Tight bounds on the Laplace transform of interference in a poisson hole process

摘要

To maintain tractability, interference field is often modeled as a homogeneous Poisson Point Process (PPP) in the analysis of wireless networks. While it provides meaningful firstorder results, it falls short in modeling the effect of interference management techniques, which typically introduce some form of spatial interaction among transmitters. In some applications, such as cognitive radio and device-to-device networks, this interaction results in the formation of holes in an otherwise homogeneous interference field. The resulting interference field can be accurately modeled as a Poisson Hole Process (PHP). Despite the importance of PHP in modeling wireless networks, exact characterization of the interference experienced by a typical node in a PHP is an open problem. In this paper, we introduce a new approach to modeling the PHP, in which we dissolve the holes in such a way that it results in an equivalent non-homogeneous PPP, which is much more amenable to shot-noise analysis. Using this approach, we derive new lower and upper bounds on the Laplace transform of interference in a PHP. The new bounds are compared numerically to the known approaches and are shown to be very tight under various operational regimes.