On white-space detection, localization and coverage

In a finite area, let one transmitter be deployed according to distribution f_T(·) and n sensors be deployed i.i.d. with distribution f_S(·). Sensors can detect a transmission only within a distance of r_n from their location. Using the sensor observations, we estimate the minimal region within which the transmitter is present, called the uncertainty interval. We obtain statistics and scaling laws on the volume of this uncertainty interval. If n nodes are deployed i.i.d. uniformly, then volume of the uncertainty interval scales as Θ(1/n). We also find the optimal sensor location distribution to maximize the probability that volume of the uncertainty interval is less than a chosen threshold.