# Spectrum Slicing for Multiple Access Channels with Heterogeneous Services
## 5 Non-Orthogonal Multiple Access
### Latency-Oriented System
In this case, the grouping scheme used \(G=2\), whereas the ALOHA and TDMA cases had the expected \(G=1\) and \(G=4\), respectively. When \(\alpha\) is very low, the inter-arrival time dominates the PAoI and the impact of the choice of access schemes is negligible. As Figure 5 shows, this is true even for a total arrival rate of \(U_{I}\alpha=0.01\), which corresponds to an average of one packet every 400 slots from each source: as the arrival process is exponentially distributed, the 90 th percentile of the inter-arrival time is 920 slots, and it is impossible to achieve a lower \(\Delta_{90}\). In cases with a higher arrival rate, OMA TDMA seems to be the best system, although NOMA ALOHA can achieve a similar performance when PAoI is more important than the broadband user throughput. Besides the achievable performance trade-offs, it is also important to observe the parameter settings that achieve Pareto efficiency, as shown in \[\mathcal{G}_{\ell}^{(n)}=\{0,\ldots,G-n\}\times\{0,\ldots,G\}^{\ell-1}. \tag{63}\]0 The difference between the optimal values of \(T_{\text{int}}\) in OMA for the three considered schemes is stark, as shown in Figure 6a. This is because collisions are the main factor driving up the age in OMA, making the age for TDMA far lower. The other factor in the age is the waiting time due to the grouping: while TDMA compensates for this by avoiding collisions entirely, the grouping scheme with \(G=2\) is the worst of both worlds, getting extremely poor performance due to having both a longer interval between allocated slots and the risk of collisions. Therefore, in age-oriented systems where the arrival rate \(\alpha\) for each intermittent user needs to be relatively high to achieve the desired AoI, orthogonal slicing among all users (broadband and intermittent) is a good choice, as the alternative will result in a high collision probability. Collisions are not so common in TDMA, as the transmissions for the intermittent users can be spread out over all slots, and are not concentrated in some reserved ones. In this case, the specific method used is not very important, as Figure 6b shows: the three schemes have a similar age with very similar coding rates. However, NOMA cannot significantly outperform OMA TDMA, as allowing collisions with the broadband user limits the achievable throughput. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Setting** \\ \hline Source block size for broadband user & \(K\) & \(\{1,2,\ldots,64\}\) \\ Coded block size & \(N\) & \(\geq K\) \\ Erasure probability for the broadband user & \(\varepsilon_{B}\) & \(0.1\) \\ Erasure probability for intermittent users & \(\varepsilon_{I}\) & \(0.05\) \\ Total intermittent arrival rate [packets per slot] & \(U_{I}\alpha\) & \(\{0.01,0.02,0.05,0.1\}\) \\ Number of intermittent users & \(U_{I}\) & \(\{4,10,100\}\) \\ OMA: Period between intermittent slots & \(T_{\text{int}}\) & \(\{1,2,\ldots,64\}\) \\ Maximum queue length & \(Q\) & \(\{1,4\}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: System parameters. Next, we consider the latency-oriented systems where the 90 th percentile of latency-reliability \(T_{90}\) is the main KPI for intermittent users. For these, we focus on illustrating the impact of the arrival rate \(U_{I}\alpha\) and the number of intermittent users \(U_{I}\). Figures 7-9 show the Pareto frontiers for the cases with \(U_{I}=4\), \(U_{I}=10\), and \(U_{I}=100\), respectively. Each of the figures includes the latency and throughput trade-offs for \(U_{I}\alpha\in\{0.01,0.02,0.05,0.1\}\). For the case with \(U_{I}=4\), we see an interesting phenomenon in Figure 7a,b: if the arrival rate is low, OMA ALOHA is the optimal choice if the main KPI is the latency-reliability. However, it is not able to achieve a high broadband user throughput \(S_{B}\). Conversely, NOMA, either with ALOHA or grouped access among the intermittent users, can achieve the greatest throughput \(S_{B}\simeq 0.8\). In addition, NOMA ALOHA achieves the lowest latency-reliability with \(S_{B}>0\).