Interference in Ad Hoc Networks with General Motion-Invariant Node Distributions

In this paper we derive the tail properties of interference for any stationary and isotropic spatial distribution of transmitting nodes. Previously the properties of interference were known only when the nodes are distributed as a homogeneous Poisson point process on the plane. We show the effect of singular path loss model on the tail distribution of the interference. When the path loss function has a singularity at the origin, the interference is shown to be a heavy-tailed distribution under very mild conditions. When the path loss is bounded, the distribution of the interference is predominantly dictated by the fading. We also provide asymptotically tight upper and lower bounds on the CDF of the interference, and discuss the effectiveness of using a Gaussian approximation for modelling the interference.