Statistical analysis of adaptive neural network inversion of Hammerstein systems for Gaussian inputs

The paper presents a statistical analysis of neural network (NN) inversion of Hammerstein systems. The system model is composed of a memoryless non linearity g(.) followed by a linear filter H. The inverse system is a nonlinear Wiener system consisting of an adaptive filter Q followed by a memoryless perceptron. The adaptive filter Q aims at inverting the linear part of the system (adaptive deconvolution). The perceptron aims at inverting the memoryless function (adaptive function inversion). The adaptive system is trained using the backpropagation algorithm (BP). The paper proposes recursions for the mean weight behavior during the learning process. The expression of the mean squared error (MSE) is given as function of the Hammerstein system parameters, the adaptive filter coefficients and the NN weights. The paper is supported with illustrations and computer simulations which show good agreement with theoretical analysis.