The misadjustment of the cascaded LMS prediction filter

In this paper, we use a stochastic fixed-point theorem to study the stochastic convergence properties (in mean-squares sense) of the cascaded LMS predictor including conditions on the stepsize for the adaptive algorithm convergence and the misadjustment. An analytic expression for the misadjustment is derived for Gaussian statistical signals and shown to be exponentially dependent on the number of stages in the cascade structure, which is higher than the misadjustment of the conventional LMS filter. It can be observed that a higher misadjusment can be expected if the input signal is extremely uncorrelated.