The value of observations in predicting transmission success in wireless networks under slotted Aloha

We consider a wireless network of static nodes where each transmitter-receiver pair employs slotted Aloha, electing to transmit with a common contention probability p, and we further assume the Rayleigh fading varies with each time slot. The random point processes of actual transmitters in a given time slot (along with their random fades) determine the interference seen by a reference receiver, and the interference across time slots is dependent due to common dependence on the underlying set of potential interferers. It follows that observations of the set of transmitters over several time slots (or summary statistics of this process) may be leveraged to yield improved estimates of the probability of success of the transmission attempted at the reference receiver. In this paper we study the value of several different forms of such observations in improving this estimated success probability. Specifically, we consider five cases: the observer has i) zero knowledge, ii) full knowledge of the point process of potential transmitters, iii) knowledge of the number of "nearby" potential transmitters, iv) N binary observations under the "physical" model at the reference receiver, and v) N binary observations under the "protocol" model at the reference receiver.