On the optimality of the likelihood-ratio test for local sensor decision rules in the presence of nonideal channels

Distributed detection has been intensively studied in the past. In this correspondence, we consider the design of local decision rules in the presence of nonideal transmission channels between the sensors and the fusion center. Under the conditional independence assumption among multiple sensor observations, we show that the optimal local decisions that minimize the error probability at the fusion center amount to a likelihood-ratio test (LRT) given a particular constraint on the fusion rule. This constraint turns out to be quite general and is easily satisfied for most sensible fusion rules. A design example using a parallel sensor fusion structure with binary-symmetric channels (BSCs) between local sensors and the fusion center is given to illustrate the usefulness of the result in obtaining optimal thresholds for local sensor observations. The study that incorporates the transmission channel in sensor system design may have potential applications in the emerging field of wireless sensor networks.