Time-varying system identification using the quantized LMS algorithm

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 predicting the mean-square error (MSE) behavior. Algorithm performance curves generated from the recursions are shown to be in excellent agreement with simulations. Our results demonstrate that linear models are inappropriate for analyzing steady-state algorithm behavior. It is shown that one cannot simply add a fixed level of quantization power to the steady-state tracking results for the unquantized algorithm. A design example illustrates the use of the theory to select the algorithm step size and the number of bits in the quantizer.