## 5 Conclusions  
In this paper, novel closed-form expressions have been developed in order to compute the average BER and outage probability of UOWC systems under empirical underwater channels in the presence of small and large air bubbles when different scattering levels are contemplated. Furthermore, simple asymptotic expressions are also obtained, which allows us to analyze the diversity order of the UOWC system of each scenario. Monte Carlo simulations verify the obtained analytic and asymptotic results.  
For the first time, the proposed system performance contemplates an empirical underwater optical channel model obtained from experimental data, which considers the impact of scattering in terms of pathloss and beam spreading. The considered UOWC measurement-based channel model is able to capture the inherent complexities and variability of absorption, scattering, and power fluctuations due to air bubbles with greater accuracy than theoretical models based on simulations. Hence, the accuracy of the empirical modeling improves the average BER and outage estimation under realistic environments. In particular, our results prove that the relative impact of air bubbles on BER performance  
Figure 5: Average BER performance when considering an empirical UOWC channel in the presence of large air bubble-induced fading under different levels of antacid concentration at a link distance of 3 m and a wavelength of 520 nm.  
Figure 6: Outage performance when considering an empirical UOWC channel in the presence of large air bubble-induced fading under different levels of antacid concentration at a link distance of 3 m and a wavelength of 520 nm.  
becomes less significant as water turbidity increases at short link distances. The reason behind this is that the diversity order highly depends on the scattering effect, increasing for higher antacid concentrations, i.e., more turbid waters. Hence, our performance analysis provides novel insights into the existing UOWC systems in realistic water bodies, since the proposed fading statistical models in [22] consider the air bubble-induced fading and light blockage, as well as the water turbidity and the scattering effect.  
Since the performance analysis of UOWC systems under a realistic oceanic medium is a critical investigation in current UOWC networks, our technical contribution is particularly important to the engineers working on UOWC systems optimization and design. Moreover, the use of experimental channel models allows for the validation and adjustment of theoretical models, thereby improving their robustness and practical applicability. Some interesting extensions of our work, including the performance evaluation of more sophisticated schemes such as coherent modulation for UOWC systems, as well as Multiple-Input/Multiple-Output (MIMO) UOWC systems, will be considered as the subject of our future research. Furthermore, the presented UOWC channel performance could be enhanced by exploring the impact of scattering and attenuation over extended link distances to provide a more comprehensive understanding of UOWC system performance.  
Conceptualization, methodology, and formal analysis, [PERSON], [PERSON], [PERSON] and [PERSON]; writing--original draft preparation, [PERSON]-[PERSON]; writing--review and editing, [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON]; supervision, [PERSON]-[PERSON], [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON]; project administration and funding acquisition, [PERSON], [PERSON] and [PERSON]-Z. All authors have read and agreed to the published version of the manuscript.  
This work was funded in part by the Universidad de Malaga; in part by the Spanish Ministerio de Ciencia, Innovacion y Universidades under Grant FPU22/02183; and in part by the Plan Andaluz de Investigacion, Desarrollo e Innovacion (PAIDI) 2021, under Grant P21_00390.  
Not applicable.  
Data Availability Statement: Data will be made available on request.  
The authors declare no conflicts of interest.