###### Abstract
In [21], closed-form expressions for the ergodic capacity and the BER were obtained over a composite channel model which considers the bubble-obstruction and turbulence effect. However, the proposed statistical model is purely mathematical and numerically obtained by using statistics of the generation, size, and horizontal movement of air bubbles. Unlike empirical measurements-based channel models which consider the complicated nature of real underwater environments, statistical channel models derived from theoretical simulations often require simplifying and assuming specific channel parameters. This can result in significant discrepancies between the simulated results and the actual behavior of underwater environments. Furthermore, it should be noted that the aforementioned works neglect the dispersive nature of the water, by ignoring different types of water in the performance analysis. Recently, novel research has proposed a statistical UOWC channel model based on experimental measurements that considers the combined effect of the scintillation and obstruction of light due to air bubbles and the water turbidity [22]. Then, small air bubble-induced fluctuations are described by a generalized Gamma distribution, and large air bubble-induced fluctuations and light blockage are described by a mixture of two generalized Gamma distributions. Channel measurements suggest that the scattering effect reduces both the scintillation effect and the obstruction of light caused by air bubbles, by inducing a more resilient link at the expense of a higher pathloss value. However, the current research has ignored the scattering phenomenon because it makes use of statistical channel models that are not fitted to realistic underwater environments. In other words, the effectiveness of UOWC systems under air bubbles in turbid waters has not yet been investigated. Therefore, there remains a need for mathematical tools and expressions that can complete the UOWC system performance of submarine links when air bubbles of different sizes perturb the optical wavefront under different types of water. In this paper, we analyze the UOWC system performance in terms of bit error rate (BER) and outage probability over underwater fading channels in the presence of small and large air bubbles and different levels of scattering following the mentioned empirical-based UOWC channel models [22]. Unlike [5; 7; 11], where the estimated PDF and the corresponding channel parameters are fitted when considering a joint effect of thermohaline gradient and air bubbles in tap water, the UOWC system is evaluated under UOWC statistical channel models where fitted PDFs and its parameters are based on measurements with optical power fluctuations due to uniquely from air bubbles of two different sizes and a wide range of in-suspension particle concentrations. Although previous research has derived analytical expressions for BER using a generalized Gamma distribution, it is essential to note that these studies do not address the performance of optical systems under air bubble-induced fading and particle-induced scattering [23; 24; 25]. Furthermore, some of these papers utilize fitted parameters derived from numerical simulation, which do not accurately capture the complexity of the underwater environment. Consequently, their findings may have limitations when applied to optimizing and designing novel UOWC systems in realistic conditions, such as environments with air bubbles in turbid water. This work extends the knowledge of existing UOWC system performance based on empirical UOWC channel models because we analyze the impact of water turbidity, which considers the oceanic pathloss and the beamwidth expansion due to the scattering effect. In particular, we provide exact and asymptotic closed-form expressions for BER and outage probability over air bubble-induced fading channels.