Analysis of LMS and NLMS algorithms with delayed coefficient updateunder the presence of spherically invariant processes

Certain conditions require a delay in the coefficient update of the least mean square (LMS) and normalized least mean square (NLMS) algorithms. This paper presents an in-depth analysis of these modificated versions for the important case of spherically invariant random processes (SIRPs), which are known as an excellent model for speech signals. Some derived bounds and the predicted dynamic behavior of the algorithms are found to correspond very well to simulation results and a real time implementation on a fixed-point signal processor. A modification of the algorithm is proposed to assure the well known properties of the LMS and NLMS algorithms