Random Access over Wireless Links: Optimal Rate and Activity Probability Selection

In this paper, we consider a random access scheme over wireless fading channels based on slotted ALOHA where each user independently decides whether to send a packet or not to a common receiver at any given time slot. To characterize the system throughput, i.e., the expected sum-rate, an information theoretic formulation is developed. We consider two scenarios: classical slotted ALOHA where no multi-user detection (MUD) capability is available and slotted ALOHA with MUD. Our main contribution is that the optimal rates and channel activity probabilities can be characterized as a function of the user distances to the receiver to maximize the system throughput. In addition, we address the issue of fairness among the users and provide solutions, which guarantee a minimum amount of individual throughput.