Variable Step-Size correlation phase algorithm: Analysis and simulations

Based on "phase" of a correlation between error signal and filter reference input, this paper first derives correlation phase algorithm (CPhiA) for adaptive filters in the complex-number domain, and further proposes a simple variable step-size control method to be combined with the CPhiA. The proposed VSS-CPhiA achieves significant improvement in convergence speed of the CPhiA, while preserving its robustness against impulse noise. Through analysis and experiment, we demonstrate effectiveness of the VSS-CPhiA 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.