Analytical linkage between theoretically-optimum and adhoc step-size establishment for nonstationary LMS filtering

For nonstationary LMS adaptive filtering, results are presented which help bridge the gap between ideal theoretical, optimal step-sizes and practical, ad hoc, automatically established step-sizes. An analytical derivation is presented which demonstrates that for the nonstationary system identification paradigm a novel automatic step-size establishment technique estimates the theoretically optimum step-size. This technique sets the step size using the gradient's signal-to-noise ratio.<>