On the asymptotic relative efficiency of distributed detection schemes

The asymptotic relative efficiency (ARE) of two centralized detection schemes has proved useful in large-sample-size and weak-signal performance analysis. In the present paper ARE is applied to some distributed detection cases which use counting fusion rules. In such cases one finds that ARE generally depends on the power of the tests which can make its application difficult. This dependence turns out to be relatively weak in the cases considered and the ARE is reasonably well approximated by the limit of the ARE as the detection probability approaches the false alarm probability. This approximation should be useful for distributed cases. Some specific results provide the best counting (k-out-of-N) fusion rules for cases with identical sensor detectors if one uses asymptotically large observation sample sizes at each sensor. These results indicate that for false alarm probabilities of less than 0.5, OR rules are generally never optimum