Document Type

Article

Date

2000

Keywords

Distributed binary hypothesis testing with idependent identical sensors, Sensor rules, Bayesian criterion, Neyman-Pearson criterion, Langrange multiplier method, Quasiconvex

Language

English

Disciplines

Electrical and Computer Engineering

Description/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 the resulting ROC is concave downward. These results are illustrated by means of three examples.

Creative Commons License

Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.

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