Fundamentals on Base Stations in Urban Cellular Networks: From the Perspective of Algebraic Topology

Abstract

In recent decades, deployments of cellular networks have been going through an unprecedented expansion. In this regard, it is beneficial to acquire profound knowledge of cellular networks from the view of topology so that prominent network performances can be achieved by means of appropriate placements of base stations (BSs). In our researches, practical location data of BSs in eight representative cities are processed with classical algebraic geometric instruments, including $\boldsymbol {\alpha }$ -shapes, Betti numbers, and Euler characteristics. At first, a fractal nature is validated in urban BS topology from both perspectives of Betti numbers and Hurst exponents. Furthermore, log-normal distribution is affirmed to provide the optimal fitness to the Euler characteristics of real urban BS deployments.