Scaling factor computation for EDSC adaptation

This paper extensively exhibits the computational procedure and circumstances of the scaling factor used in a recent variable step size normalized least-mean-square (NLMS) adaptation strategy called error-dependent step-size control (EDSC). Applied on Volterra models, it enhances the convergence of conventional methods for the same steady-state misadjustment. Entailed in the variable step-size (VSS) expression, the scaling factor needs to be selected as to maintain the step size in the stability range, but also suitable for each adaptation stage: convergence or steady-state. Thus, the scaling factor is derived on small error sequences. Also, a discussion and a comparison with a unique scaling factor using larger error sequences are considered. The EDSC is compared to the NLMS for a nonlinear acoustic system using measured Volterra kernels and input sequences with different probability density functions (PDFs). The echo-return loss enhancement (ERLE) evolution proves the advantages of the proposed method also for different error thresholds.