Medium Access Probability in Uniform Networks with General Propagation Models

In this paper, we consider a random network in which the nodes are deployed as a Poisson Point Process. Under this model, we find the medium access rate of nodes using a CSMA-type MAC protocol. For finite network areas this is a timefrequency parameter, while for infinite network areas it translates into a spatial parameter since stationarity can be assumed. The expressions found here make the definition and geometry of contenders explicit. Further, the expressions allow the use of general propagation models. We also present several practical calculations when the network coverage area is finite and regular and when different fading distributions are considered.