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

Authors:
R. Savitha;S. Suresh;N. Sundararajan
Affiliations:
School of Electrical and Electronics Engineering, Nanyang Technological University, Singapore;Korea University, Seoul, Republic of South Korea;School of Electrical and Electronics Engineering, Nanyang Technological University, Singapore
Venue:
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Year:
2009

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Abstract

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 → 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 → 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.