Shot Noise Models for the Dual Problems of Cooperative Coverage and Outage in Random Networks

The performance analysis of ad hoc networks requires the characterization of the network’s self-interference. However, thus far, the exact distribution of the interference has been analytically tractable only for a path loss exponent of 4. Further, conventional power law decay models for signal propagation have a singularity at the origin that causes all the moments of the network self-interference to diverge, resulting in no useful insight into the statistics of the interference. In this paper, we employ a 2D shot noise process with a stochastic power law impulse response function together with a bounded path loss to model the interference in large wireless networks, where the nodes are distributed according to a Poisson point process. We further show that this interference problem and the problem of coverage in cooperative sensor networks are duals of each other — they can be solved using the same shot noise-based approach.