Optimization of exponential error rates for a suboptimum fusion rule in wireless sensor networks

A simple fusion rule with multiple thresholds is presented for a distributed system to resolve multiple hypotheses. In contrast to the common assumption that the data is conditionally independent and identically distributed, only conditional independence under each hypothesis is assumed here. This allows the modeling of situations in which different sensors have different local detection probabilities as well as situations in which different sensors have communication links of different qualities or signal-to-noise ratios. A theorem is proved showing that one can select the thresholds independently in a manner that maximizes the asymptotic decay rate of the average probability of error. Furthermore, it is easy to compute these individual thresholds numerically. This is illustrated with an example.