Nonlinear communication channel equalization using wavelet neural networks

The paper investigates the application of a wavelet neural network structure to the adaptive channel equalization of a bipolar signal passed through a nonlinear channel in the presence of additive Gaussian noise. The wavelet network is a two-layer localized receptive field network whose output nodes form a linear combination of the wavelet orthonormal basis functions computed by the hidden layer nodes. The wavelet orthonormal basis is a family of functions which is built by dilating and translating the Morlet mother wavelet. An appropriate wavelet basis leads to the wavelet network which is capable of forming the best approximation to any continuous nonlinear mapping up to an arbitrary resolution. Such an approximation introduces nonlinear decision making ability into the wavelet equalizer in order to compensate the nonlinear channel distortion. Since the wavelet network network has a linear-in-the parameters structure, the fast-convergent recursive least square algorithm can readily be used to train the equalizer and the training is guaranteed to converge a single global minimum of the mean square error surface