Decentralized detection with censoring sensors over a packet-dropping network

In a "censoring" or "send/no-send" approach to decentralized detection, sensors only transmit "informative" observations to the fusion center, which is able to significantly reduce energy consumption particularly when one hypothesis is more likely. The canonical "censoring" decentralized detection, however, assumes the communication channels between sensors and the fusion center are perfect, which is not quite realistic. We consider the problem of decentralized detection with censoring sensors over networks where packet dropout may occur. A sensor decides whether to use a high or low transmission power to communicate with the fusion center. With a general energy constraint, we prove that, to minimize the probability of error, the transmitting region of likelihood ratio associated with low power level is a single interval, and we derive necessary conditions for the lower and upper thresholds of this interval. For the special case that the available energy is sufficiently small, we show that the intervals have zero lower thresholds and can be determined independently for each sensor. A numerical example is provided to illustrate the main results.