Hypothesis testing in the presence of maxwell's daemon: signal detection by unlabeled observations

In modern heterogeneous sensor networks huge volumes of information rapidly flow across the system, and it is often too difficult or costly to associate data to the sensors that produced them. Then, the set of observations appears to be unlabeled: What comes from whom? We study the classical problem of detecting a known signal embedded in Gaussian noise, but under the peculiar assumption that the signal samples have been scrambled (e.g., in time or space) in an unknown way. Our study sheds light on questions like: How much detection performance is contained in the samples' values and how much in their ordering? Are there nicely-performing detectors with affordable computational complexity?