A general class of nonlinear normalized adaptive filtering algorithms

The normalized least mean square (NLMS) algorithm is an important variant o f the classical LMS algorithm for adaptive linear filtering. It possesses m any advantages over the LR IS algorithm, including having a faster converge nce and providing for an automatic time-arising choice of the LMS step-size parameter that affects the stability, steady-state mean square error (MSE) , and convergence speed of the algorithm. An auxiliary fixed step-size that is often introduced in the NLMS algorithm has the advantage that its stabi lity region (step-size range for algorithm stability) is independent of the signal statistics. In this paper, we generalize the NLMS algorithm by deriving a class of nonl inear normalized LMS-type (NLMS-type) algorithms that are applicable to a n ide variety of nonlinear filter structures. We obtain a general nonlinear N LMS-type algorithm by choosing an optimal time-varying step-size that minim izes the nest-step MSE at each iteration of the general nonlinear LMS-type algorithm, As in the linear case, we introduce a dimensionless auxiliary st ep-size whose stability range is independent of the signal statistics. The stability region could therefore be determined empirically for any given no nlinear filter type, We present computer simulations of these algorithms fo r two specific nonlinear filter structures: Volterra filters and the recent ly proposed class of Myriad filters. These simulations indicate that the NL MS-type algorithms, in general, converge faster than their LMS-type counter parts.