Research On Distributed Detection Performance Of M-ary Tree Network In Noisy Channels

As a kind of typical distributed system capable of sensing,sampling,decision-making and transmitting in complex physical environment,Wireless Sensor Networks(WSNs)have great potential in environmental monitoring,health care,traffic management and many other fields,because of its miniaturization,low power consumption and self-organization.And therefore,the theories and applications about wireless sensor networks have been widely concerned by academia and industry.In those practical application scenarios of WSNs,an important and basic requirement is to compress the information of the physical world into the information that is easy to understand by human,hence the research of distributed detection is an important topic of wireless sensor networks.Considering the problem of distributed binary hypothesis testing in an m-ary relay tree network,the asymptotic performance of the tree network by using the majority dominance rule under the joint action of two noise channel models: link failure and unreliable communication is first studied in this paper.The leaves of the detection network of tree architecture are sensors,which are responsible for sensing the target in the monitoring area and transmitting their decisions to its parent nodes through the wireless noisy channels after the binary decisions are locally generated based on the sensing signals.All the non-leaf nodes of the tree network having m branches,generate new binary signals and transmit the decision results to their parent nodes under the majority dominance rule.And the fusion center of the network makes the final decision.Such a tree structure is widely used in distributed detection due to the ability to balance the contradiction between the detection performance and the energy consumption of the detection network.In order to explore the asymptotic detection performance of the tree network in noisy channels,the work of this paper includes the following aspects.1.Considering the m-ary relay tree network with link failures and unreliable communications,we deduced that the almost optimal information fusion rule under the Bayes rule is the majority dominance rule(break the deadlock randomly).According to the specific form of the majority dominance rule,the step-wise evolutions of the detection error probabilities in the process of information transmission are derived,which have the form of higher-order polynomials about the corresponding error probability in upper level,link failure probability and unreliable communication probability,and the algebraic relationships between them are proved.2.Based on the assumptions that the probabilities of undesirable events in noisy channels both decrease gradually with the increased height of the tree network,taking the false-alarm probability as an example,the fact that the iterative function of the false-alarm probability is a strictly convex function of the false-alarm probability in upper level is derived.Then,the existence and uniqueness of the real number roots of the equilibrium equation at each level are proved in different intervals indirectly,the convergence of the false-alarm probability under different initial conditions are also proved by using the properties of convex functions.3.According to the convexity of the iterative function of the false-alarm probability,the necessary and sufficient condition for that the false-alarm probability can gradually converge to zero with respect to the expansion of network scale is deduced,which is that the probability of the unreliable communication converges to zero gradually.Furthermore,the convergence orders of false-alarm probability under different conditions of noisy channels are derived,and an upper bound and a lower bound of the convergence rate are given.The results show that the existence of unreliable communication not only restrains the limit value of false-alarm probability,but also greatly reduces the convergence speed of false-alarm probability.Only when the link failure probability and unreliable communication probability decay fast enough,can the convergence order of false-alarm probability be the same as that of the tree network in ideal channels,but the convergence rate is still smaller than that of the ideal case.