On the <inline-formula> <tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>-Stable Distribution of Base Stations in Cellular Networks

Abstract

Cellular networks are now nearly universally deployed and are under ever-growing pressure to increase the volume of data deliverable to consumers. Understanding how base stations (BSs) are spatially deployed could prominently facilitate the performance analyses of cellular networks, as well as the design of efficient networking protocols. In this letter, inspired by the clustering reality of BSs and the intrinsic heavy-tailed characteristics of human activities, we aim to re-examine the statistical pattern of BSs in cellular networks, and find the most appropriate spatial density distribution of BSs. Interestingly, by taking advantage of large amount of realistic deployment information of BSs from on-operating cellular networks, we find that the widely adopted Poisson distribution severely diverges from the practical density distribution of BSs. Instead, heavy-tailed distributions could more precisely match the practical distribution. In particular, $\alpha$ -stable distribution, the distribution also found in traffic pattern of broadband networks and cellular networks, is most consistent with the practical one.