On the Performance of Decentralized Detection under Transmission Constraints

We consider the problem of distributed detection in a wireless network consisting of a large number of sensors having either ideal or non-ideal communication links to their respective fusion or relay node. The detection performance is characterized under a Neyman-Pearson framework using a parallel configuration and a single-rooted tree with bounded height, where only the leaves are sensors. We show that with conditionally independent observations across sensors, the Type II error exponent for a single-rooted tree of uniform height two can be equivalent to that of a parallel configuration under certain conditions. These conditions include the ability to group sensors into sub-classes, where the observations within a class are conditionally independent and identically distributed, and with binary decision throughout. We then show that a single rooted tree can achieve improved detection performance versus the parallel configuration with the same number of nodes under multipath fading communication links and a constrained transmit power budget in the non-asymptotic regime.