Underwater Visible Light Communication: Recent Advancements and Channel Modeling PDF

Optical and Quantum Electronics (2024) 56:1617 https://doi.org/10.1007/s11082-024-07426-z Underwater visible light communication: recent advancements and channel modeling Abdelrahman Elfikky1 · Ayman I. Boghdady2 · Sajid Mumtaz3 · Ebrahim E. Elsayed4 · Mehtab Singh5 · Somia A. Abd El‑Mottaleb6 · Syed Agha Hassnain Mohsan7 · Moustafa H. Aly2 Received: 29 May 2024 / Accepted: 3 September 2024 © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024 Abstract Underwater Visible Light Communication (UVLC) is a promising technology for high- speed data transmission in aquatic environments. However, the performance and reliability of UVLC systems are often challenged by factors such as absorption, scattering, and oce- anic turbulence. In this paper, we explore various UVLC modulation techniques, analyz- ing both Single Carrier Modulation and Multi-Carrier Modulation schemes, including their respective advantages and limitations. Through simulations and experimental evaluations, we investigate the effectiveness of modulation strategies such as Non-Return-to-Zero On- Off Keying, Pulse Position Modulation, and Quadrature Amplitude Modulation-Carrierless Amplitude Phase Modulation in addressing the inherent challenges of UVLC. Addition- ally, we examine advanced techniques like Orthogonal Frequency Division Multiplexing and space-domain index modulation, highlighting their potential to achieve higher data rates and improved reliability in UVLC systems. Our findings underscore the importance of selecting optimal modulation schemes to enhance spectral efficiency, reduce interfer- ence, and improve Bit Error Rate performance. Recent experimental advancements have showcased remarkable achievements, such as data rates exceeding 30 Gbps over distances up to 21 m, demonstrating significant progress in system reliability and transmission qual- ity. This paper also identifies potential challenges and open research directions in UVLC, such as the need for efficient channel estimation and system configuration algorithms, con- tributing to the design and optimization of robust and scalable underwater communication systems. Keywords Underwater visible light communication (UVLC) · Monte Carlo ray-tracing (MCRT) · Underwater wireless optical communication (UWOC) · Channel modeling · Bit error rate (BER) Extended author information available on the last page of the article Vol.:(0123456789) 1617 Page 2 of 45 A. Elfikky et al. 1 Introduction Underwater wireless optical communication (UWOC) technology has gained prominence due to its crucial role in marine resource exploration and utilization (Zhu et al. 2020). The need for efficient wireless communication among underwater devices has become evident(Shin et al. 2023), leading to applications in various domains such as the military, industry, and scientific research communities (Ghonim et al. 2021). These applications serve various purposes, such as tactical surveillance (Cayirci et al. 2006), monitoring envi- ronmental (Kaidarova et al. Sep 2023), controlling and maintaining oil-related activities, conducting offshore explorations, tracking climate changes, and advancing oceanography research (Aguzzi et al. 2020). Optical communication holds the potential to play a pivotal role across various under- water domains, as depicted in Fig. 1. Its envisioned capabilities include facilitating effi- cient data transfer, supporting underwater research endeavors, and aiding in the potential management of underwater resources (Aman et al. 2023). In the subsea oil and gas sector, ensuring real-time data transmission is imperative for the vigilant monitoring of equipment and infrastructure (Tabella et al. 2021). Consequently, Underwater Visible Light Commu- nication (UVLC) can be employed for communication in offshore oil and gas operations, facilitating the monitoring and control of underwater equipment, pipelines, and sensors to enhance the efficiency of exploration and production activities. By facilitating communica- tion among underwater research equipment, Autonomous Underwater Vehicles (AUVs), and research vessels, UVLC could play a vital role in empowering researchers in marine science and oceanography (Yang et al. 2022). Additionally, it has the potential to enable the transmission of data from underwater sensors (Palitharathna et al. 2021), proving essential Fig. 1 Integrated UVLC connectivity: exploring diversed applications in underwater environments (Ali et al. 2020) Underwater visible light communication: recent advancements… Page 3 of 45 1617 for effective data collection during marine research expeditions (Ardyna et al. 2019), help- ing in long-term environmental monitoring (Chai et al. 2020) and research (Eldeeb et al. 2023). Over