In a Wireless Sensor Network (WSN), coverage performance of the network is affected by multiple factors such as source power, sensitivity of sensors, and the quality of the channel between the source and the sensors. In most existing works on WSNs, only path‐loss of the wireless channel is considered, that with further assumption of absence of obstacles in the sensing region of a sensor, results in circular‐type of coverage for each node. However, in some WSN applications, the channel is not line‐of‐sight and exhibits multipath fading. In this paper, effect of the multipath fading on k‐coverage of randomly deployed WSNs is analytically investigated via techniques from stochastic geometry. More specifically, the k‐coverage probability is analytically derived under Rayleigh, Rician, and Nakagami fading assumptions. Numerical results are also presented to compare the derived k‐coverage probability with the commonly used k‐coverage models that do not consider the fading effect. These results reveal the level of the k‐coverage degradation due to multipath fading compared to the case of no fading (fixed range), which in some cases is shown to be very significant.

中文翻译：

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衰落对无线传感器网络的k覆盖率的影响

在无线传感器网络（WSN）中，网络的覆盖性能受多种因素影响，例如源功率，传感器的灵敏度以及源与传感器之间的通道质量。在大多数有关WSN的现有工作中，仅考虑无线信道的路径损耗，如果进一步假设传感器的感应区域中没有障碍物，则会导致每个节点的覆盖范围呈圆形。但是，在某些WSN应用中，该信道不是视线，而是呈现多径衰落。在本文中，通过随机几何技术分析研究了多径衰落对随机部署的WSN的k覆盖率的影响。更具体地说，k覆盖率是根据瑞利，里西亚和中神衰落假设分析得出的。还提供了数值结果，以将导出的k覆盖率与不考虑衰落效应的常用k覆盖率模型进行比较。这些结果表明，与没有衰落（固定范围）的情况相比，由于多径衰落导致的k覆盖率下降的水平，在某些情况下这被证明是非常重要的。