Complex-valued function approximation using a Fully Complex-valued RBF (FC-RBF) learning algorithm

In this paper, a fully complex radial basis function (FC-RBF) network and a gradient descent learning algorithm are presented. Many complex-valued RBF learning algorithms have been presented in the literature using a split-complex network which uses a real activation function in the hidden layer, i.e., the activation function in these network maps Cⁿ rarr R. Hence these algorithms do not consider the influence of phase change explicitly and hence do not approximate phase accurately. In this paper, a Gaussian like fully complex activation function sech(.) (Cⁿ rarr C) and a well defined gradient descent learning algorithm are developed for a FC-RBF network using sech(.) as activation function. The performance evaluation of the FC-RBF network has been carried out with two synthetic complex-valued function approximation problems, a complex XOR (C-XOR) problem and a non-minimum phase equalization problem. The results indicate the better performance of the FC-RBF network compared to the existing split complex RBF network methods.