Modeling End-to-end Distance for Given Number of Hops in Dense Planar Wireless Sensor Networks

We model the end-to-end distance for a given number of hops in dense planar wireless sensor networks in this paper. We derive that the closed-form formula for single-hop distance and postulate Beta distribution for 2-hop distance. When the number of hops increases beyond three, the multi-hop distance approaches Gaussian. The Gaussian approximation model is also applied to ranging, which achieves less distance error than Hop-TERRAIN and APS (ad hoc positioning system). Our error analysis also shows the distance error is be minimized by using our model