A Stochastic Geometry Model of CDMA Coverage




Baccelli, François (Paris, France)
Francois.Baccelli@ens.fr

(joint work with Bart\l omiej B\l aszczyszyn)

We define and analyze a random coverage process of the 2-dimensional Euclidean space which stems from the CDMA (Code Division Multiple Access) protocol used in mobile communications.

This model is of independent interest in stochastic geometry in that it allows one to describe a continuous spectrum that ranges from the Boolean model to the Poisson-Voronoi tessellation to the Jonson-Mehl model. Like for the Boolean model, the minimal stochastic setting consists of a Poisson point process on this Euclidean space and a sequence of real valued random variables.

In addition to analyzing and visualizing this continuum, we study various basic properties of the coverage process such as the probability that a point or a pair of points be covered by a typical cell. We also determine the distribution of the number of cells which cover a given point, and show how to provide deterministic bounds on this number. Finally, we also analyze mathematical properties of the coverage process using the framework of closed sets.

Most results obtained here allow one to compute quantities of practical interest within the CDMA setting: for instance the outage probability is obtained from the so called volume fraction; the law of the number of cells covering a point allows one to determine possible handover strategies etc.