Quasi-convexity and optimal binary fusion for distributed detection with identical sensors in generalized Gaussian noise

In this correspondence, we present a technique to find the optimal threshol d tau for the binary hypothesis detection problem with n identical and inde pendent sensors. The sensors all use an identical and single threshold tau to make local decisions, and the fusion center makes a global decision base d on the n local binary decisions. For generalized Gaussian noises and some non-Gaussian noise distributions, we show that for any admissible fusion r ule, the probability of error is a quasi-convex function of threshold tau. Hence, the problem decomposes into a series of n quasi-convex optimization problems that may be solved using well-known techniques. Assuming equal a priori probability, we give a sufficient condition of the non-Gaussian noise distribution g(x) for the probability of error to be qua si-convex. Furthermore, this technique is extended to Bayes risk and Neyman -Pearson criteria. We also demonstrate that, in practice, it takes fewer th an twice as many binary sensors to give the performance of infinite precisi on sensors in our scenario.