Stochastic Geometric Modeling and Analysis of Non-Uniform Two-Tier Networks: A Stienens Model-Based Approach

While stochastic geometric models based on Poisson point processes (PPPs) provide a tractable approach for the analysis of uniform two-tier network deployments, the performance evaluation of a non-uniform deployment remains an open issue, which we address in this paper. This is due to the fact that smaller cells can be more efficiently deployed in areas where the QoS of traditional macro base stations is poor. Therefore, in this paper, we introduce Stienen's model, which allows us to analyse such non-uniform deployment. In contrast to traditional PPP-based analysis, performance characterization under the Stienen model is more challenging due to location and density dependencies. However, we demonstrate that the performance can be approximated in a tractable manner. The developed statistical framework is employed to characterize the gains in terms of energy efficiency (EE) for non-uniform deployments. Results show an achievable 19% to 124% improvement in the macrocell coverage as compared to a uniform deployment, while the femtocell coverage and system EE are of the same order of magnitude for both deployments. These results are complemented with the fact that OPEX and CAPEX are reduced due to a lesser number of FAPs deployed.