Distributed detection with collisions in a random, single-hop wireless sensor network

We consider the problem of distributed detection in a large network of sensors under network communication constraints. Sensor nodes are randomly deployed and follow a random sleep/wake schedule. When awake, sensor nodes perform local detection tests and communicate detections over a multiple-access channel to a fusion center. The fusion center can detect both successful communications and communication collisions in the channel. We show that the optimum fusion rule is a weighted sum of the number of detections received and the number of collisions detected by the fusion node. We derive analytical expressions that characterize the performance of the system. Simulation examples compare theoretical predictions with numerical results.