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Robust Signal Detection in Non-Gaussian Noise Using Threshold System and Bistable System Open Access

Descriptions

Other title
Subject/Keyword
Bistable system
Noise-enhanced detection
Robust signal detection in non-Gaussian noise
Threshold system
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Guo, Gencheng
Supervisor and department
Jing, Yindi (Electrical and Computer Engineering)
Mandal, Mrinal (Electrical and Computer Engineering)
Examining committee member and department
Mandal, Mrinal (Electrical and Computer Engineering)
Zhang, Hong (Computer Science)
Nowrouzian, Behrouz (Electrical and Computer Engineering)
Jing, Yindi (Electrical and Computer Engineering)
Khabbazian Majid (Electrical and Computer Engineering)
Jiang, Hai (Electrical and Computer Engineering)
Department
Department of Electrical and Computer Engineering
Specialization
Digital signal and image processing
Date accepted
2012-09-25T10:53:03Z
Graduation date
2012-09
Degree
Doctor of Philosophy
Degree level
Doctoral
Abstract
Signal detection in non-Gaussian noise is fundamental to design signal processing systems like decision making or information extraction. The optimal/near-optimal detector for this problem is the likelihood ratio test (LRT) or generalized LRT (GLRT). However, since the noise is non-Gaussian, sometimes has unknown pdf, the LRT or GLRT suffers high implementation cost, low robustness, and possible poor performance. In this thesis, to deal with these challenges, we investigate two techniques. One is to propose simple and robust detectors using threshold system (TS) and bistable system (BS). The other is to exploit the noise-enhanced effect, to improve performance by adding noise to the observation, for suboptimal detectors. For the detector design using TS or BS, first, we propose binary TS based detector (TD) under Neyman-Pearson (NP) criterion to detect a known DC signal in known non-Gaussian noise. The optimal TS's, including simple binary TS and composite binary TS, are derived analytically. Secondly, we propose a TD for detecting any known signal in independent non-Gaussian noise whose pdf is unknown but is symmetric and unimodal. The optimality of the proposed TD is proved. It is shown that even without the knowledge of the noise pdf, the proposed TD has close performance to the optimal detector designed with precise noise pdf information. The practical implementation and robustness of the proposed TD are also investigated. Third, we investigate the BS based detector (BD) for watermark extraction. There is no existing efficient and systematic BS design method except exhaustive search. We propose to use the cross-correlation of the watermark signal and the BS output as the criterion. Based on this, we develop a practical BS parameter optimization method, which leads to a BS adaptive to various watermark extraction scenarios. The extraction performance based on the adaptive BD is compared with the white Gaussian noise (WGN) based maximum likelihood (ML) detector and other BDs used in watermark extraction. For the noise-enhanced effect, we focus on the general binary hypothesis test problem using a binary TD. We adopt the AUC, which refers to the area under receiver operating characteristic (ROC) curve, as the performance measure for its simplicity and robustness. The optimal TS design that maximizes the AUC has been derived. For a given binary TS, the optimal noise pdf that maximizes the AUC is shown to be a delta function. Properties of the derived results and comparisons with other designs are presented.
Language
English
DOI
doi:10.7939/R3XH25
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
G. Guo, M. Mandal, and Y. Jing, “A robust detector of known signal in non-gaussian noise using threshold systems,” Signal Processing, vol, 92, no. 11, pp. 2676–2688, Nov. 2012.G. Guo and M. Mandal, “On optimal threshold and structure in threshold system based detector,” Signal Processing, vol. 92, no. 1, pp. 170–178, Jan. 2012.G. Guo and M. Mandal, “An adaptive stochastic-resonator-based detector and its application in watermark extraction,” WSEAS Transaction on Signal Processing, vol. 7, no. 2, pp. 65–81, Apr. 2011.

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