Some new results on distributed Neyman-Pearson detection with correlated sensor observations

In this paper, we consider a parallel distributed detection network consisting of a fusion center and N sensors. We assume that the observations at different sensors are conditionally dependent, and optimize the system performance under the Neyman- Pearson criterion. Unlike previous papers dealing with the optimal N-P detection problem, we allow the sensor decision rules to be randomized, and obtain the necessary conditions for optimal fusion rule and sensor decision rules without making any assumptions on the joint density functions of sensor observations. The optimality conditions are obtained using an important property of points on the overall ROC curve that is established in the paper. And, a sufficient condition that guarantees the optimal sensor decision rules to be deterministic is also presented.