Seasonal Statistics of Shannon Rate in a Dynamical Poisson-Voronoi Cellular Network

Abstract

In this work we consider a dynamical cellular communication network in which mobile base stations (BSs) are modeled as a homogeneous Poisson point process on $\mathbb{R}^2$. Each base station moves at a constant speed in a random direction. A typical user connects to the nearest base station and it experiences variable signal and interference powers depending on the distance of all the stations. Along the motion of the stations, the user swaps its serving station, and such an event is called a {\em handover}. We are interested in the performance evaluation of the system under some classical and tropical metrics of interest at different time of events, inducing handovers, maximal proximity of serving station, nearest interferer at closest or farthest distance with respect to the user or at any typical time epoch. The main results of the paper are closed or integral form expressions for the basic metrics of interest, in particular coverage probability and Shannon rate at these epochs. We can make an analogy with ``seasons'' based on the fluctuations of signal and interference power. Strong or mild signal or interference power correspond to different seasons of Shannon rate along the evolution of the system. We also provide a complete comparison study of the metrics at interest at these epochs.