The problem of decision fusion in distributed sensor systems is considered. Distributed sensors pass their decisions about the same hypotheses to a fusion center that combines then into a final decision. Assuming that the sensor decisions are independent from each other conditioned on each hypothesis, we provide a general proof that the optimal decision scheme that maximizes the probability of detection for fixed probability of false alarm at the fusion, is the Neymann-Pearson test at the fusion and Likelihood-Ratio tests at the sensors. The optimal set of thresholds is given via a set of nonlinear, coupled equations that depend on the decision policy but not on the priors. The nonlinear threshold equations cannot be solved in general. We provide a suboptimal algorithm for solving for the sensor thresholds through a one dimensional minimization. The algorithm applies to arbitrary type of similar or disimilar sensors. Numerical results have shown that the algorithm yields solutions that are extremely close to the optimal solutions in all the tested cases, and it does not fail in singular cases.
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