Decision fusion in a wireless sensor network with a random number of sensors

For a wireless sensor network (WSN) with a random number of sensors, a decision fusion rule that uses the total number of detections reported by local sensors for hypothesis testing, is proposed. It is assumed that the number of sensors follows a Poisson distribution and the locations of sensors follow a uniform distribution within the region of interest (ROI). Both analytical and simulation results for the system level detection performance are provided. This fusion rule can achieve a very good system level detection performance even at very low signal to noise ratio (SNR), if the average number of sensors is sufficiently large. In addition, the problem of choosing an optimum local sensor level threshold is investigated for various system parameters.