The behavior of LMS and NLMS algorithms in the presence of spherically invariant processes

The behavior of least-mean-square (LMS) and normalized least-mean-square (NLMS) algorithms with spherically invariant random processes (SIRPs) as excitations is shown. Many random processes fall into this category, and SIRPs closely resemble speech signals. The most pertinent properties of these random processes are summarized. The LMS algorithm is introduced, and the first- and second-order moments of the weight-error vector between the Wiener solution and the estimated solution are shown. The behavior of the NLMS algorithm is obtained, and the first- and second-order moments of the weight-error vector are calculated. The results are verified by comparison with known results when a white noise process and a colored Gaussian process are used as input sequences. Some simulation results for a K/sub 0/-process are then shown. >