The ordered transmissions scheme requires fewer sensor nodes to transmit their measurements than the conventional unordered transmissions scheme (UTS) in which all nodes transmit. Yet, it achieves the same error probability as UTS. For the practically relevant scenario in which the measurements of the sensor nodes are spatially correlated, we present a novel correlation-aware ordered transmissions scheme (CA-OTS) for the binary hypothesis testing problem with Gaussian statistics. It uses the timer scheme to make the nodes transmit their measurements in the decreasing order of the absolute values of the measurements without any node knowing the measurements of other nodes. CA-OTS applies to the general case where the hypotheses differ in the mean vector and covariance matrix, and markedly reduces the number of transmissions. It differs from the literature that assumes that the measurements of the nodes, when conditioned on the hypotheses, are statistically independent or the covariance matrix has a special structure. When the mean vector or covariance matrix is the same for the two hypotheses, we propose novel refinements that require even fewer transmissions. We also derive insightful upper bounds for them that apply to a general product-correlation model.

中文翻译：

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空间相关的无线传感器网络中用于检测的有序传输方案

与所有节点都在其中进行传输的常规无序传输方案（UTS）相比，有序传输方案需要更少的传感器节点来传输其测量结果。但是，它实现了与UTS相同的错误概率。对于传感器节点的测量值在空间上相关的实际相关场景，我们针对具有高斯统计量的二元假设检验问题，提出了一种新颖的相关感知有序传输方案（CA-OTS）。它使用计时器方案使节点以测量的绝对值的降序发送其测量值，而任何节点都不知道其他节点的测量值。CA-OTS适用于假设在平均向量和协方差矩阵中不同的一般情况，并显着减少了传输次数。它不同于文献的假设，即假设假设条件下，节点的测量值在统计上是独立的，或者协方差矩阵具有特殊的结构。当两个假设的均值向量或协方差矩阵相同时，我们提出了新颖的改进方法，需要更少的传输。我们还为它们得出了有见地的上限，这些上限适用于一般的产品相关性模型。