Normalized correlation-newton algorithm with variable control of q-norm

This paper proposes a new adaptation algorithm named normalized correlation-Newton (NC-Newton) algorithm and a novel variable q-norm control method (NC-Newton-Varq-norm) for complex-domain adaptive filters. First, stochastic models are presented for two types of impulse noise intruding adaptive filters: one is present in observation noise and another at filter input. After reviewing q-norm and NC-Newton algorithm, we propose a variable q-norm control method. Analysis of the NC-Newton-Varq-norm algorithm is developed for theoretically calculating transient and steady-state convergence behavior. Through experiment with some examples, we demonstrate effectiveness of the proposed variable q-norm control method in improving filter convergence speed while preserving robustness of the NC-Newton algorithm in impulsive noise environments. Good agreement between simulated and theoretical convergence behavior validates the analysis.