Nonlinear adaptive RBF neural filter with Lyapunov adaptation algorithm and its application to nonlinear channel equalization

An RBF neural network, combined with a Lyapunov adaptation (LA) algorithm is proposed for linear or nonlinear channel equalization. The output observations of the nonlinear channel are regarded as inputs of the RBF neural filter. The weights of the neural network are updated by the LA algorithm that is based on Lyapunov stability theory so that the error between the reference signal and output of the RBF neural filter can converge to zero asymptotically. The stochastic properties of the signals are not required and the stability is guaranteed by the Lyapunov stability theory. The design of the LA algorithm is extremely simplified compared with existing LMS and RLS algorithms. Hence, the proposed scheme possesses distinct advantages of stability, speed of convergence, convergence properties and some key features of RBF neural networks over the conventional linear filter with RLS and LMS for channel equalization.