Detection Outage and Detection Diversity in a Homogeneous Distributed Sensor Network

The distributed detection problem over a binary target is considered with wireless sensors sending local decisions to a fusion center over slow-fading orthogonal multiple access channels, where the J-divergence between the distributions under different hypotheses is used as the performance criterion. Given the slow-fading channels between the sensors and the fusion center, two new concepts called detection outage and detection diversity are introduced to quantify the long-term system performance, where the detection outage probability is defined as the probability that the instantaneous J-divergence is smaller than a certain threshold. Based on the detection outage probability, detection diversity order is defined as the slope of the outage probability curve (versus system power consumption) when things are plotted in logarithm domain. It is shown that even with a simple uniform transmission strategy, full detection diversity can be achieved on the order of K with K the total number of sensors in the network. We further show that if the transmission power is optimized across sensors, an adaptive power gain can be achieved in addition to the full diversity gain.