Distributed detection and fusion in a large wireless sensor network of random size

For a wireless sensor network (WSN) with a random number of sensors, we propose a decision fusion rule that uses the total number of detections reported by local sensors as a statistic for hypothesis testing. We assume that the signal power attenuates as a function of the distance from the target, 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 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), as long as the average number of sensors is sufficiently large. For all the different system parameters we have explored, the proposed fusion rule is equivalent to the optimal fusion rule, which requires much more prior information. The problem of designing an optimum local sensor-level threshold is investigated. For various system parameters, the optimal thresholds are found numerically by maximizing the deflection coefficient. Guidelines on selecting the optimal local sensor-level threshold are also provided.