On some unresolved issues in finding optimum distributed detection schemes

Optimum distributed detection under the Neyman-Pearson (NP) criterion is considered for a general case with possibly dependent observations from sensor to sensor. The focus is on the parallel architecture. New necessary conditions are presented that relate the threshold used in the NP-optimum fusion rule to those used in the NP-optimum sensor rules. These results clearly illustrate that the necessary conditions for NP optimality have exactly the same form as those for Bayes optimality. Based on these conditions, a new algorithm for finding NP optimum distributed detection schemes is developed. The algorithm allows randomization at the fusion center, which we show is generally needed to achieve optimality. The algorithm allows one to attempt to optimize the fusion rule along with the sensor rules or to find the best schemes among those using each of a set of fixed possible fusion rules.