On Error Saturation Nonlinearities for LMS Adaptation in Impulsive Noise

This correspondence extends the analytic results in [N. J. Bershad, ldquoOn error nonlinearities in LMS adaptation,rdquo IEEE Transactions on Acoustics, Speech and Signal Processing, vol. ASSP-36, no. 4, pp. 440-452, April 1988] to least mean-square (LMS) adaptation in impulsive observation noise. A scalar recursion for the weight misadjustment is derived for the white input data case. Monte Carlo simulations verify the accuracy of the theoretical model. The theoretical recursion is then used to study the effects of the impulse noise on algorithm convergence speed and steady-state weight misadjustment for a wide variety of parameter values.