Performance analysis of nonlinear adaptive filter based on LMS algorithm

This paper presents a performance analysis of the adaptive Volterra nonlinear filter which employs a previously developed algorithm based on the least mean square method. In the linear case, the eigenvalue spread of the autocorrelation matrix controls the speed of convergence. The larger the eigenvalue spread, the slower the convergence speed. In the nonlinear case, the eigenvalue spreads are in general large. Therefore the performance is poor. However, based on Therrien et al. (1997), with proper manipulation, the autocorrelation matrix can be diagonalized giving less eigenvalue spread much like the linear filter. Through this analysis, the step size bounds, autocorrelation matrix misadjustment and time constant are all examined. The results of our analysis are verified by computer simulation.