Published in Viswanathan, R., & Aalo, V. (1989). On counting rules in distributed detection. IEEE Transactions on Acoustics, Speech and Signal Processing, 37(5), 772-775. DOI: 10.1109/29.17574 ©1989 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.


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.