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 perform ance analysis. In this correspondence, ARE is applied to some distribu ted detection cases which use counting fusion rules. In such eases one finds that ARE generally depends on the power of the tests which can make its application difficult. This dependence turns out to be relati vely weak in the cases we consider and the ARE is reasonably well appr oximated by the limit of the ARE as the detection probability approach es the false alarm probability. This approximation should be useful fo r distributed eases. 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 tha n 0.5, OR rules are generally never optimum.