V.I. Parfenov – Dr.Sc.(Phys.-Math.), Professor, 

Department of Radiophysics, Voronezh State University

E-mail: vip@phys.vsu.ru

Le Van Dong – Post-graduate Student, 

Voronezh State University

E-mail: levandongx93@gmail.com

A characteristic feature of the modern stage of development of telecommunication systems is the active development and implementation in various fields of science and technology of the principles of wireless sensor technologies. In particular, the use of these principles allows to effectively solve the problems associated with the joint detection of some objects or phenomena simultaneously by several sensors. Such complex information processing allows the increasing of detection efficiency. In this article, the problem of complex detection of object by a set of sensors is solved taking into account possible errors in such a system. The error probabilities that depend on the rules of functioning of both the sensors and the central node are taken into account. In addition, the possibility of failure of the sensors is taken into account. As a result, the optimal algorithm of object detection in these conditions was synthesized. The synthesized algorithm is based on the classical rule of detection, which is to compare the likelihood ratio with the detection threshold. The resulting expression for the likelihood ratio depends nonlinearly on the error probabilities listed above. This expression in some special cases coincides with known from literary sources. The detection threshold was determined numerically based on the criterion of an ideal observer. Simple exact recurrent expressions for the probability distribution densities and error probabilities of the first and second kind characterizing the efficiency of the synthesized algorithm are found. The minimum value of the total error probability was found numerically using the obtained recurrent expressions for the error probabilities of the first and second kind. The dependence of the minimum total error probability on the number of sensors in the system at different values of the probability of sensor failure, as well as the probability of sensor failure at a fixed number of sensors used, are presented. Analysis of the presented formulas and calculated graphic dependencies allows us to make some conclusions and formulate recommendations for the construction of wireless sensor networks. In particular, it is shown that with the probabilities of sensor failure exceeding 0.4…0.5, the use of such systems is practically impractical due to the excessively high minimum total probability of error. And this value does not change much even with increasing the number of sensors used. Indeed, for example, the probability of failure of the sensor, equal to 0.5, increasing the number of sensors used from three to nine leads to a slight decrease in the total probability of error by less than an order of magnitude – from 0.083 to 0.013. At the same time, with the probability of failure of sensors not exceeding 0.1, a significant increase in the efficiency of the system (reducing the minimum total probability of error) can be achieved by increasing the number of sensors used. For example, with a sensor failure probability, equal to 0.1, increasing the number of sensors from three to nine reduces the total error probability by almost three orders of magnitude – from 1.5·10−2 to 3.9·10−5. Thus, the synthesized algorithm and the given theoretical formulas allow us to determine under what conditions the functioning of the wireless sensor network can be achieved its minimum sufficient efficiency. In other words, these results allow to choose the type of sensors reasonably (taking into account the difference in their efficiency) at the given characteristics of the communication channel from the sensors to the central node and at the given probability of sensor failure.

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