the last decade, significant advancements have been achieved in the field of aquatic environmental monitoring through the utilization of AUVs or robots (Hoeher et al. 2021). This underscores the significance of UVLC in facilitating communication between under- water robots or Remotely Operated Vehicles (ROVs) and a base station (Gupta et al. 2019). This capability is particularly crucial for tasks such as underwater exploration, pipeline inspection, or archaeological surveys (Mai et al. 2016). The utilization of UVLC has the potential to enhance communication between underwater vehicles or divers, improving navigation (Zhang et al. 2023)and coordination in exploration missions or search and res- cue operations (Lyu et al. 2023). In aquaculture systems, UVLC proves useful for transmit- ting information about water quality (Saba et al. 2019), feeding schedules, and the health of aquatic organisms, contributing to the maintenance of optimal conditions. Moreover, UVLC can be seamlessly integrated into the internet of underwater things (IoUT) networks (Xu et al. 2019; Mary et al. 2021; Mohsan et al. 2023), enabling communication among various submerged devices like sensors (Huy et al. 2023), cameras, and monitoring equip- ment for diverse applications. In military and defense applications, Ultraviolet (UV) Light Communication stands out as a more secure option compared to Radio Frequency (RF) communication, being less susceptible to interception. UVLC technology proves versatile and finding application in communication between underwater sensors and surveillance devices. This facilitates cru- cial real-time data transmission, offering invaluable intelligence for naval operations (Huy et al. 2023). Moreover, UVLC enhances communication between naval vessels (Paull et al. 2014) and Unmanned Underwater Vehicles (UUVs) or underwater drones. These autono- mous drones contribute significantly to tasks such as hull inspections (Hover et al. 2012), reconnaissance, offensive operations, mine detection, and various other underwater mis- sions. In parallel, ROVs have played a historic role in military deployments, particularly in diverse rescue and recovery missions involving torpedoes, mines, and weapons. Their util- ity extends to security scanning of ports, identification of anomaly objects, and active par- ticipation in underwater criminal investigations. ROVs also proved effective in counteract- ing contraband by scanning ship hulls for concealed smuggling products, thus reducing the dependence on deploying soldier divers. This collective use of UVLC and ROVs in mili- tary applications underscores their critical roles in ensuring secure and efficient maritime operations. The increasing significance of maritime security highlights the need for robust underwater threat detection, safeguarding critical national infrastructure, ports, waterfront facilities, and private vessels (Dunbabin et al. 2009). Real-time detection of underwater intruders and AUVs at extended ranges is imperative, providing security personnel with essential response time. Simultaneously, ROVs are enhancing their capabilities, excelling in tracking (Kumar and Mondal 2021) and imaging tasks (Yan et al. 2023; Peng and Cos- man 2017). UVLC is an emerging technology that utilizes the visible range of the electromagnetic spectrum (370−780 nm) for data transmission (Ali et al. 2022). Understanding the charac- teristics of the underwater optical channel is essential for designing effective and reliable UVLC systems. This involves comprehensive characterization and statistical modeling of the channel, considering factors such as attenuation, scattering, and absorption of light in water (Mahmoud et al. 2021). UVLC offers higher data rates compared to RF communica- tion, making it well-suited for applications that require rapid data transmission, as seen in Fig. 1. It is less susceptible to interference from other underwater noise sources, providing 1617 Page 4 of 45 A. Elfikky et al. a more reliable communication channel. UVLC enhances security by being less vulner- able to eavesdropping compared to RF signals, which can be intercepted. UVLC systems are often more power-efficient, making them ideal for battery-powered devices and remote systems (Mahmoodi and Uysal 2022). As depicted in Fig 1, the application of UVLC ena- bles various underwater entities such as submarines, AUVs, ROVs, divers, and ships to establish communication links with each other. This technology enhances the connectivity and communication capabilities within the underwater domain, facilitating data exchange and coordination among these diverse underwater assets. In Kong et al. (2022), real-time underwater video surveillance using UWOC enabled high-quality video transmission across difficult channels, including those