Decentralized Detection by a Large Number of Sensors,
MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR INFORMATION AND DECISION SYSTEMS
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Consider the decentralized detection problem, in which a number N of identical sensors transmit a finite valued function of their observations to a fusion center which the decides which one of M alternative hypotheses is true. Consider the case where the number of sensors tends to infinity. Then show that it is asymptotically optimal to divide the sensors into MM-12 groups, with all sensors in each group using the same decision rule in deciding what to transmit. Show also 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 approaches infinity to have each sensor perform an identical likelihood ratio test and the optimal threshold is very easy to determine numerically.