Performance Evaluation of Finite Precision LMS Adaptive Filters using Probability Density Approach

Abstract

Least Mean Square (LMS) algorithm is the most popular adaptive algorithm (AA) for realization of a digital adaptive filter (AF). In digital implementation of AF, finite word length hardware is unavoidable. This finite precision (FP) effect on the performance of the AF is crucial in the sense that, if proper word length is not used the performance in terms of the mean square error (MSE) of the filter degrades substantially. In this paper, a new approach based on the probability theory is used to analyze the FP effect of the LMS based finite impulse response (FIR) AF. An expression of the adaptation failure in terms of word length and the step size is derived. Simulation study of a FP LMS adaptive equalizer is carried out to demonstrate and verify this effect. This study provides an important guide-line to the designers for selecting the optimum word length for a specific application for a given MSE criterion.

Indexing terms:

• Adaptive filter
• Probability of adaptation failure
• LMS algorithm