Performance analysis of Recursive Least Normalized Correlation Norms algorithm

This paper proposes an adaptation algorithm named Recursive Least Normalized Correlation Norms (RLNCN) algorithm for adaptive filters, based on a cost function of a quantity named Normalized Correlation Norm (NCN) which generically yields a family of normalized type algorithms. The RLNCN algorithm achieves a significant improvement in filter convergence speed, while it preserves robustness against two types of impulse noise: one is found in observation noise and another at filter input. Performance analysis of the RLNCN algorithm is developed for theoretically calculating transient and steady-state behavior of filter convergence in the absence of impulse noise at filter input. Through experiment with simulations and theoretical calculations of filter convergence, we demonstrate its effectiveness in making adaptive filters fast convergent and robust in the presence of both types of impulse noise. Good agreement between simulated and theoretical convergence validates the analysis.