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Outage Probability of General Ad Hoc Networks in the High-Reliability Regime

Outage probabilities in wireless networks depend on various factors: the node distribution, the MAC scheme, and the models for path loss, fading and transmission success. In prior work on outage characterization for networks with randomly placed nodes, most of the emphasis was put on networks whose nodes are Poisson distributed and where ALOHA is used as the MAC protocol. In this paper we provide a general framework for the analysis of outage probabilities in the high-reliability regime. The outage probability characterization is based on two parameters: the intrinsic spatial contention $γ$ of the network, introduced in [1], and the coordination level achieved by the MAC as measured by the interference scaling exponent $κ$ introduced in this paper. We study outage probabilities under the signal-to-interference ratio (SIR) model, Rayleigh fading, and power-law path loss, and explain how the two parameters depend on the network model. The main result is that the outage probability approaches $γη^κ$ as the density of interferers $η$ goes to zero, and that $κ$ assumes values in the range $1\leq κ\leq α/2$ for all practical MAC protocols, where $α$ is the path loss exponent. This asymptotic expression is valid for all motion-invariant point processes. We suggest a novel and complete taxonomy of MAC protocols based mainly on the value of $κ$. Finally, our findings suggest a conjecture that tightly bounds the outage probability for all interferer densities.