Capture and retransmission control in mobile radio

We consider the slotted ALOHA protocol with capture, in a mobile communication environment, in the presence of Rayleigh fading and log-normal shadowing. The capture probabilities and their asymptotic value, as the number of colliding packets tends to infinity, are computed. A sufficient condition, under which this limit is positive, is identified and expressed in terms of the spatial distribution of the users. Also, various models for this latter distribution are discussed. These results help identify the region in which the system may achieve a positive stable throughput. Finally, a retransmission control scheme, that enhances the throughput, is considered, and the stability of the system is rigorously proven. We also show that the use of retransmission control is unavoidable if the network performance predicted in some recent literature is to be achieved