Received 12 July 2022, accepted 8 August 2022, date of publication 25 August 2022, date of current version 6 September 2022. Digital Object Identifier 10.1109/ACCESS.2022.3201647 New Monte Carlo Integration Models for Underwater Wireless Optical Communication RUQIN XIAO, (Graduate Student Member, IEEE), PIERRE COMBEAU , (Member, IEEE), AND LILIAN AVENEAU XLIM, UMR CNRS 7252, Université de Poitiers, 86000 Poitiers, France Corresponding author: Lilian Aveneau (lilian.aveneau@univ-poitiers.fr) This work was supported by the French Région Nouvelle-Aquitaine through the MACOPT Project under Agreement AAPR2020-2020-8554510. ABSTRACT Underwater wireless optical communications are knowing a high interest in recent years, with many military and civil applications. The design of efficient systems relies on powerful simulation tools. The most used simulation algorithms are based on a paper from 1989, written by Prahl and designed for light propagation through human tissue. This method relies on Monte Carlo Simulation, following the path of a photon in the participating media. As such, it is difficult to propose evolution or optimization. In addition, a large amount of photons are needed to obtain good results with low error, especially for turbid water. With Monte Carlo Integration method, there exist a lot of optimization techniques to reduce the variance. This paper proposes a mathematical formalization of the propagation of light in water or any other participating medium as an integral problem. Therefore, it opens the way for a large number of future optimizations. A very straightforward and simple variance reduction technique is proposed as an example. Our simulation results show that this new technique has a lower sample variance as expected, and thus better convergence rates. INDEX TERMS Communication channels, communication systems, Monte Carlo methods, optical com- munication, optical propagation, optical propagation in absorbing media, optical propagation in dispersive media, simulation, underwater communication, underwater optical communication, underwater optical propagation. I. INTRODUCTION Underwater wireless communications are present in many different applications in both military and civil domains, like submarine communications, fishing industry, ecology, etc. [3]. There are three main technologies for this purpose: acoustic wireless communications for long distances but with high latency and low throughput; wireless radio communica- tions, but with low data rates due to high signal absorption by water; and Underwater Wireless Optical Communications (UWOC), a promising technology with good properties such as high data rates, security due to small propagation range, and large bandwidth. Over the past few decades, much litera- ture has been produced on UWOC, as evidenced by the many The associate editor coordinating the review of this manuscript and approving it for publication was Giambattista Gruosso . recent surveys dealing with applications of UWOC [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12]. The development and characterization of UWOC sys- tems require accurate and fast simulation tools, to test the developed communication protocols on different scenarios. We need to well understand the propagation mechanisms involved in UWOC channels to provide such tools. This kind of channel is characterized by different physical phenomena, inherent to ‘‘participating media’’: light absorption, due to particles that typically absorb and convert the light flux into heat; light scattering, due to particles that deflect the luminous flux in other directions, causing the dispersion of the light. The latter is particularly true for participating media like fog, clouds, and liquids such as good old Cognac or turbid harbor water. Absorption and scattering imply that the UWOC chan- nel can become very difficult to simulate. Previous works VOLUME 10, 2022 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ 91557