Abstract. We consider the decentralized detection problem. In which N independent, identical sensors transrmt a firute-valued function of their observations to a fusion center which then decides which one of M hypotheses is true. For the case where the number of sensors tends to infinity, we show that it is asymptotically optimal to divide the sensors into M(M -1)/2 groups, with all sensors in each group using the same decision rule m deciding what to transnut. We also show how the optimal number of sensors in each group may be determined by solving a mathematical programming problem. For the special case of two hypotheses and binary messages the solution simplifies considerably: it is optimal (asymptotically, as N -. co) to have all sensors perform an identical likelihood ratio test, and the optimal threshold is very easy to deterrmne numerically.
In REF , Tsitsiklis showed that using M (M −1) 2 distinct local decision rules is optimal for M -ary hypotheses testing in a distributed detection setting.
Decentralized Detection by a Large Number of Sensors*
Mathematics of Control, Signals and Systems
Mathematics Computer Science