We consider a scenario in which a DoS attacker with the limited power resource and the purpose of degrading the system performance, jams a wireless network through which the packet from a sensor is sent to a remote estimator. To degrade the estimation quality most effectively with a given energy budget, the attacker aims to solve the problem of how much power to obstruct the channel each time, which is the recently proposed optimal attack energy management problem. The existing works are built on an ideal network model in which the packet dropout never occurs when the attack is absent. To encompass wireless transmission losses, we introduce the signal-to-interference-plus-noise ratio-based network. First we focus on the case when the attacker employs the constant power level. To maximize the expected terminal estimation error at the remote estimator, we provide some more relaxed sufficient conditions compared with the existing work for the existence of an explicit solution to the optimal static attack energy management problem and the solution is constructed. For the other important index of system performance, the average expected estimation error, the associated sufficient conditions are also derived based on a different analysis approach with the existing work. And a feasible method is presented for both indexes to seek the optimal constant attack power level when the system fails to meet the proposed sufficient conditions. Then when the real-time ACK information can be acquired, a Markov decision process (MDP) based algorithm is designed to solve the optimal dynamic attack energy management problem. We further study the optimal tradeoff between attack energy and system degradation. Specifically, by moving the energy constraint into the objective function to maximize the system index and minimize the energy consumption simultaneously, the other MDP based algorithm is proposed to find the optimal dynamic attack power policy which is further shown to have a monotone structure. The theoretical results are illustrated by simulations.

我们考虑一种情况，在这种情况下，具有有限功率资源且旨在降低系统性能的DoS攻击者会阻塞无线网络，通过该网络，来自传感器的数据包将被发送到远程估计器。为了在给定的能量预算下最有效地降低估计质量，攻击者旨在解决每次阻塞信道多少功率的问题，这是最近提出的最优攻击能量管理问题。现有的工作建立在理想的网络模型上，在这种网络模型中，没有攻击时就不会发生数据包丢失。为了涵盖无线传输损耗，我们介绍了基于信号干扰加噪声比的网络。首先，我们关注攻击者使用恒定功率水平的情况。为了最大化远程估计器的预期终端估计误差，与现有工作相比，我们提供了一些更为宽松的充分条件，以针对最优静态攻击能量管理问题存在明确的解决方案，并构建了该解决方案。对于系统性能的另一个重要指标，即平均预期估计误差，相关的充分条件，也可以根据与现有工作不同的分析方法得出。提出了一种可行的方法，即当系统无法满足所提出的充分条件时，为这两个指标寻求最优的恒定攻击强度。然后，当可以获取实时ACK信息时，设计一种基于马尔可夫决策过程（MDP）的算法来解决最优动态攻击能量管理问题。我们进一步研究了攻击能量和系统退化之间的最佳折衷。具体而言，通过将能量约束移至目标函数以同时最大化系统指标和最小化能耗，提出了另一种基于MDP的算法来找到最佳动态攻击功率策略，该策略进一步显示为具有单调结构。仿真结果说明了理论结果。