Asymptotic outage analysis of general motion-invariant Ad Hoc Networks

The outage analysis of networks with randomly distributed nodes has been mostly restricted to the case of Poisson networks, where the node locations form a homogeneous Poisson point process. In this paper, we show that in great generality, the outage probability, as a function of the density of interfering nodes ¿, approaches ¿¿^¿ as ¿ goes to zero, where ¿ and ¿ are the spatial contention and the interference scaling exponent, respectively. Interestingly, ¿ is restricted to a small range of possible values: 1 ¿ ¿ ¿ ¿/2 for a path loss exponent ¿. We also prove that for ALOHA, ¿ = 1 irrespective of the point process properties, and we demonstrate how the upper bound ¿ = ¿/2 can be achieved.