Unstructured sequential testing in sensor networks

We consider the problem of quickly detecting a signal in a sensor network when the subset of sensors in which signal may be present is completely unknown. We formulate this problem as a sequential hypothesis testing problem with a simple null (signal is absent everywhere) and a composite alternative (signal is present somewhere). We introduce a novel class of scalable sequential tests which, for any subset of affected sensors, minimize the expected sample size for a decision asymptotically, that is as the error probabilities go to 0. Moreover, we propose sequential tests that require minimal transmission activity from the sensors to the fusion center, while preserving this asymptotic optimality property.