A variable step-size affine projection algorithm with a step-size scaler against impulsive measurement noise

•We propose a variable step-size affine projection algorithm using a step-size scaler.•The step-size scaler improves the robustness by scaling the step size.•To reduce the computational complexity, we also propose a simple step-size scaler.

This letter proposes a variable step-size (VSS) affine projection algorithm (APA) associated with a step-size scaler to improve the APA's robustness against impulsive measurement noise. In the proposed VSS APA, the step-size scaler is applied to the equations for updating the step size, which are developed by interpreting the behavior of the mean square deviation (MSD) of the conventional APA. To reduce the computational complexity, we also propose a simplified version of the step-size scaler, which is suitable for application in the APA. Simulations show that the proposed algorithm leads to an excellent transient and steady-state behavior with colored inputs in impulsive-noise environments.