Modeling of Cellular Networks Using Stationary and Nonstationary Point Processes

The spatial topology of the base stations in wireless networks has a profound impact on their performance evaluation and analysis. It is important to identify a proper and accurate point process model before applying any theoretical stochastic geometry analysis. In this paper, we present and describe a network-data-supported technique for fitting stationary and nonstationary point process models to real-life cellular networks using maximum likelihood/pseudolikelihood and minimum contrast methods. Nonstationary processes are of particular interest, since real-life wireless networks most often do not have a homogeneous spatial distribution. When fitting with nonstationary models, both spatial inhomogeneity and covariate effects are considered. We introduce covariates into the point process models as a potential (or secondary) effect that further influences the distribution of wireless nodes, in order to bridge the gaps between the results and measures of stationary models and simulations of real-life cellular networks. The covariates considered account for population densities in urban areas and distance from the base stations to their closest main roads in rural areas. Simulated envelope tests are used for the evaluation of goodness-of-fit. However, such envelope tests are insufficient to conclusively distinguish between the fitted models. Thus, we apply other metrics such as the Akaike information criterion and root mean square deviation to differentiate among different fitted models. Additionally, the probability of coverage is also considered as the supplementary criterion for the goodness-of-fit and model selection.