# Spatial Distribution of Base Stations

• ### Motivation

Confronting the fundamental challenges of the long-term evolution of the ever-growing complication, heterogeneity and densification in wireless cellular networks (2G/3G/LTE/5G), the networking architecture and the base stations spatial distribution have been expressing the features of geometric topology irregularity.

Basically, in the wireless cellular networks, the base stations (BSs) appear to be the essential part in the whole system.  The spatial structure of BSs has a great impact on the performance of cellular networks, since the received signal strength varies depending on the distance between transmitter and receiver. Moreover, interference characterization is very complicated and challenging due to path loss and multipath fading effect, in particular for a heterogeneous networking (HetNets) scenario consisting of different types of BSs. In order to evaluate the network performance more accurately and tractably, it is essential to obtain realistic spatial models for the BSs deployment in cellular networks.Recently, Poisson distribution has been widely adopted to characterize the spatial distribution of BSs, and leads to a tractable approach to calculate the coverage probability and rate distribution in cellular networks, by taking advantage of a Poisson point process (PPP) based theory (i.e., stochastic geometry). However, the modeling accuracy of Poisson distribution has been recently questioned in regard to a number of realistic cellular networking scenarios. Consequently, in order to reduce the modeling error between Poisson distributed BSs and the practical distributed ones, some variants of PPP have been exploited to obtain precise analysis results. On the other hand, the actual deployment of BSs in long term is highly correlated with human activities.

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 around the world, we find that the widely adopted Poisson distribution (i.e. PPP) severely diverges from the practical/actual spatial distribution of BSs. Instead, heavy-tailed distributions could more precisely match the practical/actual distribution. In particular, α-Stable distribution, the heavy-tailed distribution also found in various traffic patterns of wired broadband networks and wireless cellular networks, is most consistent with the practical/actual measured data. 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 wireless “cellular” networks.

Moreover, by in-depth statistical comparisons based on the above large-scale (Big Data) identification, we also investigated the Gibbs point processes (Geyer, Strauss & PHCP) as well as the Neyman-Scott point processes (MCP & TCP: Matern cluster process & Thomas cluster process),  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 (see the following Table).

In summary, we have carried out an large-scale identification based on real data of base station locations from both Chinese and European mobile operators. For detailed description, please check the subsections on this topic as well as the following references.

• Yifan Zhou, Rongpeng Li, Zhifeng Zhao, Xuan Zhou, and Honggang Zhang, “On the $$\alpha$$-Stable Distribution of Base Stations in Cellular Networks“, IEEE Communications Letters, vol. 19, no. 10, pp. 1750-1753, Aug. 2015. PDF

• Rongpeng Li, Zhifeng Zhao, Yi Zhong, Chen Qi, and Honggang Zhang, “The Stochastic Geometry Analyses of Cellular Networks with α-Stable Self-Similarity,” IEEE Trans. on Communications, March 2019.  PDF

• Ying Chen, Rongpeng Li, Zhifeng Zhao, and Honggang Zhang, “Study on Base Station Topology in National Cellular Networks: Take Advantage of Alpha Shapes, Betti Numbers, and Euler Characteristics,” IEEE Systems Journal, Q3/Q4 2019.

• Ying Chen, Rongpeng Li, Zhifeng Zhao, and Honggang Zhang, “Fundamentals on Base Stations in Urban Cellular Networks: From the Perspective of Algebraic Topology,” IEEE Wireless Communications Letters, April 2019. PDF

• Yifan Zhou, Zhifeng Zhao, Yves Louet, Qianlan Ying, Rongpeng Li, Xuan Zhou, Xianfu Chen, and Honggang Zhang, “Large-scale Spatial Distribution Identification of Base Stations in Cellular Networks,”  IEEE Access, vol. 3, pp. 2987-2999, Dec. 2015. PDF

• Zhifeng Zhao, Meng  Li, Rongpeng Li, and Yifan Zhou, “Temporal-Spatial Distribution Nature of Traffic and Base Stations in Cellular Networks,” IET Communications, Q3 2017.

• Luca Chiaraviglio, Francesca Cuomo, Maurizio Maisto, Andrea Gigli, Josip Lorincz, Yifan Zhou, Zhifeng Zhao, Chen Qi, Honggang Zhang, “What is the Best Spatial Distribution to Model Base Station Density? A Deep Dive in Two European Mobile Networks,” IEEE Access, Apr. 2016.

• Luca Chiaraviglio, Francesca Cuomo, Andrea Gigli, Maurizio Maisto, Yifan Zhou, Zhifeng Zhao, Honggang Zhang, “A Reality Check of Base Station Spatial Distribution in Mobile Networks,” IEEE INFOCOM 2016 (Poster), San Francisco, Apr. 2016. PDF