# Performance Analysis of Dual-Hop Hybrid RF-UOWC NOMA Systems
## 6 Results and Discussion  
In this section, we provide a detailed discussion on the derived metrics of the proposed system under varying conditions of air bubbles for both fresh/salty and thermally uniform waters under heterodyne or IM/DD detection techniques to gain more insight and highlight some conclusions. The correctness of the obtained analysis is verified via a Monte-Carlo simulation with \(10^{6}\) samples. Throughout this section, we used the distribution parameters provided in Tables 1 and 2. Unless otherwise mentioned, the system parameters are set to \(a_{1}=b_{1}=0.7\), \(\eta=0.1\), \(R_{1}=0.5\) bits/sec/Hz, and \(R_{2}=0.75\) bits/sec/Hz; \(d=0.8\) is the normalized distance with respect to the cell radius, and \(v=2\), \(\rho_{s}=\rho_{R}=\rho\), and \(\Omega_{x}=1\). In the following, we denote \"Ana\" as the analytical result, \"Asym\" as an asymptotic result, and \"Sim\" as Monte-Carlo simulation results. Figure 2 presents the outage probability for the proposed system under uniform temperature salty water for both IM/DD and heterodyne techniques. As expected, it can be deduced that the OPs significantly improve when heterodyne detection is implemented compared to IM/DD. This result is due to the ability of the heterodyne receiver to overcome the UOWC link's turbulence effects, while this leads to a more complex receiver compared to IM/DD receiver. For example, the \(OP_{sys}\) of \(10^{-2}\) is achieved at \(\rho=37\) dB under the heterodyne receiver and \(\rho=46\) dB using the IM/DD receiver. It is remarkable that the analytical and the simulation results are a match, which validates our analytical derivations. Additionally, they match the asymptotic curves at high SNR regime. In addition, to validate the \(DO\) derived in Section 3.5, we can observe that for heterodyne detection \(r=1\), the \(OP_{sys}=0.0004747\) at \(\rho=50\) dB and \(OP_{sys}=0.00004747\) at \(\rho=60\) dB; therefore, the \(OP_{sys}\) falls with a slope of \(\log(0.0004747)-\log(0.00004747)=1\). Following the same procedure for IM/DD, we can observe that the \(OP_{sys}=0.006119\) at \(\rho=50\) dB while \(OP_{sys}=0.001835\) at \(\rho=60\) dB, so the \(OP_{sys}\) falls with a slope of \(\log(0.006119)-\log(0.001835)\approx 0.5\). These results are consistent with the diversity order \(DO_{l}\). Figure 3 depicts the OPs for the proposed system under uniform temperature salty water with varying air bubbles levels \(BL=2.4\) and \(BL=4.7\) L/min. It is clear that the increase in the level of air bubbles leads to a degradation in the OPs performance. This is due to the rise of the water turbulence. To evaluate the performance of the proposed system in this work, we compared its performance with a benchmark scheme: the OMA-based dual-hop hybrid RF-UOWC system. Figure 3 provides the comparison between the proposed NOMA-based system versus the OMA-based system under the same system settings. According to the figure, the proposed system outperforms the benchmark in terms of OPs performance. This is due to the fact that the NOMA technique is more spectral efficient than the OMA technique. Figure 3: OPs versus SNR for thermally uniform UOWC links for varying air bubbles levels applicable to NOMA and OMA based systems. Figure 4 illustrates the influence of the residual power factor of imperfect SIC on OPs performance of the proposed system under uniform thermally salty water at \(BL=2.4\) L/min utilizing three varying levels of \(\eta=0,\ 0.1,\ 0.2\). We can see that the OPs performance degrades by increasing \(\eta\) while the best performance is achieved with the perfect SIC scenario (\(\eta=0\)). This is due to the fact that an increase in \(\eta\) leads to a higher interference level, hence the SINRs \(\gamma_{R}^{2}\) and \(\gamma_{\rm D2}^{2}\) decrease while decoding the near user message. However, the SINRs \(\gamma_{R^{\prime}}^{1}\), \(\gamma_{\rm D1}^{1}\), and \(\gamma_{\rm D2}^{1}\) are not affected by changing \(\eta\).