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

To understand the spatial deployment of base stations (BSs) is the first step to analyze the performance of cellular networks and further design efficient networking protocols. Poisson point process (PPP), which has been widely adopted to characterize the deployment of BSs and established the reputation to give tractable results in the stochastic geometry analyses, usually assumes a static BS deployment density in homogeneous PPP (HPPP) models or delicately designed location-dependent density functions in in-homogeneous PPP (IPPP) models. However, the simultaneous existence of attractiveness and repulsiveness among BSs practically deployed in a large-scale area defies such an assumption, and the $\alpha$-stable distribution, one kind of heavy-tailed distributions, has recently demonstrated superior accuracy to statistically model the varying BS density in different areas. In this paper, we start with these new findings and investigate the intrinsic feature (i.e., the spatial self-similarity) embedded in the BSs. Afterwards, we refer to a generalized PPP setup with $\alpha$-stable distributed density and theoretically derive the related coverage probability. In particular, we give an upper bound of the derived coverage probability for high signal-to-interference-plus-noise ratio (SINR) thresholds and show the monotonically decreasing property of this bound with respect to the variance of BS density. Besides, we prove that our model could reduce to the single-tier HPPP for some special cases, and demonstrate the superior accuracy of the $\alpha$-stable model to approach the real environment.