Exact LMS learning curve analysis under finite word length effects

Abstract

A mathematical model for the LMS learning curve under finite word length effects is presented in this paper. The impact of the finite word length effects on the LMS adaptive filter is a major concern during its implementation because it has repercussions on both the convergence speed and the stability of the adaptive filter. Two typical cases of quantization, such as rounding and two’s complement truncation are considered. Explicit equations that allow to the designer accurately predict the behavior of the LMS learning curve under quantization errors are provided