# Study of Coded ALOHA with Multi-User Detection under Heavy-Tailed and Correlated Arrivals
## 1 Introduction
Further improvement is obtained by exploiting the capture effect, which can be achieved by introducing transmit power diversity or exploiting the natural fading [29]. In [30] enhancing the physical layer of CSA-like protocols is investigated and an optimal received packet power distribution is obtained. In [31], transmit power diversity is proposed to enhance the performance of CSA-like protocols and an optimal transmit power distribution is derived and analyzed. In [32], author exploit non-orthogonal multiple access techniques (NOMA) into FA-CSA-like systems, optimizing the degree distribution to maximize the throughput. Related to the FS-CSA and FA-CSA techniques, several of the studies assume that users join the system according to a slot-based Poisson arrival process, and that arrivals in different slots are statistically independent. This has the main advantage of allowing a tractable mathematical model for the packet loss ratio (PLR) and an analysis of the system stability [33]. This mathematical framework can be extended to the case of multi-packet or multi-user detection (MUD) [34; 35], which consists in having receivers capable of successfully decoding \(k>1\) packets transmitted in the same slot, by employing successive interference cancellation (SIC) at the receiver. Under \(k\)-MUD, the throughput scales almost linearly with \(k\) until saturation (for Poisson arrival processes), increasing significantly the capacity of the system. Nevertheless, it has long been noted that traffic of communications networks is statistically long-range dependent and heavy-tailed, and these properties cannot be overlooked in their performance studies (see [36] and references therein). For instance, in massive random access or in mMTC, network traffic at the packet level is a superposition of numerous individual data flows between pairs of hosts, possibly correlated. A high variance in the on and off periods in these individual streams can physically induce LRD in the aggregated traffic, which can be mathematically modeled with heavy-tailed distributions. Further, though CSA has been extensively analyzed in the literature under the throughput-stability trade-off, these works assume a Poisson point process for the packet arrivals for mathematical tractability, so their results and insights are limited to an idealized traffic model. For this reason, in this work, we study the impact of the correlation and the marginal distribution of the load process on the performance of the system. On the one hand, we model the arrival process with a version of the M/G/\(\infty\) process able to exhibit a correlation structure decaying slowly in time. Given the independence among frames in FS-CSA, this variation should only take effect on FA-CSA. On the other hand, we vary the marginal distribution of the arrival process using discrete versions of the Lognormal and the Pareto distributions, with the objective of investigating the influence of the right tail. In this case, both techniques should be affected by the change. Results obtained confirm these hypotheses. The remainder of the paper is organized as follows. In Section 2, we review the operations of frame-synchronous and frame-asynchronous slotted ALOHA multiple access protocols. The different arrival processes considered in this work are introduced in Section 3. The performance evaluation and numerical results are presented in Section 4, and finally some concluding remarks are summarized in Section 5.