Robust normalised LMS filtering

Several types of robust LMS adaptive filter algorithm have been proposed, to reduce misadjustment when impulsive noise is added to the input or reference signal. In many applications a normalised LMS algorithm is required, to increase convergence speed. This paper shows that if impulsive noise is present at the filter input (which is a realistic problem, for example, in some communications equalisers), the standard NLMS algorithm provides some robustness to this impulsive noise. New normalised LMS algorithms are then presented with improved robustness to impulsive input noise. An approximate theoretical analysis is confirmed by simulations. Finally, we show that, as for NLMS, simplified approximate arithmetic may be used to reduce the implementation cost of the new algorithms.