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Optimal Distributed Binary Hypothesis testing with Independent Identical Sensors (2000)
| Venue: | Department of Computer Engineering and Informatics, University of Patras |
| Citations: | 3 - 1 self |
BibTeX
@INPROCEEDINGS{Zhang00optimaldistributed,
author = {Q. Zhang and P. K. Varshney and R. D. Wesel},
title = {Optimal Distributed Binary Hypothesis testing with Independent Identical Sensors},
booktitle = {Department of Computer Engineering and Informatics, University of Patras},
year = {2000},
pages = {pp.}
}
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Abstract
We consider the problem of distributed binary hypothesis testing with independent identical sensors. It is well known that for this problem the optimal sensor rules are a likelihood ratio threshold tests and the optimal fusion rule is a K-out-of-N rule [1]. Under the Bayesian criterion, we show that for a fixed K-out-of-N fusion rule, the probability of error is a quasiconvex function of the likelihood ratio threshold used in the sensor decision rule. Therefore, the probability of error has a single minimum and a unique optimal threshold achieves this minimum. We obtain a sufficient and necessary condition on the optimal threshold, except in some trivial situations where one hypothesis is always decided. We present a method for determining whether or not the solution is trivial. Under the Neyman-Pearson criterion, we show that when the Lagrange multiplier method is used for a fixed K-out-of-N fusion rule, the objective function is quasiconvex and hence has a single minimum point, and t...
Keyphrases
independent identical sensor optimal distributed binary hypothesis fixed k-out-of-n fusion rule likelihood ratio threshold test unique optimal threshold necessary condition k-out-of-n rule single minimum point objective function sensor decision rule bayesian criterion optimal sensor rule neyman-pearson criterion optimal fusion rule lagrange multiplier method optimal threshold distributed binary hypothesis likelihood ratio threshold quasiconvex function single minimum trivial situation
