STATISTICAL-ANALYSIS OF A 2-LAYER BACKPROPAGATION ALGORITHM USED FOR MODELING NONLINEAR MEMORYLESS CHANNELS - THE SINGLE NEURON CASE

Neural networks have been used for modeling the nonlinear characterist ics of memoryless nonlinear channels using backpropagation (BP) learni ng with experimental training data. In order to better understand this neural network application, this paper studies the transient and conv ergence properties of a simplified two-layer neural network that uses the BP algorithm and is trained with zero mean Gaussian data. The pape r studies the effects of the neural net structure, weights, initial co nditions, and algorithm step size on the mean square error (MSE) of th e neural net approximation. The performance analysis is based on the d erivation of recursions for the mean weight update that can be used to predict the weights and the MSE over time. Monte Carte simulations di splay good to excellent agreement between the actual behavior and the predictions of the theoretical model.