Characterizing random CSMA wireless networks: A stochastic geometry approach

We charachterize the random CSMA wireless networks by statistically quantifing the intensity of simultaneously active nodes and the aggregate interference experienced by a generic node in the network. First, starting from a Poisson point process to model the spatial distribution of the network nodes, we propose a modified hard core point process (MHCPP) to model the spatial distribution of the simultaneously active users in a random CSMA network. Our motivation to propose the MHCPP is to mitigate the node intensity underestimation problem of the traditional hard core point process (HCPP). Then, we use the shot noise theory to statistically quantify the interference experienced by a generic node in the network. Closed-form expressions for the intensity of the simultaneously active nodes and the Laplace transform of the probability density function (and hence the moment generating function and the characteristic function), mean, and variance of the approximate aggregate interference are obtained. The accuracy of our model is validated by simulations.