Abstract
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 \(\frac{2-\sqrt{3}}{2}\), the total error probability will continue to increase with the increase in the network size.
Highlights
Target detection based on wireless sensor networks (WSNs) has a very wide and important application background and has received constant attention from industryYu-Ping Tian, Wenbo Zhu and academia [1,2,3,4]
Comparing the dynamic model of the balanced binary relay tree (BBRT) model derived in this paper and the model of the M-ary tree network given in [22], we find that the former is much more complicated because it is a switched system besides nonlinearity while the latter is just a nonlinear stationary system
Since M is related to b but R is not, it can be expected that when b is large enough, the entire invariant set R may fall into M, which means that when k is large enough, the total error probability Lk is continuously increasing
Summary
Target detection based on wireless sensor networks (WSNs) has a very wide and important application background and has received constant attention from industry. Under the unit threshold LRT (UT-LRT) rule, paper [12] studies the binary hypothesis testing in the BBRT network, analyzes the dynamical properties of false-alarm probability (probability of Type I error) and missed-detection probability (probability of Type II error), and derives a globally attractive invariant set in the state space of error probabilities of two types. We consider the distributed detection problem in the BBRT network with bit error communication channels, and analyze the asymptotic detection performance of the network under BSC model. The result obtained in this paper is quite different from that of [13]: the conclusion that the total error probability will decay to zero with the infinite growth of network size is no longer true for the BSC model.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
