# Covert Communications in Active-RIS-Aided NOMA Systems: Element Grouping or Not?
## 4 Simulation Results
In Figure 3, the impacts of the ARIS's location on the covert communication rate and Carol's achievable rate were investigated, where we set \(p_{a}^{\max}=p_{c}^{\max}=35\) dBm, \(p_{r}^{\max}=30\) dBm, \(M=4\), \(N=16\), and \(\epsilon=0.1\). Figure 2(a) shows the covert communication rate versus the ARIS's horizontal position under different ARIS schemes, including the considered w-EG and w/o-EG schemes, where the vertical position of ARIS was fixed at 45 m. It shows that the covert communication rates achieved by the ARIS-aided NOMA system increased with the increasing horizontal position, until reaching about 45 m when they began to decrease, which indicated that when the ARIS was properly deployed close to [PERSON] and the users, the highest covert communication rate could be achieved. Furthermore, Figure 2(a) reveals that the covert communication performance of the w/o-EG scheme outperformed that of the w-EG scheme in an ARIS-aided NOMA system. On the contrary, the covert communication rates achieved by the randomized \(\mathbf{\Theta}\) and \(\{\mathbf{\Theta},\mathbf{W}\}\) changed slightly with the increase in the horizontal position of the ARIS, whereas the achieved covert communication rates were far less than those achieved by the w-EG and w/o-EG schemes. Also, a higher \(\eta^{2}\) rendered a higher covert rate for the proposed schemes. Furthermore, Figure 2(b) presents the results of [PERSON]'s achievable rate versus the ARIS's horizontal position for the considered ARIS schemes. The curves in Figure 2(b) show that the w/o-EG scheme obtained [PERSON]'s highest achievable rate. Similarly to the covert communication rate, the location of the ARIS also affected [PERSON]'s achievable rate. [PERSON]'s highest achievable rate was obtained with a horizontal position of 45 m, which was the same position at which the maximum covert communication rate was obtained. The covertness level \(\epsilon\) versus the covert communication rate and [PERSON]'s achievable rate for different schemes were investigated in Figure 4, where we set \(p_{a}^{\max}=P_{c}^{\max}=35\) dBm, \(P_{r}^{\max}=30\) dBm, \(M=4\), and \(N=16\). As clearly shown by the curves in Figure 3(a), the covert communication rates achieved by all the considered schemes increased with the increasing \(\epsilon\). This result is consistent with the theoretical analysis, i.e., when \(\epsilon\) becomes larger, the covertness constraint becomes loose, and the allocatable transmit power for Alice and the reflection beamforming power towards the BS increase, which leads to a higher covert communication rate for the ARIS-aided NOMA system. The covert communication rate achieved in the ARIS-aided NOMA system increased dramatically at first from \(\epsilon=0.01\) to \(\epsilon=0.05\), and then increased smoothly with the continued increase in \(\epsilon\). Moreover, the AO algorithm without employing element grouping achieved a higher covert communication rate than the AO algorithm with element grouping, while the achieved covert communication rate for the randomized \(\{\mathbf{\Theta},\mathbf{W}\}\) was lower than that of the randomized \(\mathbf{\Theta}\). In Figure 3(b), the curves of [PERSON]'s achievable rate are plotted. The curves in Figure  
increased from 0.01 to 0.05, the achievable rate had a significant increase. After \(\epsilon\) surpassed 0.05, [PERSON]'s achievable rate increased slowly, having a trend similar to that of the covert communication rate in Figure 4a. The curves in Figure 5 compare the covert communication rate and [PERSON]'s achievable rate versus the number of ARIS elements \(N\). In Figure 5, we set \(P_{a}^{\text{max}}=P_{c}^{\text{max}}=35\) dBm, \(P_{r}^{\text{max}}=~{}30\) dBm, \(M=4\), and \(\epsilon=0.1\). For the ARIS-aided NOMA system with the w/o-EG scheme, it is obvious that more reflecting elements of the ARIS provide a larger reflection beamforming gain and achieve a higher covert communication rate due to the exploitation of more DoFs to manipulate the propagation environments.