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An upper bound on transmission capacity of wireless CSMA networks

Outage probability and transmission capacity are two metrics that are often used together to quantify the achievable capacity of decentralized wireless networks, where the outage probability measures the probability that a direct transmission fails and the transmission capacity measures the maximum spatial density of successful concurrent transmissions, subject to a constraint on the outage probability. In CSMA networks, spatial correlations between concurrent transmitters makes the analysis of the outage probability and the transmission capacity a challenging task. In this paper, we analyze the transmission capacity of CSMA networks subject to a designated outage probability constraint by first deriving an upper bound on the outage probability in CSMA networks subject to Rayleigh fading, which is applicable for any node distribution. On that basis, we provide a sufficient condition on the transmission power required to meet a designated outage probability constraint. Finally, we obtain an upper bound on the transmission capacity in CSMA networks satisfying a pre-determined outage probability constraint.