In this paper we address the utility of the unbounded path-loss model G 1 (x) = x -alpha  in wireless networking research problems. It is known that G 1 (x) is not valid for small values of x due to the singularity at 0. We compare G 1  to a more realistic bounded path-loss model, showing that the effect of the singularity on the total network interference power is significant and cannot be disregarded when the nodes are  uniformly   distributed  over the network domain. In particular, we show that the interference probability density function becomes  heavy-   tailed  under the unbounded path-loss model. However, it decays to zero exponentially fast under the bounded path- loss model. We also prove that a phase transition occurs in the interference behavior at a critical value alpha* of alpha. For alpha les alpha*, as the network size grows to infinity, interference converges (either  in   probability   or   in   distribution ) only if we scale it by an appropriate sequence of constants c n middot with c n   rarr  infin as n rarr infin. On the other hand, it naturally converges  in   distribution  to a real valued random variable without needing any scaling constants for alpha > alpha*. All of our results are invariant under any finite node density lambda > 0.
['Hazer Inaltekin', 'Stephen B. Wicker']
The Behavior of Unbounded Path-loss Models and the Effect of Singularity on Computed Network Interference