# An Insight to the Outage Performance of Multi-Hop Mixed RF/FSO/IWOC System
## 5 Numerical Results  
For the proposed model, the numerical results are plotted for the outage probability at low- and high-SNR regimes for fresh water and salty water in the presence of air bubbles and temperature gradient. We are considering the intensity modulation and direct deduction technique; thus, \(r=2\). The threshold SNR (\(\gamma_{th}\)) is set at 5 dB. The FSO link parameters such as atmospheric attenuation, \(h_{l}=0.9\), length of the turbulent FSO link, \(d_{FSO}=1\) km, beam radius of the turbulent link, \(w_{d_{1}}=2.5\) m, the jitter, \(\sigma_{s}=30\) cm, and turbulence parameters, \(\alpha_{f}\) and \(\beta_{f}\), for the FSO link are assumed to be 5.42 and 3.8. Further, the FOV angle of the FSO transceiver at \(R_{2}\) is 7 mrad and the standard deviation of AOA fluctuations is considered to be \(\sigma_{\theta}=7\) mrad. The values of considered UWOC link parameters i.e., bubble levels, temperature gradient, \(w,\lambda,a,b,c\) have been adopted from [33]. Figure 2 presents the outage performance of the proposed system under the influence of the AOA fluctuations. It has been demonstrated that the outage performance of the system is not good for the low values of the AoA. However, the outage performance of the system improves significantly with increase in the AOA, \(\theta_{FOV}\). For example, at SNR = 25 dB and \(\theta_{FOV}=4\) mrad, the \(P_{out}^{DF}\) is equal to \(2.499\times 10^{-3}\), and at SNR = 25 dB and \(\theta_{FOV}=8\) mrad, the \(P_{out}^{DF}\) is equal to \(6.238\times 10^{-8}\). Moreover, it is also noticed that after a certain value of average SNR, the other impairments dominate over AOA fluctuations, and the effect of the AOA fluctuations becomes negligible. Figure 3 shows the outage performance of the proposed system under varying pointing errors assuming moderately turbulent conditions. It is observed from the plots that the outage probability of the considered system decreases as the value of \(\zeta\) increases; hence, the system performance increases as pointing errors, parameter \(\zeta\), increase. It can be said that the system's performance improves with the decreasing impact of the pointing errors in the FSO channel. The pointing errors result from misalignment between the transmitter and receiver or turbulence. Figure 4 presents the outage probability of the system w.r.t. the Nakagami fading factor, \(m\) with varying average SNR (dB) for the salty water type. It is observed that the system shows high values of outage probability at low values of \(m\) (severity is high). The severity decreases as the value of \(m\) increases. Further, it is also observed that after a certain value, i.e., \(m=5\), the outage performance of the system becomes stable as the impact of fading due to the RF link becomes negligible. Further, the impact of the fading in the RF link also reduces with an increase in the average SNR of the system. For example, at \(m=5\), SNR = 5 dB, the outage probability is equal to \(7.401\times 10^{-4}\) and at \(m=5\), SNR = 20 dB, the outage probability is equal to \(3.756\times 10^{-6}\). Figure 3: Outage performance of the system with varying pointing errors. Figure 2: Outage probability variations vs. angle\(-\)of\(-\)arrival fluctuations. The plot in Figure 5 demonstrates the outage probability of the mixed system under the impact of turbulent water conditions in both water types, i.e., fresh water and salty water types. As expected, the outage performance of the system improves with the decrease in temperature gradient and air bubbles. For example, for fresh water with average SNR at 8 dB and bubble level 4.7 L/min, the \(P_{out}^{DF}\) is \(2.8836\times 10^{-6}\), and with bubble level 16.5 L/min, the \(P_{out}^{DF}\) is \(3.4207\times 10^{-4}\). Also, for salty water with average SNR at 8 dB and bubble level 4.7 L/min, the \(P_{out}^{DF}\) is \(2.2815\times 10^{-6}\), and with bubble level 16.5 L/min, the \(P_{out}^{DF}\) is \(2.0146\times 10^{-3}\). Figure 6 shows the outage performance of the system at low-SNR and high-SNR regimes.