Successful Packet Reception Analysis in Multi-Packet Reception Wireless Systems

In this letter, we analyze the individual probability of receiving a packet when $n$ nodes transmit simultaneously to a single receiver and a multi-packet reception (MPR) scheme is adopted at the physical layer. The main contribution of this letter is the characterization of the average number of packets successfully received. The generic methodology proposed to compute the probability of successful reception of a packet is obtained taking into account the stochastic nature of the path loss due to the spatial distribution of the nodes, as well as shadowing and fast fading effects. The accuracy of the theoretical approach is finally assessed through simulations, showing that for a generic MPR system, there is an optimal number of transmitters that maximize the average number of received packets.