A STOCHASTIC GRADIENT ADAPTIVE FILTER WITH GRADIENT ADAPTIVE STEP-SIZE

This paper presents an adaptive step-size gradient adaptive filter. Th e step size of the adaptive filter is changed according to a gradient descent algorithm designed to reduce the squared estimation error duri ng each iteration. An approximate analysis of the performance of the a daptive filter when its inputs are zero mean, white, and Gaussian and the set of optimal coefficients are time varying according to a random -walk model is presented in the paper. The algorithm has very good con vergence speed and low steady-state misadjustment. Furthermore, the tr acking performance of these algorithms in nonstationary environments i s relatively insensitive to the choice of the parameters of the adapti ve filter and is very close to the best possible performance of the le ast mean square (LMS) algorithm for a large range of values of the ste p size of the step-size adaptation algorithm. Several simulation examp les demonstrating the good properties of the adaptive filter as well a s verifying the analytical results are also presented in the paper.