Performance Evaluation of an Equalizer using BLMS Adaptive Algorithm under Constrained Word Length

Abstract

The finite precision issue of an adaptive digital equalizer of a communication channel is dealt in this paper. The equalizer is assumed to employ a computationally efficient Block Least Mean Square (BLMS) Finite Impulse Response (FIR) Adaptive Filter (AF). The concept of adaptation failure of the equalizer under constrained word length is discussed and an analysis is carried out to account for this effect using a new approach based on probability density. This analysis has led to an important relation between the Probability of Adaptation Failure (PAF), the word length and the filter length of the equalizer. This relation shows that for a specified PAF, the word length requirement decreases with increase in the filter length. This theoretical finding has also been verified by computer simulation. Exhaustive finite and infinite precision simulations reveal that below a word length of 6 bit (excluding the sign bit) the performance of the equalizer degrades drastically and at 9 bits its performance becomes identical to that of the infinite precision case. Optimum word length required to achieve a given performance can be selected from the results of this paper.

Indexing terms:

• Block least mean square algorithm
• Adaptive equalizer
• Probability of adaptation failure
• Finite precision effect