BURSTING IN THE LMS ALGORITHM

The least mean square (LMS) algorithm is known to converge in the mean and in the mean square. However, during short time periods, the error sequence can blow up and cause severe disturbances; especially for no n-Gaussian processes. This contribution discusses potential short time unstable behavior of the LMS algorithm for spherically invariant rand om processes (SIRP) like Gaussian, Laplacian, and lie. The result of t his investigation is that the probability for bursting decreases with the step size. However, since a smaller step size also causes a slower convergence rate, one has to choose a tradeoff between convergence sp eed and the frequence of bursting.