Adaptive algorithms with an automatic gain control feature

New Gradient Based Variable Step-Size LMS Algorithm

“…Many VSSLMS algorithms have been proposed to improve the performance of the LMS algorithm. An important class of VSSLMS algorithms is the one in which the step size is updated using the gradient vector [3] [4][5] [6] [7]. In our opinion, all of these algorithms utilize two properties of the gradient vector:…”

“…The polarity of the gradient vector will generally be consistent during the early stages of the adaptive process and change frequently after the system converges. Methods proposed in [4][5] utilize property 1, whereas that proposed in [3] utilizes property 2. Techniques introduced in [6] [7] utilize both of the properties.…”

Automatic variance control and variance estimation loops

“…The problem is that with large k, equation (2) pays little attention to new information and "switches off." Sometimes a factor of safety is used, and the variance magnitude is underestimated to allow for any sudden changes, or if the dynamic range of the signal (as is the case with speech) is known, a worst-case upper estimate can be used.…”

“…Conversely, if the variance is overestimated, the convergence of the LMS algorithm may well be too slow [1 ]. This basic problem has been recognized in [2], where the authors alter the LMS algorithm to implicitly include automatic gain control (AGC). It is usual in the literature to use some form of exponential weighting of past data to track the variance.…”

“…Increasing/3 gives smoother estimates at the expense of worse tracking. The implicit approach in [2] uses a forgetting factor approach similar to the one above. Although methods like these can be made to work for certain applications, they are generally used ad hoc and are a compromise between smoothness of the estimate and tracking ability.…”