## 5 Results  
This section is concerned with the ABER performance investigation of the proposed expressions provided in (21) and (25) for the cooperative AF-based dual-hop TU-FSO system. Most of the figures (Figures 3-6) presented here offer the same information particularized for the concrete coding technique under analysis. Thus, in solid lines, the performance of the system when only oceanic turbulence is considered is represented; whereas the dashed, dashed-dotted, dotted or the line with a '\(+\)' marker show the behavior of the system when including both oceanic and atmospheric turbulences. The corresponding Monte Carlo simulation results are displayed as circles. For all these cases and considering the approach employed in (12), we can assume that \(\gamma_{0}\) can be seen merely as an SNR since ISI is included as an additional variance term previously averaged over oceanic turbulence. Regarding oceanic turbulence and for the sake of clarity, we offer a correspondence between specific salinity-induced turbulence magnitudes, \(\sigma_{h_{2}}^{2}\), employed in Figures 3-6, and their associated underwater distance lengths. To this aim, we use a simple analytic approximation for the scintillation index proposed in Appendix A in [58], which is provided by the following. \[\sigma_{h_{2}}^{2}\simeq\lambda_{1}d^{2}+\lambda_{2}d+\lambda_{3},\qquad\quad d \leq 100\;\mathrm{m}. \tag{26}\]  
In (26), the scintillation index parameters \(\lambda_{1}\), \(\lambda_{2}\) and \(\lambda_{3}\) were obtained after the curve-fitting approach. For the case of both plane wave and mostly salinity-induced turbulence, we can establish \(\lambda_{1}=0.000536\), \(\lambda_{2}=0.00507\) and \(\lambda_{3}-0.013\), as summarized in Table 3 in [58]. Then, and for the values of \(\sigma_{h_{2}}^{2}\) considered in Figures 3-6 (0.0496, 0.2453 and 1.0652), we can obtain their associated underwater optical wireless communication link distances: \(d=7.07\), \(17.73\) and \(40.37\) m, respectively. Namely, this fact means that, when the distance is \(7.07\) m, the scintillation index reaches a value of \(0.0496\); but the longer the distance, the stronger the intensity of turbulence and, for example, when \(d=40.37\) m, \(\sigma_{h_{2}}^{2}=1.0652\). Nevertheless, these values of distance are obtained by assuming perfect transmitter-receiver alignment. In this respect, the total underwater fading coefficient is defined as two factors: \(h=L\cdot h_{2}\), with \(L\) being the oceanic path loss, whereas \(h_{2}\) denotes salinity-induced oceanic turbulence. Without a loss of generality and as commented in Section 2, our results, displayed in Figures 3-6, did not consider the effects of absorption in water (nor the effect of weather-induced attenuation in the FSO link). Since oceanic absorption can be included as a pure loss term acting as a scaling factor, we offer an estimation to update the results, including \(L\) (geometric spread effect will not be considered). Thus, following the BeerLambert law as the classical exponential attenuation model, the intensity loss at a distance \(d\) is given by the following [58]:  
\[L=\exp{(-Fc_{T}d)}, \tag{27}\]  
where \(c_{T}\) is the extinction coefficient, including absorption and scattering effects. On the other hand, \(F\) denotes the increase in received power due to scattering. The values for \(c_{T}\) are provided in Table 1 in [58] for both clear ocean water and coastal water. If we suppose \(F=1\), then, in that case, for the aforementioned distance values of \(d=7.07\), \(17.73\) and \(40.37\) m, intensity loss equates to \(L=0.3438\), \(0.0688\) and \(0.0023\) (\(-9.27\) dB, \(-23.25\) dB and \(-52.94\) dB), respectively, when clear ocean water is considered. Whilst for coastal water, \(L=5.997\times 10^{-2}\), \(8.6175\times 10^{-4}\) and \(1.052\times 10^{-7}\), again for \(d=7.07\), \(17.73\) and \(40.37\) m, respectively. The penalties in dBs, in this latter scenario, are as follows: \(L=-24.44\), \(-61.29\) and \(-139.55\) dBs, respectively.