New Lagrange Multipliers for the Blind Adaptive Deconvolution Problem Applicable for the Noisy Case
Recently, a new blind adaptive deconvolution algorithm was proposed based on a new closed-form approximated expression for the conditional expectation (the expectation of the source input given the equalized or deconvolutional output) where the output and input probability density function (pdf) of...
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doaj-3468a41e6c194a14a59292abd9daadf32020-11-24T23:01:33ZengMDPI AGEntropy1099-43002016-02-011836510.3390/e18030065e18030065New Lagrange Multipliers for the Blind Adaptive Deconvolution Problem Applicable for the Noisy CaseMonika Pinchas0Department of Electrical and Electronic Engineering, Ariel University, Ariel 40700, IsraelRecently, a new blind adaptive deconvolution algorithm was proposed based on a new closed-form approximated expression for the conditional expectation (the expectation of the source input given the equalized or deconvolutional output) where the output and input probability density function (pdf) of the deconvolutional process were approximated with the maximum entropy density approximation technique. The Lagrange multipliers for the output pdf were set to those used for the input pdf. Although this new blind adaptive deconvolution method has been shown to have improved equalization performance compared to the maximum entropy blind adaptive deconvolution algorithm recently proposed by the same author, it is not applicable for the very noisy case. In this paper, we derive new Lagrange multipliers for the output and input pdfs, where the Lagrange multipliers related to the output pdf are a function of the channel noise power. Simulation results indicate that the newly obtained blind adaptive deconvolution algorithm using these new Lagrange multipliers is robust to signal-to-noise ratios (SNR), unlike the previously proposed method, and is applicable for the whole range of SNR down to 7 dB. In addition, we also obtain new closed-form approximated expressions for the conditional expectation and mean square error (MSE).http://www.mdpi.com/1099-4300/18/3/65Lagrange multipliersBayesian approachconditional expectationdeconvolutionmaximum entropy density approximation technique |
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DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Monika Pinchas |
spellingShingle |
Monika Pinchas New Lagrange Multipliers for the Blind Adaptive Deconvolution Problem Applicable for the Noisy Case Entropy Lagrange multipliers Bayesian approach conditional expectation deconvolution maximum entropy density approximation technique |
author_facet |
Monika Pinchas |
author_sort |
Monika Pinchas |
title |
New Lagrange Multipliers for the Blind Adaptive Deconvolution Problem Applicable for the Noisy Case |
title_short |
New Lagrange Multipliers for the Blind Adaptive Deconvolution Problem Applicable for the Noisy Case |
title_full |
New Lagrange Multipliers for the Blind Adaptive Deconvolution Problem Applicable for the Noisy Case |
title_fullStr |
New Lagrange Multipliers for the Blind Adaptive Deconvolution Problem Applicable for the Noisy Case |
title_full_unstemmed |
New Lagrange Multipliers for the Blind Adaptive Deconvolution Problem Applicable for the Noisy Case |
title_sort |
new lagrange multipliers for the blind adaptive deconvolution problem applicable for the noisy case |
publisher |
MDPI AG |
series |
Entropy |
issn |
1099-4300 |
publishDate |
2016-02-01 |
description |
Recently, a new blind adaptive deconvolution algorithm was proposed based on a new closed-form approximated expression for the conditional expectation (the expectation of the source input given the equalized or deconvolutional output) where the output and input probability density function (pdf) of the deconvolutional process were approximated with the maximum entropy density approximation technique. The Lagrange multipliers for the output pdf were set to those used for the input pdf. Although this new blind adaptive deconvolution method has been shown to have improved equalization performance compared to the maximum entropy blind adaptive deconvolution algorithm recently proposed by the same author, it is not applicable for the very noisy case. In this paper, we derive new Lagrange multipliers for the output and input pdfs, where the Lagrange multipliers related to the output pdf are a function of the channel noise power. Simulation results indicate that the newly obtained blind adaptive deconvolution algorithm using these new Lagrange multipliers is robust to signal-to-noise ratios (SNR), unlike the previously proposed method, and is applicable for the whole range of SNR down to 7 dB. In addition, we also obtain new closed-form approximated expressions for the conditional expectation and mean square error (MSE). |
topic |
Lagrange multipliers Bayesian approach conditional expectation deconvolution maximum entropy density approximation technique |
url |
http://www.mdpi.com/1099-4300/18/3/65 |
work_keys_str_mv |
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