Modeling and Performance Analysis of Uplink Laser Transmission Across Sea Surfaces: A Channel Characterization Study  
[PERSON] College of Marine Technology, Faculty of Information Science and Engineering, Ocean University of China, Qingdao 266100, China; [EMAIL_ADDRESS] (H.G. ); [EMAIL_ADDRESS] (R.Y. ); [EMAIL_ADDRESS] (L.H. ); [EMAIL_ADDRESS]. surface model can considerably improve the design and functionality of ocean engineering and remote sensing applications [1; 3; 4; 5; 6; 8; 9; 10; 11]. This improvement is crucial for ensuring the reliability and efficiency of these systems, especially water-air laser transmission systems, in complex marine environments. Initially, the sea surface model was simplified to assume a flat and static sea surface to streamline the setup of laser transmission links between underwater and satellite terminals and to facilitate power budget calculations [11; 12]. However, a series of controlled laboratory tank experiments has clearly shown that alterations in the water surface and its slopes considerably influence the performance of laser transmission [4; 5; 6; 10; 13; 14; 15]. Even minor wave slope changes can deflect the laser beam, causing fluctuations in the received optical power, particularly in uplink transmissions [10]. In practical laser transmission systems, the varying sea-air interface can randomly alter the laser trajectory, intermittently disrupting the transmission channel. This variability compromises the reliability of the channel and causes the connection to switch intermittently between active and inactive states [13; 14; 15]. Hence, the sea surface model must accurately reflect the dynamic and temporal variations in surface slope and topography to improve the accuracy and performance of channel simulations. Currently, the most widely used sea surface model is the Cox-Munk empirical model [16], which is used to simulate the statistical properties of ocean surface slopes for optical calculations [17; 18; 19; 20; 21; 22; 23]. Although this model accurately represents wave slopes across the full range of spatial scales, it overlooks the temporal and spatial dynamics of sea surface topographies, failing to display variations in received power [11; 24]. In contrast, the wave spectrum-based model can effectively integrate the spatiotemporal characteristics of the sea surface topography and its slopes. To date, various wave spectral models have been utilized in cross-media laser transmission studies. For example, [PERSON] et al. [2], employing the Neumann spectrum, explored the dynamic interaction between underwater nodes and wave action, focusing on alignment deviations. [PERSON] et al. [11] studied the influence of wind-driven waves through the Elfouhaily spectrum and bubbles on WOC systems under varying sea conditions. [PERSON] et al. [14] employed Pierson-Moskowitz and JONSWAP (Joint North Sea Wave Project) spectra to assess the slope of water surfaces and refraction angles under varying environmental conditions. Similarly, [PERSON] et al. [25] examined the optical field distribution of an upward-transmitted laser across the water-air interface via the Pierson-Moskowitz spectrum. These studies underscore the utility of wave spectral models in enhancing the knowledge of laser interactions with complex oceanic surfaces. However, these methods are limited to examining one or two specific models without a performance assessment in simulating the optical properties of sea surfaces. Selecting an optimal spectrum according to the experimental objectives remains an important prerequisite, especially in comparison with the classical statistical model. In this study, the uplink process of laser transmission from seawater to air channels is modeled based on the ray tracing technique and Monte Carlo simulation. To simulate sea surfaces efficiently, this study first evaluates the spectral characteristics of six typical wave spectra.