On counting rules in distributed detection

A distributed network of n identical sensors sending their binary decisions to a fusion center is studied. The asymptotic performance of k out of n rules at the fusion center for finite k (finite (n-k)) is evaluated. For these rules, the error probability of making a wrong decision does not tend to zero as n to infinity , unless the probability distributions under the hypothesis satisfy certain conditions. For a specific detection example, the asymptotic performances of the OR (k=1) rule and the AND (k=n) rule are worse than that of a single sensor.<>