We consider the composite hypothesis testing problem of time-bandwidth-constrained distributed detection. In this scenario, the probability distribution of the observed signal when the event of interest is happening is unknown. In addition, local decisions are censored and only those uncensored local decisions will be sent to the fusion center over a shared and noisy collision channel. The fusion center also has a limited time duration to collect transmitted decisions and make a final decision. Two types of medium access control that the sensor nodes apply to send their decisions are investigated: time division multiple access and slotted-Aloha. Unlike using the time division multiple access protocol, the slotted-Aloha-based distributed detection will experience packet collisions. However, in this article, since only uncensored decisions are sent, packet collisions are informative. We derive fusion rules according to generalized likelihood ratio test, Rao test, and Wald test for both the time division multiple access–based distributed detection and the slotted-Aloha-based distributed detection. We see that the fusion rules for the slotted-Aloha-based distributed detection here also exploit packet collisions in the final decision-making. In addition, the asymptotic performances and energy consumption of both schemes are analyzed. Extensive simulation and numerical results are provided to compare the performances of these two schemes. We show that, for a given time delay, the slotted-Aloha-based distributed detection can outperform the time division multiple access–based distributed detection by increasing the number of sensor nodes which results in higher energy consumption.

中文翻译：

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共享和嘈杂冲突信道上无线传感器网络复合假设检验的决策融合

我们考虑时间带宽约束分布式检测的复合假设检验问题。在这种情况下，当感兴趣的事件发生时，观察到的信号的概率分布是未知的。此外，本地决策会被审查，只有那些未经审查的本地决策才会通过共享且嘈杂的碰撞通道发送到融合中心。融合中心也有一个有限的持续时间来收集传输的决定并做出最终决定。研究了传感器节点用于发送其决策的两种类型的媒体访问控制：时分多址访问和时隙 Aloha。与使用时分多址协议不同，基于时隙 Aloha 的分布式检测会遇到数据包冲突。但是，在本文中，由于只发送未经审查的决定，数据包冲突是信息性的。我们根据广义似然比检验、Rao 检验和 Wald 检验推导出基于时分多址的分布式检测和基于时隙 Aloha 的分布式检测的融合规则。我们看到，这里基于时隙 Aloha 的分布式检测的融合规则也在最终决策中利用了数据包冲突。此外，分析了两种方案的渐近性能和能耗。提供了广泛的模拟和数值结果来比较这两种方案的性能。我们表明，对于给定的时间延迟，通过增加导致更高能耗的传感器节点的数量，基于时分 Aloha 的分布式检测可以优于基于时分多址的分布式检测。