Fundamental Limits in Cellular Networks with Point Process Partial Area Statistics

Despite the huge number of contributions dealing with the evaluation of cellular networks performance, tackling with more and more complex systems including multi-tier networks or MIMO systems, the fundamental limits in terms of capacity in an information theory sense is not known for these networks. Stochastic geometry helped doing a step forward, relying on Palm theory and providing coverage statistic at the network scale. However, this statistic is not sufficient to establish a fundamental limit, namely to characterise a Shannon capacity region of the network. In this paper, we propose a new approach exploiting the cell capacity of the Spatial Continuum Broadcast Channel (SCBC) recently introduced for an isolated cell. The network capacity is linked to the cells' geometry statistics in a Voronoi tessellation. The fundamental limit is characterised by the minimal average cell power required in a network modelled as a Point Process (PP) to achieve a desired rate distribution. A direct relation is established between this minimum average power and the partial area statistics of the cells geometry, which constitute a sufficient statistic. Our approach is validated through Monte-Carlo simulations.