The Stochastic Geometry Analyses of Cellular Networks with {\alpha}-Stable Self-Similarity

To understand the spatial deployment of base stations (BSs) is the first step to facilitate the performance analyses of cellular networks, as well as the design of efficient networking protocols. Poisson point process (PPP) has been widely adopted to characterize the deployment of BSs and established the reputation to give tractable results in the stochastic geometry analyses. However, given the total randomness assumption in PPP, its accuracy has been recently questioned. On the other hand, the actual deployment of BSs during the past long evolution is highly correlated with heavy-tailed human activities. The αstable distribution, one kind of heavy-tailed distributions, has demonstrated superior accuracy to statistically model the spatial density of BSs. In this paper, we start with the new findings on α-stable distributed BSs deployment and investigate the intrinsic feature (i.e., the spatial self-similarity) embedded in the BSs. Based on these findings, we perform the coverage probability analyses and provide the relevant theoretical results. In particular, we show that for some special cases, our work could reduce to the fundamental work by J. G. Andrews in [1]. We also examine the network performance under extensive simulation settings and validate that the simulations results are consistent with our theoretical derivations.