On Counting Rules in Distributed Detection

A network of n sensors receiving independent and identical observations in RN, regarding certain binary hypotheses, pass their decisions to a fusion center which then decides which one of the two hypotheses is true. We consider the situation where each sensor employs a likelihood ratio test with its own observation and a threshold, which is the same for all the sensors, and the fusion center decision based on k out of n decision rule. The asymptotic (n → ∞) behavior of k out of n rules for finite k and finite n - k are considered. For these rules, the error probability of making a wrong decision does not tend to zero as n → ∞, unless the probability distributions under the hypotheses 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