Nonlinear quantization effects an the LMS algorithm-analytical models for the MSE transient and convergence behavior

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 μ. These recursions are solved numerically and shown to be in very close agreement with Monte Carlo simulations. Simulation examples are presented which demonstrate the accuracy of the theory in predicting the transient behavior and cancellation performance in steady-state for the quantized LMS algorithm