affected by bubble-induced turbulence and ocean water. Monitoring was effectively conducted at distances of 46 m and 5 m. In Kong et al. (2022), authors developed continuous underwater environmental monitoring using optical wireless sensor networks. The system provides real-time data on temperature, salinity, and conductivity in aquatic environments. Accurate modeling of the underwater channel can help in optimizing the design of UVLC systems (El-Fikky et al. Oct 2019), including the choice of appropriate modulation and coding schemes (Singh et al. 2023), receiver archi- tectures, and power management strategies. It can also aid in the development of efficient and reliable communication protocols and algorithms for UVLC networks (Ali et al. 2021). 1.1 Motivation and contribution The motivation behind conducting this survey on UVLC systems from the increasing importance of efficient and secure communication in underwater environments. Traditional communication methods face limitations, especially in underwater scenarios, and UVLC holds the promise of addressing these challenges. The need for a comprehensive under- standing of UVLC, including recent experimental achievements and dynamic channel modeling, is driven by the potentially transformative impact this technology can have in various fields such as marine exploration, defense applications, and maritime security. This paper makes a significant contribution by delving into the complete communica- tion system of UVLC, thoroughly examining both the transmitter and receiver aspects, and extending to encompass detailed channel modeling. By focusing on these integral com- ponents, the survey consolidates existing knowledge, providing a nuanced understanding of UVLC’s capabilities and limitations. The comprehensive exploration of the underwater optical channel, UVLC components, and channel modeling techniques consolidates exist- ing knowledge in the field. By presenting recent experimental results, including data rates, transmission distances, and BER values, the paper offers insights into the practical feasibil- ity of UVLC. Moreover, the discussion of challenges and potential applications in UVLC aims to guide future research directions, fostering advancements in secure and efficient underwater communication. Overall, the survey provides valuable insights that can con- tribute to the further development and application of UVLC technology. 1.2 Outline The rest of this study is structured as follows. In Sect. 2, we delve into the underwater optical channel, providing a comprehensive discussion covering UVLC absorption, UVLC scattering, optical water types, and oceanic turbulence. Moving to Sect. 3, we present an in-depth examination of UVLC components, encompassing the transmitter, receiver, and modulation techniques such as non-return-to-zero on-off-keying (NRZ-OOK) and Pulse Underwater visible light communication: recent advancements… Page 5 of 45 1617 Modulation (PM). Section 4 brings attention to channel modeling techniques, including the Beer–Lambert law, Radiative Transfer Equation (RTE), Analytical RTE, Numerical RTE, and Monte Carlo (MC) simulation. Section 5 is dedicated to showcasing recent experi- mental results, presenting data rates, transmission distances, and BER values. Finally, in Sect. 6, we engage in a discourse on the challenges and potential applications of UVLC, with the overarching goal of providing insights to guide future research directions. In order to facilitate understanding of the abbreviations and acronyms used throughout this paper, a comprehensive list of these terms is provided in Table 1. 2 Underwater wireless optical channel Conventional underwater communication technologies consist of underwater acoustic communication, underwater RF communication, and UWOC. Acoustic communication, functioning within the lower frequency range of KHz, stands out for its remarkable abil- ity to cover extensive distances in underwater environments. This makes it particularly well-suited for certain applications, where long-range communication is dominant, such as deep-sea exploration. However, this advantage comes at the cost of higher latency and comparatively lower data rates, typically in the Kbps range (Sun et al. 2020). Furthermore, acoustic wave systems can consume power in the tens of watts, while RF power consump- tion varies depending on distance, ranging from milliwatts to hundreds of watts (Schir- ripa et al. 2020). RF communication relies on electromagnetic (EM) waves as the carrier, operating within a broad bandwidth spanning from 3 kHz to 300 GHz. This expansive fre- quency range allows for versatile applications, but when it comes to underwater commu- nication, certain challenges arise. EM waves, while adept at penetrating through various substances and covering