Statistical analysis of optimal distributed detection fusion rule in wireless sensor networks

The problem of optimal distributed detection in wireless sensor networks (WSNs) is revisited. The optimal fusion rule (OFR) of the local detection decisions is derived under the general case of unknown sensor nodes location and number. The OFR is usually used as a benchmark for comparison with other suboptimal fusion rules. However its performance is difficult to characterize due to the complexity of finding its probability distribution under both, null and alternative hypothesis. In this paper, this issue is addressed by instrumenting stochastic geometry to model the distributed detection system in WSNs. Under this framework, we are able to derive an insightful form of the characteristic function of the OFR. Furthermore, the first and second moments of OFR are accurately computed. Equipped with those moments, the OFR distribution is approximated by a Gamma and Gaussian distributions via moment matching method. Simulation results shows that the Gamma distribution fits the OFR distribution to high extent when compared with Gaussian distribution.