Stochastic gradient adaptive filters with gradient adaptive step sizes

Two adaptive step-size gradient adaptive filters are presented. The step sizes are changed using a gradient descent algorithm designed to minimize the squared estimation error. The first algorithm uses the same step-size sequence for all the filter coefficients, whereas the second algorithm uses different step-size sequences for different adaptive filter coefficients. An analytical performance analysis of the first algorithm is also presented. Analyses and experiments indicate that (1) the algorithms have fast convergence rates and small midadjustment errors and (2) in nonstationary environments, the algorithms tend to adjust the step sizes so as to give close to the best possible performance. Several simulation examples demonstrating the good properties of the adaptive filters are also presented.<>