Distance distributions for real cellular networks

This paper presents the general distribution for the distance between a mobile user and any base station (BS). We show that a random variable proportional to the distance squared is Gamma distributed. In the case of the nearest BS, it can be reduced to the well established result of the distance being Rayleigh distributed. We validate our results using a random node simulation and real Vodafone 3G network data, and go on to show how the distribution is tractable by deriving the average aggregate interference power.