New performance function and variable step size LMS algorithm derived by Karni and Zeng

The variable step size LMS algorithm (Karni-Zeng) (1989) can be derived from a new performance function which has an additional exponential term to that of the conventional LMS algorithm. Its fast convergence and low misadjustment error properties can be interpreted and analysed through the new performance function. The algorithm uses a large step size when the gradient on the surface of the performance function is large and a small step size when the gradient is small.