Nonlinear quantization effects in the LMS and block LMS adaptive algorithms-a comparison

Analog implementations of the LMS (least-mean squares) and block LMS (BLMS) adaptive filtering algorithms have been shown to be equivalent with respect to adaptation speed and steady-state misadjustment errors. However, the BLMS algorithm offers significant reductions in computational speed due to block processing. Digital implementations of the two algorithms are compared with respect to finite word effects. The algorithm stalling phenomena is studied using Gaussian data and conditional expectation arguments. It is shown that the BLMS algorithm requires 1/2(log₂L-K) fewer bits for the same stalling behavior (L=block length and K lies between 0.2 and 1, depending on the precise definition of algorithm stalling). The LMS algorithm requires log₂L fewer bits than BLMS for the same level of saturation behavior (transient response) at algorithm initialization. Hence, overall the LMS algorithm requires 1/2(log₂L+K) fewer bits than the BLMS algorithm for the same saturation and stalling effects