On the variance of the LMS algorithm squared-error sample curve

Most studies of adaptive algorithm behavior consider performance measures based on mean values such as the mean value of the squared error. Behavior models based on average measures models are useful for understanding the algorithm behavior under different environments and can be used for design. Nevertheless, from a practical point of view, the adaptive filter user has only one realization of the algorithm to obtain the desired result. This article derives a model for the variance of the squared-error sample curve of the least-mean-square (LMS) adaptive algorithm, so that the achievable cancellation level can be predicted based on the properties of the steady-state squared error. The derived results provide the user with useful design guidelines.