New insights into the transient and steady-state behavior of the quantized LMS algorithm

The digital implementation of the least mean squares (LMS) algorithm is certainly one of the most popular for real-time high-speed adaptive filters. This article investigates the transient and steady-state behavior of the quantized LMS algorithm. It is shown that the so-called "stopping" phenomenon is really a "slow-down" phenomenon, which, because of an extremely slow convergence rate, looks as if the algorithm has stopped. The true steady-state MSE is shown to be nearly independent of the number of bits in the digital wordlength and very nearly the steady-state MSE of the infinite precision LMS realization. Since the true steady-state is rarely achievable with a finite number of iterations, determination of the step size /spl mu/ that minimizes the residual MSE must be based upon a stochastic model for the transient mode of algorithm operation. It is shown that the finite wordlength and infinite precision design cases differ only in degree and not in kind as far as the selection of /spl mu/ is concerned.