TY - JOUR

T1 - The Residual ISI for Which the Convolutional Noise Probability Density Function Associated with the Blind Adaptive Deconvolution Problem Turns Approximately Gaussian

AU - Pinchas, Monika

N1 - Publisher Copyright:
© 2022 by the author.

PY - 2022/7

Y1 - 2022/7

N2 - In a blind adaptive deconvolution problem, the convolutional noise observed at the output of the deconvolution process, in addition to the required source signal, is—according to the literature—assumed to be a Gaussian process when the deconvolution process (the blind adaptive equalizer) is deep in its convergence state. Namely, when the convolutional noise sequence or, equivalently, the residual inter-symbol interference (ISI) is considered small. Up to now, no closed-form approximated expression is given for the residual ISI, where the Gaussian model can be used to describe the convolutional noise probability density function (pdf). In this paper, we use the Maximum Entropy density technique, Lagrange’s Integral method, and quasi-moment truncation technique to obtain an approximated closed-form equation for the residual ISI where the Gaussian model can be used to approximately describe the convolutional noise pdf. We will show, based on this approximated closed-form equation for the residual ISI, that the Gaussian model can be used to approximately describe the convolutional noise pdf just before the equalizer has converged, even at a residual ISI level where the “eye diagram” is still very closed, namely, where the residual ISI can not be considered as small.

AB - In a blind adaptive deconvolution problem, the convolutional noise observed at the output of the deconvolution process, in addition to the required source signal, is—according to the literature—assumed to be a Gaussian process when the deconvolution process (the blind adaptive equalizer) is deep in its convergence state. Namely, when the convolutional noise sequence or, equivalently, the residual inter-symbol interference (ISI) is considered small. Up to now, no closed-form approximated expression is given for the residual ISI, where the Gaussian model can be used to describe the convolutional noise probability density function (pdf). In this paper, we use the Maximum Entropy density technique, Lagrange’s Integral method, and quasi-moment truncation technique to obtain an approximated closed-form equation for the residual ISI where the Gaussian model can be used to approximately describe the convolutional noise pdf. We will show, based on this approximated closed-form equation for the residual ISI, that the Gaussian model can be used to approximately describe the convolutional noise pdf just before the equalizer has converged, even at a residual ISI level where the “eye diagram” is still very closed, namely, where the residual ISI can not be considered as small.

KW - Lagrange multipliers

KW - Laplace’s integral method

KW - MET

KW - blind adaptive deconvolution

KW - moment truncation technique

KW - residual ISI

UR - http://www.scopus.com/inward/record.url?scp=85136402577&partnerID=8YFLogxK

U2 - 10.3390/e24070989

DO - 10.3390/e24070989

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AN - SCOPUS:85136402577

SN - 1099-4300

VL - 24

JO - Entropy

JF - Entropy

IS - 7

M1 - 989

ER -