Complex-valued growing and pruning RBF neural networks for communication channel equalisation

A complex-valued radial basis function (RBF) network is proposed for solving the communication channel equalisation problem with quadrature amplitude modulation signals. The network uses a sequential learning scheme, referred to as the complex-valued growing and pruning (CGAP) algorithm, and is an extension of the generalised growing and pruning network of Huang et al. developed for real-valued radial basis function (RBF) networks. The learning algorithm in this network makes use of the concept of 'significance' for hidden neurons. By linking the significance of a neuron to the learning accuracy, a growing and pruning strategy for an RBF neural network with complex inputs is derived. Further, for both growing and pruning, one needs to check only the nearest neuron (based on the Euclidean distance to the latest input data) for its significance, resulting in a more compact network. When there is no growing or pruning, a complex, extended Kalman filter is used to adjust the RBF network parameters. The performance of the CGAP-RBF equaliser is compared with several other equalisers such as CMRAN, CRBF and ASNN on several nonlinear, complex channel equalisation problems. The results show that the CGAP-RBF equaliser is superior to other equalisers in terms of symbol error rate and network complexity.