Complex-valued neural networks with adaptive spline activation function for digital-radio-links nonlinear equalization

In this paper, a new complex-valued neural network based on adaptive activation functions is proposed. By varying the control points of a pair of Catmull-Rom cubic splines, which are used as an adaptable activation function, this new kind of neural network can be implemented as a very simple structure that is able to improve the generalization capabilities using few training samples. Due to its low architectural complexity (low overhead with respect to a simple FIR filter), this network can be used to cope with several nonlinear DSP problems at a high symbol rate. In particular, this work addresses the problem of nonlinear channel equalization. In fact, although several authors have already recognized the usefulness of a neural network as a channel equalizer, one problem has not yet been addressed: the high complexity and the very long data sequence needed to train the network. Several experimental results using a realistic channel model are reported that prove the effectiveness of the proposed network on equalizing a digital satellite radio link in the presence of noise, nonlinearities, and intersymbol interference (ISI).