Variable Step-Size correlation phase algorithm: Analysis and simulations

Abstract

Based on “phase” of a correlation between error signal and filter reference input, this paper first derives Correlation Phase Algorithm (CΦA) for adaptive filters in the complex-number domain, and further proposes a simple Variable Step-Size control method to be combined with the CΦA. The proposed VSS-CΦA achieves significant improvement in convergence speed of the CΦA, while preserving its robustness against impulse noise. Through analysis and experiment, we demonstrate effectiveness of the VSS-CΦA in realizing sufficiently fast-convergent and robust adaptive filters. Good agreement between simulated and theoretical convergence behavior in transient phase and steady state proves the validity of the analysis.