The Tap-Length Associated with the Blind Adaptive Equalization/Deconvolution Problem

Monika Pinchas

doi:10.3390/iec2020-06968

Abstract

The step-size parameter and the equalizer’s tap length are the system parameters in the blind adaptive equalization design. Choosing a large step-size parameter causes the equalizer to converge faster compared with applying a smaller value for the step size parameter. However, a higher step-size parameter leaves the system with a higher residual inter-symbol-interference (ISI) than does a lower step-size parameter. The equalizer’s tap length should be set large enough to compensate for the channel distortions. However, since the channel parameters are unknown, the required equalizer’s tap length is also unknown. The system parameters are usually designed via simulation trials, in such a way that the equalizer’s performance from the residual ISI point of view reaches a system desired residual ISI level. Recently, a closed-form approximated expression was derived for the residual ISI as a function of the system parameters, input sequence statistics and channel power. This expression was obtained under the assumption having a value for the equalizer’s tap length that is sufficient to compensate for the channel distortions. Based on this approximated expression, the outcome from the step-size parameter multiplied by the equalizer’s tap length can be derived when the residual ISI is given. By choosing a step-size parameter, we automatically have also the value for the equalizer’s tap length which might now not be large enough to compensate for the channel distortions and thus leaving the system with a higher residual ISI than the required one. In this work, we derive an expression that sets a condition on the equalizer’s tap length based on the input sequence statistics, on the chosen equalizer’s characteristics and required residual ISI. In addition, highlights are supplied on how to set the equalizer’s tap length for different channel cases based on this new derived expression. The findings are accompanied by simulation results.

Highlights

In this work we consider the blind adaptive equalization problem [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]
The equalizer’s tap length should be set large enough to compensate for the channel distortions
([1,21]), a closed-form approximated expression was derived for the achievable residual ISI case that depends on the step-size parameter, equalizer’s tap length, input signal statistics, signal-to-noise ratio (SNR), the chosen equalization method and channel power

Summary

Introduction

In this work we consider the blind adaptive equalization (blind adaptive deconvolution) problem [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]. This closed- form approximated expression for the residual ISI is applicable for blind adaptive equalizers where the error signal that participates in the update mechanism of the equalizer’s coefficients is a polynomial function of order up to three of the equalized sequence as it is in the case of Godard’s [2] algorithm Based on this closed-form approximated expression for the residual ISI, the system designer has on hand the value for the step-size parameter multiplied by the equalizer’s tap length for a given residual ISI level. We solve the problem of how to set correctly the equalizer’s tap length based on a new derived expression that sets a condition on the equalizer’s tap length This new expression is based on the input sequence statistics, on the chosen equalizer’s characteristics and required residual ISI and is applicable for blind adaptive equalizer’s where the error signal that participates in the update mechanism of the equalizer’s coefficients is a polynomial function of order up to three of the equalized sequence.

Methods

Equalized constellation for 16QAM

N m2p m2p where

Discussion