Optimal Distributed Detection in Clustered Wireless Sensor Networks
In a clustered, multihop sensor network, a large number of inexpensive, geographically-distributed sensor nodes each use their observations of the environment to make local hard decisions about whether an event has occurred. Each node then transmits its local decision over one or more wireless hops to the clusterhead (CH). When all local decisions have been gathered by the CH, it fuses them into a final hard decision about the event. Two sources of error affect the CH's final decision: 1) local decision errors made by the sensor nodes because of noisy measurements or unreliable sensors and 2) bit errors affecting each hop on the wireless communication channel. We show that if both of these sources of error are considered, then the optimal decision at the CH is obtained by thresholding a weighted sum of the nodes' local decisions or, equivalently, computing a weighted order statistic of these decisions. The optimal weights are shown to be functions of the bit error probability of the channel and the ring from which the local decision originated. We determine the error probability of this optimal fusion algorithm, the effect of adding more nodes or rings to the cluster, and the tradeoffs involving the energy consumed in the network, the decision error probability, and the time to reach a decision. This paper thus provides tools to determine the effect of measurement and communication errors on other tradeoffs in the design of clustered sensor networks.