Stochastic Geometry Based Research on the Topology Evolution of Base Stations Distribution in Cellular Networks

Confronting the fundamental challenges of the long-term evolution of the ever-growing complication, heterogeneity and densification in mobile cellular networks (2G/3G/LTE/5G), the networking architecture and the base stations spatial distribution have been expressing the features of geometric topology irregularity. Within this research, based on Stochastic Geometry theory and techniques, various representative spatial point processes, including the Poisson point process (PPP), the Geyer point process, the Strauss point process, PHCP, TCP, MCP and the stable point process (α-Stable distribution), will be investigated thoroughly.

On the other hand, by taking advantage of the real data (Big Data) sources of several telecommunications operators from different countries, the abovementioned spatial point process models will be evaluated and verified by the actually measured data of the base stations spatial distribution, covering different regions (urban & rural) and different base station types (Macrocells & Microcells). Finally, the aim is to establish the most suitable (convinced) point process model for base stations topology evolution in future mobile cellular networks.

 Illustration of the Deployment of Base Stations in Typical Regions (Urban & Rural) with Geographical Landforms

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 (Big Data) of realistic deployment information of BSs from on-operating cellular networks, we find that the widely adopted Poisson distribution (i.e. PPP) severely diverges from the practical/actual density distribution of BSs. Instead, heavy-tailed distributions could more precisely match the practical/actual distribution. In particular, α-Stable distribution, the distribution also found in traffic pattern of broadband networks and cellular networks, is most consistent with the practical/actual one. Moreover, rooted in the α-Stable distribution, it has also been found that fractal patterns, scale-free law and Small-World features coexist in the complex "cellular" networks.

The Log-Log Comparison between Practical BS Density Distribution in a Typical City with Various Candidate Distributions

Recently, we have carried out the large-scale identication of spatial modeling of BS locations in cellular networks. Based on large amount of real data (Big Data) from the on-operating base stations, we have investigated the accuracy of PPP's usage in modeling BSs spatial distributions, and verified that the complete randomness property of PPP model is NOT valid in on-operating well-developed cellular networks. This result would obviously challenge the rationality of networking performance characterization based on the overwhelming PPP assumption in heterogeneous cellular networks.

Moreover, by in-depth statistical comparisons based on the above large-scale (Big Data) identication, we also investigated the Gibbs point processes (Geyer, Strauss & PHCP) as well as the Neyman-Scott point processes (MCP & TCP),  and compared their performance in the view of a large-scale modeling test, and finally found the general clustering nature of BSs deployment. However, either Gibbs point processes (Geyer, Strauss & PHCP) or Neyman-Scott point processes (MCP & TCP), diverged from the practical/actual spatial distribution of BSs, to some extent.

Note:

For the relevant detailed information, please visit the specific website:Alpha-Stable Distribution and its Applications in Cellular Networks (http://www.rongpeng.info/stable/).

[References]

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