Optimal binary distributed detection

In this paper we present a technique to find the optimal threshold /spl tau/ and fusion rule for local sensors in the distributed detection of s/spl isin/(-m,m), where the ith of n local sensors observes x/sub i/=s+z/sub i/ with i.i.d, additive noise z/sub i/. The fusion center makes a decision based on the n local binary decisions. For generalized Gaussian noises and some non-Gaussian noise distributions, we show that for any admissible fusion rule, the probability of error is a quasi-convex function of threshold /spl tau/. Hence, the problem decomposes into a series of n quasi-convex optimization problems that mall be solved using well known techniques. Our results indicate that at most one quasi-convex problem needs to be solved in practice, since the optimal fusion rule is always essentially a majority vote.