# Misalignment-Resilient Propagation Model for Underwater Optical Wireless Links +
## 1 Introduction  
Exploration of the sea, either for monitoring and data collection or for industrial exploitation of sea resources, including sea mining, is an important area of application with a potentially strong impact on society, in line with the United Nations Sustainable Development Goals [1]. This interest is essentially motivated by the fact that existing natural resources are becoming increasingly scarce, with it being of paramount importance to guarantee access to and use of marine resources. This is especially relevant to countries with large coastal areas, such as Portugal, which is the 5 th European country and 20 th in the world with the largest exclusive economic zone, detaining a maritime area of more than \(1.7\,\mathrm{mill}\,\mathrm{km}^{2}\)[2]. To effectively achieve this purpose, undersea communications are of paramount importance for different applications, such as the transference of data from the underwater sensors integrated into underwater wireless sensor networks (UWSNs) to autonomous underwater vehicles (AUVs), as represented in Figure 0(a), or the download of large amounts of data from the AUVs to the docking stations, which are collected from the UWSN after a mission, as illustrated in Figure 0(b). In this scenario, underwater optical wireless communication (UOWC) in the blue and green region of wavelengths plays a vital role in pursuing this objective, albeit while supporting relatively short distances, allowing for the development of low-cost, low-latency, high-bandwidth, and high-robustness transmission systems, which find relevant applications [3]. Other concurrent wireless technologies for use underwater are acoustic and radio-frequency communications. The former one, despite providing long-distance transmission, suffers from low bandwidth and signal distortion due to the Doppler effect, and it is also affected by multi-path propagation that leads to inter-symbol interference. The latter is limited in bandwidth due to the scarcely available spectrum and also severely degraded by the attenuation resulting from the high conductivity and permittivity of saline water [3]. Hence, these two technologies fall short of accommodating applications that require high-speed communications. Nevertheless, UOWC is very challenging since optical signals are affected by misalignment [4; 5], ocean turbulence [6; 7] and the absorption existing in the underwater channel, aside from scattering due to the presence of suspended particles, especially in turbid waters [8; 9]. Even though UOWC is the most suitable model for the scenarios depicted in Figure 1, practical systems still need to be improved with increasingly innovative tools and techniques. For example, the UOWC system must be misalignment-tolerant (i.e., a sub-system capable of adjusting the emitter's divergence (to one which the system is most tolerant to the offset) is required to maintain a stable and reliable communication link). In this light, it is imperative to design sophisticated models increasingly capable of simulating a real underwater system. The development of these models is of extreme importance, as they can provide comprehensive knowledge of underwater channel operation,  
Figure 1: (**a**) Underwater wireless energy and communications enabling a long-term deep-sea presence. (**b**) Underwater wireless data transfer from the AUV to the docking station. namely photon propagation in different water types, the effect of misalignment caused by water turbulence or the difficulty of maintaining the position of the transmitter or receiver, allowing one to obtain relevant guidelines such as the ideal link geometry and divergence of the emitter, contributing actively with valuable insights to the practical implementation of these systems. To simulate the underwater channel, simple models generally do not capture the full underlying phenomena, such as the Beer-Lambert law, and hence they are not accurate, as they may not account for the real detected power.