# NOMA or OMA in Delay-QoS Limited Satellite Communications: Effective Capacity Analysis
## 4 Results  
In this section, simulation results are conducted to validate the analytical results derived in the previous section. Without loss of generality, we assume \(T_{f}B=1\), the carrier frequency as \(1.6\,\mathrm{GHz}\), FSL as \(L_{c}=L_{t}=187.6\,\mathrm{dB}\), \(G_{c}=G_{t}=3.5\,\mathrm{dBi}\), and \(G_{max}=52.1\,\mathrm{dBi}\)[7; 8]. We first show the impacts of delay-Qos exponent \(\theta_{c}\) and power allocation factor \(\alpha\) on User \(c\)'s performance when it experiences frequent heavy shadowing (FHS) and average shadowing (AS) in Figures 2 and 3, respectively. From these two figures, we can find that the capacity of User \(c\) begins at zero, as the value of \(\rho\) increases, this capacity first increases, and then converges to a constant, whose value is determined by parameters \(\theta_{c}\) and \(\alpha\), as the results given in (15). In addition, although the convergence is derived by assuming \(\rho\to\infty\) in (15), the effective capacity of User \(c\) saturates when \(\rho\geq 40\,\mathrm{dB}\) and \(\rho\geq 20\,\mathrm{dB}\) in these two fading scenarios. We can also see that either a larger \(\theta_{c}\) or a larger \(\alpha\) can significantly degrade the achievable capacity for User \(c\). While a larger \(\theta_{c}\) means a smaller tolerated delay outage and a lower supported constant arrival rate, a larger \(\alpha\) means a smaller power resource is allocated to User \(c\). Although a lighter shadowing can increase the achieved capacity, it leads to a fast convergence as well. Moreover, we find from these two figures that the superiority of the NOMA scheme for User \(c\) can only be found when \(\rho\) is relatively small, i.e., \(\rho\leq 20\,\mathrm{dB}\) and \(\rho\leq 10\,\mathrm{dB}\) in heavy and average fading cases, respectively. Figure 2: The impacts of \(\theta\) and \(\alpha\) on User \(c\)’s performance, when User \(c\) experiences FHS. Figure 4 and 5 examine the impacts of delay-Qos exponent \(\theta_{t}\) and power allocation factor \(\alpha\) on User \(t\)'s performance when it experiences light shadowing (LS) and AS in Figures 4 and 5, respectively. We observe that the curves of capacity achieved with both NOMA and OMA schemes all increase with the increasing of \(\rho\), which agrees well with the derivations given in (16). Moreover, the larger the value of \(\alpha\), the better the capacity achieved with the NOMA scheme. Contrary to User \(c\), the superiority of the NOMA scheme lies in relatively large \(\rho\), i.e., when \(\rho>7\) dB and \(\rho>10\) dB in light and average fading cases, respectively. Figure 4: The impacts of \(\theta\) and \(\alpha\) on User \(t\)’s performance, when User \(c\) experiences LS. Figure 3: The impacts of \(\theta\) and \(\alpha\) on User \(c\)’s performance, when User \(c\) experiences AS. Finally, Figure 8 illustrates the sum capacity difference between NOMA and OMA versus \(\rho\) for various fading conditions, \(\theta_{c,t}\), \(\alpha\) values, and the label (AS/FHS) is the link fading severity of User \(t\) / User \(c\). As can be observed, analytical results computed by (34) agree well with the Monte Carlo simulations. Moreover, when \(\rho\to 0\), with the \(\alpha\) value rising, it can be observed from Figure 8 that the value of the difference becomes smaller. While when \(\rho\gg 0\), i.e., \(\rho=40\) dB in this figure, for the special case \(\theta_{c}=\theta_{t}\), the sum difference is irrelevant to the power allocation coefficient \(\alpha\) and transmission SNR \(\rho\), which corresponds to our derivation in (34). In addition, a better/worse fading condition of User \(t\) / \(c\), can result in a higher sum capacity difference. However, the sum difference improvement is much more significant when the fading condition of User \(c\) degrades. This observation demonstrates that the NOMA scheme outperforms the OMA scheme when \(\rho\) is sometimes high and users with greater fading disparity should be selected to form a NOMA pair from the perspective of achieved sum capacity.