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Entropy 2016, 18(3), 65; doi:10.3390/e18030065

New Lagrange Multipliers for the Blind Adaptive Deconvolution Problem Applicable for the Noisy Case

Department of Electrical and Electronic Engineering, Ariel University, Ariel 40700, Israel
Academic Editor: Raúl Alcaraz Martínez
Received: 6 September 2015 / Revised: 31 December 2015 / Accepted: 18 February 2016 / Published: 23 February 2016
(This article belongs to the Section Information Theory)
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Abstract

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). View Full-Text
Keywords: Lagrange multipliers; Bayesian approach; conditional expectation; deconvolution; maximum entropy density approximation technique Lagrange multipliers; Bayesian approach; conditional expectation; deconvolution; maximum entropy density approximation technique
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Pinchas, M. New Lagrange Multipliers for the Blind Adaptive Deconvolution Problem Applicable for the Noisy Case. Entropy 2016, 18, 65.

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