims at demonstrate that this novel bi-dimentional complex activation function outperforms the separation in every environment in which the real and the imaginary part of the complex signal are not decorrelated. This situation is realistic in a large number of cases.