Performance analysis of distributed detection in a random sensor field

For a wireless sensor network (WSN) with randomly deployed sensors, the performance of the counting rule, where the fusion center employs the total number of detections reported by local sensors for hypothesis testing, is investigated. It is assumed that the signal power decays as a function of the distance from the target. For both the case where the total number of sensors is known and the wireless channels are lossless, and the case where the number of sensors is random and the wireless channels have nonnegligible error rates, the exact system level probability of detection is derived analytically. Some approximation methods are also proposed to attain an accurate estimate of the probability of detection, while at the same time to reduce the computation load significantly. To obtain a better system level detection performance, the local sensor level decision threshold is determined such that it maximizes the system level deflection coefficient.