Evolution of distributed detection performance over balanced binary relay tree networks with bit errors

Yu‐Ping Tian

doi:10.1007/s11071-021-06736-1

2022-01-17

田

田玉平 (Yu‐Ping Tian) *

Wenbo Zhu

DOI：10.1007/s11071-021-06736-1

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摘要

En 中文

Target detection based on wireless sensor networks can be considered as a distributed binary hypothesis testing problem. In this paper, the evolution of detection error probability with the increase in the network scale is studied for the balanced binary relay tree network with channel noise. Firstly, the iterative expressions of false-alarm probability and missed-detection probability depending on the number of tree network layers are given. Then, the iterative process of two types of error probabilities in the network space is described as a discrete nonlinear switched dynamic system, and the dynamic properties of two types of error probabilities are analyzed in a plane rectangular coordinate system. A globally attractive invariant set of the state of the dynamic system, which is not related to the channel noise, is derived. The switching mode of the system and the total error probability in the invariant set are further analyzed, and a necessary and sufficient convergence condition of the total error probability is provided. Based on this condition, the following detection properties of the network are revealed: (1) as long as the channel bit error probability is not zero, the total error probability does not tend to zero as the network size grows to infinity; (2) when the channel bit error probability is greater than 2-root 3/2, the total error probability will continue to increase with the increase in the network size.

Keyword:

Distributed detection

Distributed hypothesis testing

Nonlinear switched system

Invariant set

Channel noise