Ordered Transmissions Schemes for Detection in Spatially Correlated Wireless Sensor Networks

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.