Higher-order statistic-based detection of non-Gaussian signals
Garth, Lee McCandless
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https://hdl.handle.net/2142/22898
Description
Title
Higher-order statistic-based detection of non-Gaussian signals
Author(s)
Garth, Lee McCandless
Issue Date
1996
Doctoral Committee Chair(s)
Bresler, Yoram
Department of Study
Electrical and Computer Engineering
Discipline
Electrical and Computer Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Engineering, Electronics and Electrical
Language
eng
Abstract
Using the Gaussian noise rejection property of higher-order spectra (HOS), HOS-based detectors can outperform conventional second-order (SOS) techniques in certain scenarios. In this thesis we study the strengths and limitations of HOS detection techniques, as well as proper applications for them. We first compare existing frequency-domain HOS detection techniques with new tests that we propose. We formulate a new F-test statistic and derive refined conditional distributions for the test proposed by Hinich. We calculate the optimal smoothing bandwidth for the HOS estimate components of our F-test and his test, producing the best detector performance. These new bandwidths yield significant improvements in detector performance over previous results.
We next consider when HOS detection techniques produce performance gains over traditional SOS-based techniques. We study the tradeoff between HOS and analogous SOS detectors given a processing bandwidth constraint. We demonstrate that, as the bandwidth is decreased, the performance of HOS detectors degrades faster than that of SOS detectors. We examine similar effects on a distributed wideband scenario.
We finally propose novel fourth cumulant-based array detectors. We construct detectors for various levels of knowledge regarding the receiving sensor array and the emitter locations and statistics. We analyze both binary hypothesis detectors and information theoretic criteria. Our detectors are designed for the general case of unconstrained and unknown asymptotic covariances of the sample cumulant estimates.
In an appendix we illustrate the importance of a finite dimensionality assumption when using functions of asymptotic statistics. We also point to subtleties in using detection statistics stemming from the Central Limit Theorem and Taylor series without entering the Large Deviations regime.
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