A Modified Hard Core Point Process for Analysis of Random CSMA Wireless Networks in General Fading Environments

For spectrum sharing and avoidance of mutual interference, carrier-sense multiple access (CSMA) protocols are very popular in distributed wireless networks. CSMA protocols aim to maximize the spatial frequency reuse while limiting the mutual interference and outage. The hard core point process (HCPP) is a very popular tool for modeling and analysis of random CSMA networks. However, the traditional HCPP suffers from the node intensity (and hence the interference) underestimation flaw. Therefore, we propose a modified hard core point process to mitigate this flaw. The proposed modified HCPP is generalized for any fading environment. To this end, we derive a closed-form expression for the intensity of simultaneously active transmitters in a random wireless CSMA network. Then, we derive a closed-form expression for approximating the outage probability experienced by a generic receiver in the network, and subsequently, use it to obtain the transmission capacity of the network. Finally, we show the existence of an optimal carrier-sensing threshold for the CSMA protocol that maximizes the transmission capacity of the network. Simulation results validate the analysis and also provide interesting insights into the design of practical CSMA networks.