NEW ADAPTIVE ALGORITHMS BASED ON THE METHOD OF STEEPEST DESCENT

A new simple formulation for governing the choice of the convergence parameter mu in adaptive algorithms using the method of steepest descent techniques is given. Two algorithms are derived and examined here. The first, the steepest descent algorithm, results in a time-varying mu which is the same for each filter but is updated at each iteration to yield optimum performance. The second, the fast convergence algorithm, has a time-varying convergence parameter which is chosen suitably for each adaptive filter coefficient and is updated at each iteration. These algorithms have been tested successfully to yield faster convergence and more accurate adaptation compared with the existing least-mean-square (LMS) algorithm that uses a constant value of mu. Substantial improvements in transient behaviour in comparison to stochastic-gradient or LMS algorithms are efficiently achieved by the presented algorithms. This true solution is recursively calculated at a relatively modest increase in computational requirements in comparison to stochastic-gradient algorithm. The expressions developed are verified by computer simulations which are in good agreement with theory.