A General Class of Nonlinear Normalized LMS-type Adaptive Algorithms

The Normalized Least Mean Square (NLMS) algorithm is an important variant of the classical LMS algorithm for adaptive linear FIR ltering. It provides an automatic choice for the LMS step-size parameter which aaects the stability, convergence speed and steady-state performance of the algorithm. In this paper, we generalize the NLMS algorithm by deriving a class of Nonlinear Normalized LMS-type (NLMS-type) Algorithms that are applicable to a wide variety of nonlinear lters. These algorithms are developed by choosing an optimal time-varying step-size in the class of LMS-type adaptive nonlinear ltering algorithms. An auxiliary xed step-size can be introduced in the NLMS-type algorithm. However, unlike in the LMS-type algorithm, the bounds on this new step-size for algorithm stability are independent of the input signal statistics. Computer simulations demonstrate that these NLMS-type algorithms have a potentially faster convergence than their LMS-type counterparts.