Exact expectation analysis of the sign-data LMS algorithm for i.i.d. input data

The author presents an automated method of deriving an exact description of the convergence behavior of a class of nonlinearity modified data adaptive algorithms for system identification modeling with independent, identically distributed (i.i.d.) samples as input data. Using the method, a set of linear equations that exactly describes a nonlinear data algorithm´s stochastic behavior at each time step is identified. Moreover, precise bounds upon the step size to guarantee convergence of the algorithm in the mean and in mean square are obtained. Simulations indicate that the equations produced by the exact method are much more accurate than previous analyses in predicting convergence behavior of the sign-data LMS adaptive algorithm particularly in fast adaptation situations