Throughput performance of multiuser detection in unslotted contention channels

In this work we analyze the throughput of a centralized packet receiver which utilizes multiuser detection in an unslotted contention channel. The receiver is capable of demodulating all overlapping, unit-length packets, provided that the T-length packet headers do not overlap, and at most K packets overlap at any one time. If one of these conditions is violated, the remainder of the busy period is assumed to be unresolvable. Assuming that the aggregate packet arrival process is Poisson, we analyze the throughput as a function of the total offered load (λ), the maximum number of resolvable overlapping packets (K), and the fractional header duration (T). We derive an iterative expression for the throughput for K = 2 or 3, generalizable to larger K, which permits solution of the throughput to arbitrary accuracy. A closed form solution is given for the case K = 2 and T = 0.5. We provide bounds on the throughput for arbitrary K, λ, and T, which are more convenient than the exact approach for T > 0 or large K. Numerical results illustrate the improvement in throughput due to multiuser detection, and suggest a technique for finding the minimum complexity multiuser receiver (minimum K) as a function of other system parameters.