Analysis of pure and slotted ALOHA with multi-packet reception and variable packet size

Multiple packet reception (MPR) is becoming a viable reality for wireless random access protocols thanks to advances in the physical layer and new coding techniques. In the simplest $K$ -MPR model, a receiver can resolve up to $K\geq 1$ parallel transmissions. We extend the classical analysis of pure and slotted ALOHA to $K$ -MPR devices with arbitrary degree $K$ for fixed and variable packet size. Through a parsimonious modeling approach, we derive relatively simple analytical expressions. In this way, we gain insight and quantitative understanding on the fundamental tradeoffs between pure and slotted ALOHA and on the scaling of maximum achievable throughput with $K$.