## 4 Numerical Results and Discussion
### Small Air Bubble Scenario  
In Figure 3, the average BER of a SISO UOWC system under small air bubbles for different levels of scattering are compared. As can be readily observed, the analytical and asymptotic results show an excellent agreement with Monte Carlo simulation results for all considered cases by validating the accuracy of the exact and asymptotic closed-form expressions in Equations (6) and (12), respectively. Firstly, it is interesting to note that for scenarios with a low antacid concentration, the asymptotic expression approaches Monte Carlo and analytic results even at low SNR faster than higher antacid concentrations. Secondly, as one would expect, the high pathloss due to increased antacid concentration deteriorates the average BER performance compared with the tap water case, as evident in the 3.6 mg/L scenario, which shows a higher average BER than the 0 mg/L scenario. However, the increase in diversity order due to higher water turbidity, as shown in Figure 2, reverses this trend at high SNR regime, especially for more turbid scenarios. While the cases with 3.6 mg/L and 7.3 mg/L of antacid exhibit higher average BER than the 0 mg/L case within the presented SNR range, the scenarios with the highest water turbidity, i.e., 11 mg/L and 14.5 mg/L of antacid concentration, significantly improve the  
Figure 2: Diversity order when considering small air bubbles and large air bubbles for different levels of antacid in the experimental UOWC link. performance of the UOWC system at high SNR under the same population of air bubbles. Thus, antacid-induced scattering mitigates the impact of air bubbles on the performance of UOWC systems. For instance, at 40 dB, the average BER for 14.5 mg/L is \(1.35\times 10^{-1}\), while for 0 mg/L, it is \(1.7\times 10^{-3}\). However, at 70 dB, the average BER for 14.5 mg/L is \(6\times 10^{-6}\), while for 0 mg/L, it is \(1.2\times 10^{-5}\). In practice, when the system is assured of having an SNR greater than 58 dB, the scenario with the highest turbidity will exhibit better performance in terms of average BER compared with the scenario with tap water. To illustrate this point, let us consider the natural optical beam spreading and geometric losses due to scattering. Hence, this effect can offer a great degree of robustness to air bubble-induced scattering and light blocking. These findings are in line with previous simulation and experimental results reported in [12; 22], where the impact of pointing error and scintillation index also decreases as the water gets more turbid, respectively. Therefore, we conclude that this change in trend can be perfectly attributable to an increase in the severity of scattering. However, this interpretation is limited to the 3 m experimental water tank from which fitted channel model parameters have been obtained. The impact of scattering over longer link distances may not be accurately reflected. For shorter distances, the attenuation effect of turbid waters might be less significant than the beam spreading effect, potentially improving BER performance, as mentioned above. Nevertheless, over longer distances, the pathloss calculated from the Beer-Lambert law as \(e^{-cd}\), where \(d\) is the link distance, becomes significantly greater in turbid waters, potentially resulting in higher BER performance. Therefore, beam spreading due to scattering can benefit short-range communication links by mitigating air bubble blockage, but overall performance can degrade over longer link distances due to increased pathloss. The outage probability for small air bubbles is represented in Figure 4. As expected, the Monte Carlo simulation results agree with the analytical and asymptotic expression described in Equations (18) and (19), respectively. Note that the outage probability results reveal similar insights as the average BER into the impact of water turbidity on UOWC system performance.