Modeling Finite Precision Lms Behavior Using Markov Chains

We propose a new model for the behavior of the Least Mean Square (LMS) algorithm when implemented in finite precision. We model the adaptive filter coefficients as a Markov chain and determine its transition probability matrix for the one-dimensional case. We also determine conditions to avoid the so-called stopping phenomenon. The proposed model eliminates the linearizations used in previous models, accounts for saturation effects and leads to accurate estimations of the mean-square error behavior. Monte Carlo simulation results illustrate the quality of the proposed model.