  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.
