On Protocol and Physical Interference Models in Poisson Wireless Networks

This paper analyzes the connection between the protocol and physical interference models in the setting of Poisson wireless networks. A transmission is successful under the protocol model if there are no interferers within a parameterized guard zone around the receiver, while a transmission is successful under the physical model if the signal to interference plus noise ratio at the receiver is above a threshold. The parameterized protocol model forms a family of decision rules for predicting the success or failure of the same transmission attempt under the physical model. For Poisson wireless networks, we employ stochastic geometry to determine the prior, evidence, and posterior distributions associated with this estimation problem. With this in hand, we proceed to develop six sets of results: 1) the maximum correlation of protocol and physical model success indicators; 2) the minimum Bayes risk in estimating physical success from a protocol observation; 3) the receiver operating characteristic (ROC) of false rejection (Type I) and false acceptance (Type II) probabilities; 4) the impact of Rayleigh fading versus no fading on the correlation and ROC; 5) the impact of multiple prior protocol model observations in the setting of a wireless network with a fixed set of nodes in which the nodes employ the slotted Aloha protocol in each time slot; and 6) a numerical investigation of the effect of different pathloss models.