Topology and irregularity in cellular networks

The analysis of cellular systems has been carried out modeling the access network by means of deterministic and stochastic methods. Deterministic models include hexagonal geometries or real-world data. Stochastic methods, given their nature, capture (in a statistical manner) the inhomogeneities found in realistic deployments. Beyond pros and cons of each approach, the notion of `topology´ associated to these models is either geometric (regular or non-regular) or architectonic (heterogeneous or not), but it is not enough to describe many aspects of real-world deployments. Despite the term is widely used in the context of cellular communications, there is no precise (mathematical) definition for it. In the light of this situation, this paper presents a set of proper definitions to describe network topology and its compatibility with service demand distribution in a way that is useful from the planning and optimization perspective. In addition, a novel view of `irregularity´ is also introduced. Due to its generality, this statistical framework is timely for 5G where 1) hyper-dense and hierarchical deployments are foreseen, and 2) more complex performance indicators such as energy, spectral, and deployment efficiency per area unit need to be accurately estimated. In addition, operator-specific criteria such as QoS can be taken into account in the model presented herein.