THE BEHAVIOR OF LMS AND NLMS ALGORITHMS IN THE PRESENCE OF SPHERICALLY INVARIANT PROCESSES

In this paper, the behavior of the least mean square (LMS) and normalized least mean square (NLMS) algorithms with spherically invariant random processes (SIRP's) as excitation is shown. SIRP's are of particular interest because many random processes fall under this category and SIRP's closely resemble speech signals. Consequently, it is of great interest to know the influence of SIRP's on the stability and convergence speed of stochastic gradient algorithms. The properties of SIRP's and the methods used in this paper are not restricted to LMS and NLMS algorithms but also allow a deeper insight into the behavior of some derivatives of the LMS algorithm.