substantial distances in air, face hurdles in aquatic environments (Palmeiro et al. 2011). In seawater, the characteristics of EM waves present notable limita- tions. The electrical conductivity and permittivity of water contribute to a phenomenon where EM waves rapidly attenuate as the frequency increases (Sun et al. 2020). This atten- uation occurs exponentially, posing a significant challenge for maintaining reliable com- munication over extended distances in underwater scenarios (Jimenez et al. 2016). The sus- ceptibility to EM interference further complicates the use of RF communication in aquatic environments. With moderate data rates in the Mbps range, RF communication finds its specialized area in applications, where a balance between communication speed and cov- erage distance is essential. This makes it suitable for tasks like underwater monitoring or short-range communication needs. Among these options, UWOC has gained significant attention as a promising alternative to traditional wireless technology due to its capacity to deliver high data rates, wide band- width, and cost-effective deployment (Saeed et al. 2019). Optical communication, leverag- ing the higher frequency spectrum in the THz range, emerges as a high-performance con- tender in the underwater communication landscape. With impressive data rates reaching into the Gbps range and low latency, optical technology becomes the technology of choice for scenarios demanding rapid and voluminous data transfer. Its balanced characteristics in terms of coverage distance and bandwidth make it a versatile option for various underwater applications, ranging from real-time surveillance to high-resolution imaging. Beyond data rates and distance considerations, the physical attributes of the technol- ogies play a crucial role. Acoustic and optical technologies boast smaller antenna sizes compared to their RF counterparts, facilitating deployment in constrained underwater Table 1 List of acronyms 1617 Acronym Definition Acronym Definition ACO Asymmetrically clipped optical BER Bit error rate A-MIMO Angular MIMO BPPM Binary pulse position modulation APD Avalanche photodiodes CAP Carrierless amplitude phase Page 6 of 45 APM Amplitude and phase modulation CIR Channel impulse response C-MIMO Conventional MIMO DBMLP Dual-branch multi-layer perceptron DD Direct-detection DPIM Digital pulse interval modulation DPWM Differential pulse width modulation EE Energy efficiency EM Electromagnetic FD Full-duplex FDE Frequency-domain equalization FFIR Fading-free impulse response FoV Field of view GSM Generalized SM GSSK Generalized SSK GoF Goodness of fit IAS Inter-antenna synchronization IM Intensity modulation I-OSIC Improved-order successive interference cancellation ISI Inter-symbol interference IoUT Internet of underwater things LED Light emitting diode LoS Line of sight MCM Multi-carrier modulation MC Monte Carlo MIMO Multiple-input multiple-output ML Machine learning MPAPM Multiple pulse amplitude and position modulation MPPC Multi-pixel photon counter NLoS Non-line-of-sight NRZ Non-return-to-zero OOK On-off-keying OPCI Orthogonal polarization and code-indexing OPPM Overlapping pulse position modulation OFDM Orthogonal frequency division multiplexing OSM Optical spatial modulation OWC Optical wireless communication PAT Pointing, acquisition, and tracking PD Photodiode PAA Power allocation algorithm PAM Pulse amplitude modulation PDF Probability density functions PM Pulse modulation PMT Photomultiplier tubes PPM Pulse position modulation QAM Quadrature amplitude modulation A. Elfikky et al. QSM Quadrature SM QSSK Quadrature SSK Table 1 (continued) Acronym Definition Acronym Definition PWM Pulse wave modulation RZ Return zero RF Radio frequency RC Repetition coding RTE Radiative transfer equation SE Spectral efficiency SIM Subcarrier intensity modulation SSK Space shift keying SM Spatial modulation SIMO Single-input multi-output SMX Spatial multiplexing SNR Signal-to-noise ratio SSD Single-shot detector SC Single carrier SCM Single carrier modulation STBC Space-time block coding SiPMs Silicon photo-multipliers UV Ultraviolet VPPM Variable pulse position modulation WDGF Weighted double gamma function VR-MPPM Variable rate multi pulse modulation VSOP Variable-size optical packets VSF Volume scattering function UWLT Underwater wireless laser transmission UWOC Underwater wireless optical communication VLC Visible-light communication Underwater visible light communication: recent advancements… Page 7 of 45 1617 1617 Page 8 of 45 A. Elfikky et al. spaces. Furthermore, the transmission power requirements for acoustic and optical tech- nologies are notably lower than those for RF, aligning with the growing demand for energy-efficient solutions in underwater communication systems (Zuberi et al. 