The Behavior of Unbounded Path-loss Models and the Effect of Singularity on Computed Network Interference
Hazer İnaltekin, Stephen B. Wicker · 2007
In this paper we address the utility of the unbounded path-loss modelG1(𝓍) = 𝓍-αin wireless networking research problems. It is known thatG1(𝓍)is not valid for small values of 𝓍 due to the singularity at 0. We compareG1to 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 areuniformlydistributedover the network domain. In particular, we show that the interference probability density function becomesheavy-tailedunder 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 valueα*ofα. Forα ≤ α*, as the network size grows to infinity, interference converges (eitherinprobabilityorindistribution) only if we scale it by an appropriate sequence of constants𝒸𝓃with𝒸𝓃→∞as𝓃 →∞. On the other hand, it naturally convergesindistributionto a real valued random variable without needing any scaling constants forα > α*. All of our results are invariant under any finite node densityλ > 0.