Studying the Relationships between Spatial Structures of Wireless Networks and Population Densities

In this paper we show how to quantify dependency between the node distributions of wireless networks and the underlying population densities. Furthermore, we show that a quantitative analysis of this relation can be beneficial for understanding and generating realistic network models. Towards this direction we argue that spatial statistics is an appropriate method for this purpose. As a case study we analyze the correlations of GSM-900 and UMTS base stations, with the underlying population densities of Germany. We find that there is a significant statistical similarity between the locations of GSM-900 base stations and population, due to the immense penetration of the network, and a less tight relation in the case of UMTS network. We consider the problem of covering a given population pattern and use the concept of fractal dimension to show how the number of required base stations changes when their maximum coverage range decreases, according to the population pattern.