Residual ISI Obtained by Blind Adaptive Equalizers and Fractional Noise

Monika Pinchas

doi:10.1155/2013/972174

Abstract

Recently, a closed-form approximated expression was derived by the same author for the achievable residual intersymbol interference (ISI) case that depends on the step-size parameter, equalizer’s tap length, input signal statistics, signal-to-noise ratio (SNR), and channel power. But this expression was obtained by assuming that the input noise is a white Gaussian process where the Hurst exponent (H) is equal to 0.5. In this paper, we derive a closed-form approximated expression (or an upper limit) for the residual ISI obtained by blind adaptive equalizers valid for fractional Gaussian noise (fGn) input where the Hurst exponent is in the region of0.5≤H<1. Up to now, the statistical behaviour of the residual ISI was not investigated. Furthermore, the convolutional noise for the latter stages of the deconvolutional process was assumed to be a white Gaussian process (H=0.5). In this paper, we show that the Hurst exponent of the residual ISI is close to one, almost independent of the SNR or equalizer’s tap length but depends on the step-size parameter. In addition, the convolutional noise obtained in the steady state is a noise process having a Hurst exponent depending on the step-size parameter.

Highlights

We consider a blind deconvolution problem in which we observe the output of an unknown, possibly nonminimum phase, linear system (SISO-FIR system) from which we want to recover its input using an adjustable linear filter
We derive a closed-form approximated expression for the residual intersymbol interference (ISI) obtained by blind adaptive equalizers valid for fractional Gaussian noise (fGn) input where the Hurst exponent is in the region of 0.5 ≤ H < 1
We proposed a closed-form approximated expression for the residual ISI obtained by blind adaptive equalizers valid for the fGn input case where the Hurst exponent is in the region of 0.5 ≤ H < 1

Summary

Introduction

We consider a blind deconvolution problem in which we observe the output of an unknown, possibly nonminimum phase, linear system (SISO-FIR system) from which we want to recover its input (source) using an adjustable linear filter (equalizer). [7, 8], a closed-form approximated expression was derived by the same author 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), and channel power. This expression was obtained by assuming that the input noise is a white Gaussian process where the Hurst exponent (H) is equal to 0.5. We derive a closed-form approximated expression (or an upper limit) for the residual ISI obtained by blind adaptive equalizers valid for fGn input where the Hurst exponent is in the region of 0.5 ≤ H < 1.

System Description

Derivation of the Residual ISI

The Statistical Behaviour of the Residual ISI and Convolutional Noise

Conclusion