This concept covers the steady-state error analysis of the adaptive LMS (Least Mean Squares) filter, specifically why the weight vector never converges exactly to the optimal Wiener solution but instead fluctuates around it, producing an excess mean-square error above the minimum attainable value. Using an eigen-decomposition of the input autocorrelation matrix (R = TDT^T) to transform the weight-deviation vector into a decoupled coordinate system, the analysis derives a recursive update for the covariance matrix of the transformed weight-deviation vector, invoking the independence and joint-Gaussian assumptions on the input and error signals to evaluate second- and fourth-order moment terms. This belongs to the field of adaptive signal processing / stochastic gradient adaptive filtering, and forms the theoretical basis for characterizing convergence, stability, and misadjustment of LMS-type algorithms within statistical signal processing and estimation theory.
This concept covers the steady-state error analysis of the adaptive LMS (Least Mean Squares) filter, specifically why the weight vector never converges exactly to the optimal Wiener solution but inst…