Distributed Detection of Binary Decisions with Collisions in a Large, Random Network

We consider the problem of distributed detection in a large network of sensors. A random number of sensor nodes are randomly deployed. Sensor nodes perform local detection tests and communicate detections over a multiple-access channel to a fusion center. The fusion center can recognize both successful communications and communication collisions in the channel. We derive decision rules for both perfect communications and a delay-constrained communications protocol, and show that each are functions of count statistics only. We derive analytical expressions that characterize the performance of the system in terms of detection performance. We analyze performance with respect to sensor density and with respect to communications delay. Simulation examples validate theoretical predictions with numerical results. We show that the detection performance improves with network density despite increasing communication collisions. In addition, we show that detection performance using the protocol model, with imperfect communications, rapidly converges to the perfect communications case as the number of communication slots increase.