Sensor selection for distributed detection via multiaccess channels

We consider a network of sensors whose decisions are used to discriminate between two alternative hypotheses, after communication over a multiaccess channel. Each sensor makes independent local binary decisions. Using a distance measure, we consider optimizing the entire network under the assumption that sensors are grouped into classes with identical characteristics. We prove that it can be optimal to remove some sensors from the network, and when this is the case, every sensor within that class should be removed. We also prove that any class that consists of a sufficiently large number of sensors should not be removed.