A nonlinear analytical model for the quantized LMS algorithm - The arbitrary step size case

This paper extends conditional moment techniques previously developed for the study of nonlinear versions of the LMS algorithm to the study of the effects of quantizers in the finite precision case, Deterministic nonlinear recursions are derived for the mean and second moment matrix of the weight vector about the Wiener weight for white Gaussian data models and small algorithm step sizes mu. These recursions are solved numerically and shown to be in very close agreement with the Monte Carlo simulations during all phases of the adaptation process. A design example is presented that demonstrates how the theory can be used to select the number of quantizer bits and the adaptation step size mu to yield a desired transient behavior and cancellation performance.