Study on Base Station Topology in Cellular Networks: Take Advantage of Alpha Shapes, Betti Numbers, and Euler Characteristics

Faced with the ever-increasing trend of the cellular network scale, how to quantitatively evaluate the effectiveness of the large-scale deployment of base stations (BSs) has become a challenging topic. To this end, a deeper understanding of the cellular network topology is of fundamental significance to be achieved. In this paper, $ \alpha $-Shape, a powerful algebraic geometric tool, is integrated into the analysis of real BS location data for six Asian countries and six European countries, respectively. Firstly, the BS spatial deployments of both Asian and European countries express fractal features based on two different testifying metrics, namely the Betti numbers and the Hurst coefficients. Secondly, it is found out that the log-normal distribution presents the best match to the cellular network topology when the practical BS deployment is characterized by the Euler characteristics.