Detecting the Number of Active Users in IRSA Access Protocols

We develop a maximum a posteriori detector for the number of unrecovered users in coded random access systems based on the irregular repeat slotted Aloha (IRSA) protocol, where each user transmits in random slots multiple packet replicas whose number (known as the user degree) is drawn according to a given probability mass function and where successive interference cancellation (SIC) is exploited at the receiver. The detector is capable to track over SIC iterations the a posteriori probability distribution of a vector whose elements are the numbers of not yet recovered active users of the various degrees. Numerical results are provided to illustrate the capability of the detection algorithm to considerably reduce the mean square error on the number of active users, taking advantage of the iterative SIC process.