2023). Table 2 offers a comparison of underwater wireless communication technologies, pro- viding valuable insights into the unique features and performance metrics of each tech- nology within underwater environments. The possible replacement of acoustic communication with UVLC is contingent upon the specific requirements of the application. Acoustic communication is favoured for long-range communication in deep water owing to its lower attenuation. In contrast, UVLC proves more suitable for short-range applications. Moreover, UVLC emerges as a cost-effective solution for applications that demand short-range communication with high data rates. The transmission of EM waves within the optical spectrum for underwa- ter communication is influenced by various environmental factors. These factors encom- pass molecular absorption, molecular dispersion, absorption attributed to suspended particles and plankton, as well as beam spread, among others. The intricate interplay of these factors can exert a substantial influence on the dynamics of the optical channel in underwater communication. The optical factors can be classified as inherent or apparent (Saxena and Bhatnagar 2019). Inherent Optical Properties (IOPs) are only dependent on the medium and include the absorption coefficient, scattering coefficient, and attenu- ation coefficient (Gabriel et al. 2011). On the other hand, Apparent Optical Properties (AOPs) are influenced by both the water medium and the geometric structure of the water body (Zeng et al. 2017), as well as processing such as transmission and reflection by the sea surface and bottom. Table 2 Comparison of underwater wireless communication technologies(Mohammed et al. 2022; Kaushal and Kaddoum 2016; Schirripa et al. 2020) Parameter Acoustic RF Optical Frequency band 10 − 15 kHz 30 − 300 MHz 1012 − 1014 Hz Attenuation Distance and frequency Frequency and conductivity ∼ 0.39 dB∕m (ocean) dependent ∼ (3.5 − 5) dB∕m ∼ 11 dB∕m (turbid) ∼ (0.1 − 4) dB∕km Distance ∼ Up to kms ∼ 10 m ∼ 10 − 200 m (Dai et al. 2021; Chen et al. 2020) Speed ( ) ( ) 1500 m∕s 2.255 × 108 m∕s 2.255 × 108 m∕s Bandwidth Distance dependent: ∼ MHz ∼ (10 − 150) MHz ∼ 1000 km < 1 kHz ∼ 1 − 10 km ≈ 10 kHz ∼< 100 m ≈ 100 kHz Data rate ∼ Kbps ∼ Mbps ∼ Gbps Latency High Moderate Low Antenna size (0.1) m (0.5) m (0.1) m Transmission power Tens of Watts Distance dependent: Few Watts mW - hundreds of Watts Underwater visible light communication: recent advancements… Page 9 of 45 1617 2.1 Absorption and scattering Attenuation in the wireless link, as light propagates through water, is primarily influenced by absorption and scattering, as discussed in Khalighi et al. (2017). The absorption and scattering observed in UVLC channels stem from the interaction between individual pho- tons and particles in seawater, occurring as the optical beam progresses through the water medium. Energy loss occurs due to absorption as some photons absorbed and converted into heat energy. This absorption process reduces the overall intensity of the transmitted light, impacting the efficiency of the communication link. On the other hand, scattering alters the propagation direction of each photon, which can cause energy loss since fewer photons will be captured by the receiver aperture (Jamali et al. 2018). The extinction coefficient, denoted as c(𝜆), represents the combined effect of absorption and scattering coefficients in underwater optical communication. It can be calculated based on a geometric model proposed in Mobley et al. (Dec 1993) as c(𝜆) = a(𝜆) + b(𝜆), (1) where, a(𝜆) is the absorption coefficient at the wavelength 𝜆 and b(𝜆) is the scattering coef- ficient at the wavelength 𝜆. By summing the absorption and scattering coefficients, the extinction coefficient quanti- fies the overall reduction of light intensity as it propagates through the water medium due to both absorption and scattering processes (El-Mottaleb et al. 2023). This formulation is essential for understanding and predicting the behavior of optical signals in underwater communication systems, taking into account the combined impact of absorption and scat- tering on signal attenuation. Water absorption and scattering spectra are influenced by various biological factors. These include absorption by pure water, chlorophyll-a in phytoplankton, and humic and fulvic acids. The complete absorption spectrum is the sum of these individual spectra, mul- tiplied by their respective concentrations (Haltrin 1998). These factors play a significant role in how light interacts with the underwater environment. The total absorption coeffi- cient a(𝜆) for an underwater optical communication system is represented by: a(𝜆) = aw (𝜆) + ac (𝜆)Cc0.602 + af (𝜆)Cf exp(−kf 𝜆) (2) + ah (𝜆)Ch exp(−kh 𝜆), where This equation encompasses the sum of the