On the performance of distributed Neyman-Pearson detection systems

The performance of a distributed Neyman-Pearson detection system is considered. We assume that the decision rules of the sensors are given and that decisions from different sensors are mutually independent conditioned on both hypotheses. The purpose of decision fusion is to improve the performance of the overall system, and we are interested to know under what conditions can a better performance be achieved at fusion center, and under what conditions cannot. We assume that the probabilities of detection and false alarm of the sensors can be different. By comparing the probability of detection at fusion center with that of each of the sensors, with the probability of false alarm at fusion center constrained equal to that of the sensor, we give conditions for a better performance to be achieved at fusion center