CONTROL-THEORETIC DESIGN OF THE LMS AND THE SIGN ALGORITHMS IN NONSTATIONARY ENVIRONMENTS

The feedback structure of the LMS algorithm proposed by Widrow et al. [1] is reexamined from a control system design viewpoint. The minimization of the misadjustments due to gradient noise and lag can then be recasted as the disturbance rejection and tracking problems in control. A frequency-domain approach to the latter problems is presented, which has the advantages of transparency, ease of computation, and generality compared with the time-domain approach previously used. With the same set of assumptions of white input and a Markovian plant, it is shown that the optimum step size obtained by the present approach is identical to that obtained in [1], Applying the same approach, the optimum step size of a simplified version of the LMS algorithm—the sign algorithm—is derived for the case when the plant is slowly varying and the input signals are Gaussian. © 1990 IEEE