absorption coefficients of various com- ponents, including pure water (aw (𝜆)), chlorophyll-a (ac (𝜆))-the primary substance in phytoplankton-and humic and fulvic acids (af (𝜆) and ah (𝜆)), which serve as nutrients for phytoplankton. The terms exp(−kf 𝜆) and exp(−kh 𝜆) account for the wavelength-dependent attenuation caused by these factors. The coefficients Cc, Cf , and Ch represent the concentrations of chlorophyll-a, humic acid, and fulvic acid, respectively, and can be expressed in terms of the chlorophyll concen- tration Cc (Vavoulas et al. 2014; Ali 2015) Cf =1.74098 ⋅ Cc ⋅ exp0.12327⋅Cc , (3) Ch =0.19334 ⋅ Cc ⋅ exp0.12343⋅Cc. (4) 1617 Page 10 of 45 A. Elfikky et al. The scattering originates from both pure water and particles of different sizes. Small par- ticles are characterized by a refractive index of 1.15, while large particles have a refractive index of 1.03. The total scattering coefficient, b(𝜆), is represented by Johnson et al. (2013), Malathy et al. (2020) b(𝜆) = bw (𝜆) + bs (𝜆)Cs + bl (𝜆)Cl , (5) where bw (𝜆) represents the scattering due to pure water, Cs and Cl are the concentrations of small and large particles, respectively. bs (𝜆) corresponds to the scattering coefficient of small particles, while bl (𝜆) refers to the scattering coefficient of large particles and is expressed by Ali (2015), Johnson et al. (2013) )4.322 400 ( bw (𝜆) =0.005826 × (6) 𝜆 )1.7 400 ( bs (𝜆) =1.1513 × (7) 𝜆 )0.3 400 ( bl (𝜆) =0.3411 × (8) 𝜆 2.2 Water types in UVLC The optical properties of light in underwater environments are influenced by the type of water present (Schirripa et al. 2020), and various factors come into play, such as the presence of dissolved substances, suspended particles, and impurities as seen in Fig. 2. Researchers have conducted precise measurements of the water absorption coefficient across a range of wavelengths from 300 to 700 nm (Pope and Fry 1997), revealing that blue-green visible light in the 450–550 nm range experiences lower attenuation, making it a more suitable choice for underwater communication (Wang et al. 2022; Ali 2015). Water can be classified into four types according to its scattering and absorption prop- erties; namely pure sea water, clear ocean water, coastal ocean water, and Turbid Harbor water (Schirripa et al. 2020). In pure sea water, absorption acts as the primary limiting factor. Clear ocean waters have a higher concentration of dissolved particles, leading to the scattering of light in various directions (Singh et al. 2023). Coastal ocean water contains a significantly higher concentration of planktonic matters, detritus, and mineral components, which greatly influence both absorption and scattering of light. Turbid harbor water has an exceptionally high concentration of dissolved and suspended matter, resulting in sig- nificant absorption and scattering of light that can severely limit the range and clarity of underwater optical communication. Table 3 presents the typical values of a(𝜆), b(𝜆), and c(𝜆) corresponding to the four different types of water. These variations in water types have implications for underwater communication systems, as they directly affect the transmis- sion and propagation of light signals underwater (Gabriel et al. 2013). Understanding these different types of water is crucial to optimize and design reliable underwater optical com- munication systems. Underwater visible light communication: recent advancements… Page 11 of 45 1617 Table 3 Typical coefficients Water Type a(𝜆) (m−1) b(𝜆) (m−1) c(𝜆) (m−1) corresponding to different water types (Kaushal and Kaddoum Pure sea water 0.053 0.003 0.056 2016) Clear ocean water 0.069 0.08 0.151 Coastal ocean water 0.088 0.216 0.305 Turbid harbor water 0.295 1.875 2.170 Fig. 2 Schematic representation of the underwater ecosystem, showcasing the interaction of laser beams with minerals, phytoplankton, detritus, and bubbles Wang et al. (2021) proposed a model and simulation platform to analyze the per- formance of underwater optical wireless communication (UOWC) systems, taking into account the influence of seawater inherent optical properties and solar noise. Tang et al. (2014) addressed the issue of the temporal spread of beam pulse in UWOC links caused by multiple scattering, leading to Inter-Symbol Interference (ISI) and degradation of system error performance. Regarding the choice of light source, Sticklus et al. (2019) highlighted the suitability of green light emitting diodes (LEDs) for optical communica- tions in the Baltic Sea due to the minimum light attenuation spectrum at 520-590 nm. 1617 Page 12 of 45 A. Elfikky et al. 2.3 Oceanic turbulence Oceanic turbulence pertains to the unpredictable and irregular changes in the refractive index within the water medium, induced by fluctuations in temperature, density, and