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The paper presents an adaptive RBFNNE (radial basis function neural network equalizer) of nonlinear time-varying UMTS channel; the architecture of the RBFNNE implements the Bayesian decision function. Centers of hidden layer neurons, equal to the channel states, are determined by an unsupervised classification algorithm based on the rival penalized competitive algorithm. To determine the other parameters (spreads of hidden layer neurons and connections weights), the gradient descent algorithm applying the on-line and offline training modes is used. The mobile communication channel UMTS, is generally modeled by a tapped delay line (TDL) model, where the coefficients implement the delay profile and the Doppler effect of the doubly-selective channel. Furthermore, a nonlinear distortion is added to the transmitted symbols; good performance results are obtained as compared to the classical equalizers i.e. minimum mean-squared error equalizer (MMSE) and the decision feedback equalizer (DFE) are obtained for the case of nonlinear time-varying UMTS channel.