Analysis of normalized correlation algorithm for adaptive filters in impulsive noise environments

This paper proposes normalized correlation algorithm (NCA) for complex-domain adaptive filters with Gaussian inputs. Stochastic models are presented for two types of impulse noise intruding adaptive filters: one in observation noise and another at filter input. Performance analysis of the NCA is developed to derive difference equations for calculating transient and steady-state convergence behavior. Through experiment with simulations and theoretical calculations of filter convergence for some examples, we demonstrate high robustness of the NCA in impulsive noise environments. Good agreement between simulated and theoretical convergence proves the validity of the analysis.