On the Throughput Region of Wireless Random Access Protocols with Multi-Packet Reception Using Multi-Objective Optimization

This paper presents a new approach for the analysis and characterization of the throughput region of wireless random access protocols enabled with multi-packet reception (MPR) capabilities. The derivation of a closed-form expression for the envelope of the throughput region under the assumption of an arbitrary number of terminals is an open issue in the literature. To partially fill this gap, a new method based on multi-objective optimization tools is herein presented. This innovative perspective allows us to identify the envelope of the throughput region as the Pareto frontier solution that results from maximizing simultaneously all individual terminal throughput functions. To simplify this problem, a modified MPR model is proposed that mimics the conditions of collision model protocols, but it also inserts new physical (PHY) layer features that allow concurrent transmission or MPR. The N-reception model is herein introduced, where collisions of up to N signals are assumed to be always correctly resolved from a population of J terminals, where N can be related to the number of antennas or degrees of freedom of the PHY-layer used at the receiver to resolve a collision. It is shown that by using this model and under the assumption of $N=J-1$ , the Pareto frontier expression can be obtained as a simple extension of the ALOHA solution. Unfortunately, for cases with $N<J-1$ , the structure of the resulting determinant matrix does not allow for a simple explicit solution. To overcome this issue, a symmetrical system is proposed, and the solution is obtained by the analysis of the roots of the resulting polynomial expression. Based on this result, an equivalent sub-optimal solution for the asymmetrical case is herein identified for systems where $N<J-1$ . An extension to more general reception models based on conditional reception probabilities is also presented using the proposed equivalence between the symmetric and asymmetric solutions. The results intend to shed light on the performance of MPR systems in general, and in particular to advance towards the solution of the conjecture of the equivalence between throughput and stability regions in random access.