Directivity in RF Sensor Networks for Widespread Spectrum Monitoring

Widespread RF spectrum monitoring could enable data-driven modeling of spectrum usage, enhance spectral utilization, and help automate policy enforcement. Previous works in wireless sensor networks offer design insights for RF sensors, but they assume emitters that radiate omnidirectionally. This paper develops a new framework for directional sensors and emitters, which are increasingly common with the growth of millimeter wave technologies. We focus on two-dimensional random sensor deployments modeled as Poisson point processes. Specifically, we determine the probability that a sensor network detects a single emitter for a channel model including path loss, fading, and the directivity of emitters and sensors with random orientations and locations. Our results suggest that with a path loss exponent of 4, quartering the emitter half-power beamwidth doubles the required average sensor density. We also conclude that omnidirectional sensors optimize detection probability. For multiple emitters, we develop a lower bound on the probability of multi-emitter detection and find the average number of undetected emitters. Finally, assuming higher sensor quality results in higher sensor cost, we consider a fixed-budget deployment and observe that decreasing the individual sensor cost by a decade and therefore increasing the quantity of sensors reduces the missed detection probability by about a decade.