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Achievable rate region of CSMA schedulers in wireless networks with primary interference constraints

We consider Carrier Sense Multiple Access (CSMA) schedulers for wireless networks. For networks where all nodes are within transmission range of each other, it has been shown that such schedulers achieve the network capacity in the limiting region of large networks with a small sensing delay. However the design and analysis of CSMA schedulers for general networks has been an open problem due to the complexity of the interaction among coupled interference constraints. For networks with primary interference constraints, we introduce a tractable analysis of such CSMA schedulers based on a fixed point approximation. We then use the approximation to characterize the achievable rate region of static CSMA schedulers. We show that the approximation is asymptotically accurate for the limiting regime of large networks with a small sensing delay, and that in this case the achievable rate region of CSMA converges to the capacity region.