A modified Matérn hard core point process for modeling and analysis of dense IEEE 802.11 networks

Stochastic geometry is a powerful tool for modeling wireless networks employing various MAC protocols with random topologies. For wireless networks operating carrier sense multiple access/collision avoidance (CSMA/CA) protocol, there are distance constraints between simultaneous transmitters, and only one node is allowed to transmit within its carrier sensing range. Matérn hard core point process is generally used to model and analyze the performance of this type of networks, because it is a repulsive point process that also defines a minimum distance between any two points. However, the traditional Matérn HCPP has the defect of underestimating the intensity of concurrent transmission nodes, which will affect the accuracy of analysis results, when wireless nodes are densely deployed. In this paper, we propose a modified Matérn HCPP called TM-HCPP which can mitigate the intensity underestimation problem to model dense IEEE 802.11 networks. Then, we simulate the network coverage probability using the traditional Matérn HCPP and the proposed TM-HCPP, and compare the simulated results with the theoretical analyzed results. Simulation results validate the accuracy of the proposed TM-HCPP.