Analysis of adaptive step-size Correlation Phase-Newton Algorithm

This paper first reviews Correlation Phase Algorithm (CPhiA) for adaptive filters in the complex-number domain with colored Gaussian reference inputs. Stochastic models are presented for two types of impulse noise intruding adaptive filters: one in observation noise and another at filter input. To improve the filter convergence speed for a strongly correlated filter reference input, we combine the CPhiA with simple recurrent calculation of the inverse covariance matrix of the filter input using the Newton´s method (CPhi-Newton algorithm). We further propose a new adaptive step-size (ASS) control algorithm to be combined with the CPhi-Newton algorithm. We develop performance analysis of the ASS-CPhi-Newton algorithm to derive difference equations for theoretically calculating transient and steady-state convergence behavior. Through experiment with some examples, it is demonstrated that faster convergence and high robustness are realized with the proposed ASS-CPhi-Newton algorithm in impulsive noise environments. Good agreement between simulated and theoretical convergence validates the analysis.