带有通信噪声的平衡二叉树的全局吸引不变集

Globally Attractive Invariant Set of Error Probability over Balanced Binary Relay Trees with Channel Noise

以带有通信噪声的平衡二叉树传感器网络为研究对象,研究了虚警概率和漏检概率的动力学性质。首先推导出了虚警概率和漏检概率依赖于网络层数的迭代表达式,将两类错误概率的迭代过程描述成一个动力学系统;然后在平面直角坐标系下对两类错误概率的迭代模式进行了研究分析;最后推导出了上述动力学系统的全局吸引不变集,该不变集与通信噪声无关且可以很大程度上简化对该系统的分析。

This paper studys the dynamics of false alarm probability and missed detection probability in a balanced binary relay tree with channel noise as the tree height goes to infinity and pairs the false alarm probability and missed detection probability according to the level of the tree,then describe the evolutional process of two kinds of error probabilities as a dynamic system.Then,this paper characterizes the switching modes of the pair dynamics in rectangular coordinates.Finally,this paper obtain a globally attractive invariant set of the pair dynamics,which is not related to the channel noise and contains at most two possible switching modes.