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Stochastic analysis of gradient adaptive identification of nonlinear systems with memory

Gradient search adaptive algorithm for identifying an unknown nonlinear system comprised of a discrete-time linear system H followed by a zero-memory nonlinearity g(.). The LMS algorithm first estimates H. The weights are then frozen. Recursions are derived for the mean and fluctuation behavior of LMS which agree with Monte Carte simulations. When the nonlinearity is modelled by a scaled error function, the second part of the gradient scheme is shown to correctly learn the scale factor and the error function scale factor. Mean recursions for the scale factors show good agreement with Monte Carlo simulations.