Complex-valued radial basis function networks

Abstract

We propose a novel complex radial basis function
(RBF) network. The network has complex centres and weights but the response of its hidden nodes remains real. Several leaming algorithms for the existing real RBF network are extended to this complex network. The proposed network is capable of generating complicated nonlinear decision surface or approximating an arbitrary nonlinear function in multidimensional complex space and it provides a powerful tool for nonlinear signal processing involving complex
signals. This is demonstrated using two practical
applications to communication systems. The first case considers the equalisation of time-dispersive communication channels, and we show that the underlying Bayesian solution has an identical structure to the complex RBF network. In the second case, we use the complex RBF network to model nonlinear channels, and this application is typically found in channel estimation and echo cancellation involving nonlinear distortion.

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