Transient and tracking performance analysis of the quantized LMS algorithm for time-varying system identification

This paper investigates the statistical behavior of the finite precision LMS adaptive filter in the identification of an unknown time-varying stochastic system. Nonlinear recursions are derived for the mean and mean-square behavior of the adaptive weights. Transient and tracking algorithm performance curves are generated from the recursions and shown to be in excellent agreement with Monte Carlo simulations. Our results demonstrate that linear models are inappropriate for analyzing the transient and the steady-state algorithm behavior. The performance curves indicate that the transient and tracking capabilities cannot be determined from perturbations about the infinite precision case. It is shown that the transient phase of the algorithm increases as the digital wordlength or the speed of variation of the unknown system decrease. Design examples illustrate how the theory can be used to select the algorithm step size and the number of bits in the quantizer