salin- ity of the water (Baykal et al. 2022). As a result of these variations, the transmitted light signal in an underwater optical communication system experiences fluctuations in both its intensity and phase when received at the receiver (Zhao et al. 2023). These fluctuations can pose challenges to the reliability and stability of underwater communication systems (Jamali et al. 2018), as they can lead to signal distortions and fading effects (Baykal et al. 2022). Researchers demonstrated the impact of salinity and temperature on underwater optical channels and their correlation with turbulence in Ata and Korotkova (2021). Oceanic turbulence distorts the propagating wave, leading to intensity fluctuations known as scintillation (Xu and Lai 2020). The received optical signal is measured using the scintillation index (Baykal 2016), which varies with different optical wave models (Wang et al. 2016). In addition to temperature and salinity fluctuations, the presence of air bubbles in the water channel also induces random variations in the refractive index (Kumar et al. 2020). Dealing with these effects is crucial in the design and implementation of robust underwater optical communication systems (Singh et al. 2021). The presence of air bub- bles, caused by factors like wave action, significantly affects light propagation and scat- tering behavior in optical communication systems resulting in performance degradation in UWOC links (Oubei et al. 2018). Designing and implementing reliable communication systems in such conditions pose considerable challenges. The authors in Shin et al. (2020) considered complete blockage caused by air bubbles and combined this bubble-obstruction model with a Gamma–Gamma turbulence model to derive the distribution for the compos- ite channel model. Jamali et al. (2018) explored different scenarios with random tempera- ture, salinity variations, and air bubbles to simulate water refractive index fluctuations. To gain a deeper understanding of how turbulence affects optical signals in the under- water channel, statistical methods are employed for analysis (Jamali et al. 2016). The fit- ting methodology plays a crucial role as it helps identify the best-fitting probability den- sity functions (PDFs) that accurately describe the collected data. PDFs provide valuable insights into the distribution of intensity fluctuations in the underwater channel (Bernotas and Nelson 2016). By optimizing the scale and shape parameters of the PDFs based on the collected data, valuable insights are extracted into how underwater optical turbulence impacts communication links. This understanding is essential in assessing signal quality and devising effective strategies for mitigation. Furthermore, efforts are made to develop more generalized equations for the PDFs that can be applied to different underwater optical links (Mahmoud et al. 2021). The authors in Jamali et al. (2018) assessed the random tem- perature, salinity variations, and air bubbles using Goodness of Fit (GoF) and found that Generalized Gamma distribution (GGD) and exponential Weibull distributions provided good matches. Also, the authors in Oubei et al. (2017) effectively modeled UWOC chan- nels with temperature gradients using the GGD. This broader applicability led to a better understanding of how various underwater environments influence optical communication, enabling the design of more robust and efficient underwater communication systems. Oubei et al. (2017) have introduced the Weibull model as a way to describe and under- stand the fading characteristics of underwater wireless optical channels influenced by salin- ity-induced turbulence. Also, Weibull distribution has been proven to exhibit exceptional accuracy in characterizing the fading phenomenon caused by oceanic turbulence influ- enced by salinity (Jurado-Navas et al. 2018). However, the authors in Bariah et al. (2022) Underwater visible light communication: recent advancements… Page 13 of 45 1617 assumed that the PDF governing the optical channel, considering both path loss and turbu- lence effects, can be described by a log-normal distribution. The log-normal distribution is employed to model the performance of UOWC systems when underwater turbulence is present (Peppas et al. 2017; Jamali et al. 2018). Kumar et al. (2022) employed the Expo- nential Generalized Gamma (EGG) distribution to model and measure the received signal fluctuations in underwater turbulence. Also, the turbulence channel model for UWOC sys- tems was proposed by Romdhane et al. (2023). This model employed the unified mixture EGG distribution, showcasing its effectiveness in accurately depicting turbulence effects. The lognormal distribution is frequently used to characterize the variations caused by weak atmospheric turbulence follows (Jamali et al. 2018) ̃ − 2𝜇X 2 ( ( ) ) 1 ln(h) ̃ = √ fh̃ (h) exp − 8𝜎X2 (9) 2h̃ 2𝜋𝜎 2 X where The mean (𝜇X ) and variance (𝜎X2 ) represent the average and spread, respectively, of a Gaussian-distributed fading log-amplitude factor, where the factor is defined as ̃. The authors in Wang et al. (2023), Elamassie et al. (2021) utilized the X = 12 ln(h) Gamma–Gamma (GG) distribution to describe the moderate-to-strong turbulence condi- tions. The PDF of the GG distribution is given by Wang et al. (2023), Ali and Jayakody (2023), Elamassie et al. (2021) 𝛼+𝛽 ( ) 2(𝛼𝛽) 2 𝛼+𝛽 −1 fΓΓ IaΓΓ = I 2 Γ(𝛼)Γ(𝛽) aΓΓ (10) ( √ ) × K𝛼−𝛽 2 𝛼𝛽IaΓΓ , IaΓΓ > 0, where 𝛼 and 𝛽 are shape parameters, Γ is the Gamma function, and K𝛼−𝛽 is the modified Bessel function of the second kind. The expressions for 𝛼 and 𝛽 are formulated as Elamas- sie and Uysal (2020), Ali et al. (2022) −1 ⎡ ⎛ ⎞ ⎤ ⎢ ⎜ 0.49𝜎l2 ⎟ ⎥ 𝛼 = ⎢exp ⎜ 7∕6 ⎟ − 1⎥ , ⎢ ⎜ 1 + 1.11𝜎 12∕5 ⎟ ⎥ l (11) ⎣ ⎝ ⎠ ⎦ −1 ⎡ ⎛ ⎞ ⎤ ⎢ ⎜ 0.51𝜎l2 ⎟ ⎥ 𝛽 = ⎢exp ⎜ 5∕6 ⎟ − 1⎥ , ⎢ ⎜ 1 + 0.69𝜎 12∕5 ⎟ ⎥ ⎣ ⎝ l ⎠ ⎦ where 𝜎l2 is the Rytov variance which represents the scintillation index (Ali et al. 2022). The study described in Afifah et al. (2023) examined how an UWOC system performs under various saline water conditions, taking into account changes in temperature and water flow. The study showed that random fluctuations in the refractive index of ocean water due to changes in local temperature and salinity of seawater can result in intensity and phase fluctuations of the average received signal of the UWOC system. An efficient UWOC turbulence model is presented in Zedini et al. (2017). Authors proposed the mixed Exponential-Gamma model to characterize irradiance changes in fresh and salty waters under diverse turbulence situations.The effectiveness of adaptive optics in improving the 1617 Page 14 of 45 A. Elfikky et al. performance of laser communication links is discussed in Toselli and Gladysz (2020), where it is found that an optimum aperture size must be used to achieve optimal results. The study showed that, similar to laser beam propagation in atmospheric turbulence, adap- tive optics can significantly reduce scintillation in oceanic turbulence-affected beams. In Kammoun et al. (2019), the impact of water turbidity and wavelength on non-line-of- sight (NLoS) underwater communication links was investigated using a chlorophyll-based model proposed in Haltrin (1999). The paper (Guo et al. 2022) proposed a Full-Duplex (FD) UWOC system using a 450 nm-laser/scintillating-fiber-based omnidirectional signal detector to overcome the challenges of Pointing, Acquisition, and Tracking (PAT) in real scenarios. The system achieved a 250-Mbit/s data rate with a low self-interference level and is robust in different underwater turbulence scenarios induced by air-bubbles, tempera- ture, salinity, turbidity, and mobility. The authors in Ji et al. (2022) proposed an oblique optical link model for UWOC that considers temperature and salinity variations with depth. They analyzed the performance of UWOC systems for vertical and oblique links by using oceanic power spectrums and seawater data from different ocean areas. 2.4 Underwater optical communication links There are two basic types of underwater optical link configurations: line of sight (LoS) links and NLoS links as seen in Fig. 2. The LoS communication link refers to the direct link between the transmitter and the receiver (Mohsan et al. 2023). Extensive theoretical and experimental studies have investigated this configuration (Mohammed et al. 2024; Al- Zhrani et al. 2021). In NLoS, the communication scenario involves an obstruction in the direct path between the transmitter and the receiver. This obstruction can arise from inter- actions between light waves and particles or impurities in the water, such as minerals, phy- toplankton, detritus, and bubbles as seen in Fig. 2. When the direct LoS is hindered, light navigates around obstacles, resulting in scattering phenomena. Research on NLoS remains relatively limited, establishing comprehensive NLoS models and addressing the associated challenges that should be considered a significant research goal to advance the understand- ing and capabilities of underwater optical communication technologies (Mahmoud et al. 2021; Fang et al. 2022). Authors in Ijeh et al. (2021), showed the impact of parameter optimization on link per- formance under different link configurations and misalignment conditions. The results demonstrated the significant performance improvement achieved by optimizing the trans- mitter beam divergence and the receiver Field of View (FoV) in the presence of pointing errors (Hayal et al. 2023). The article (Elamassie et al. 2019) explored the performance limits of UVLC systems by developing a formula for path loss as a function of transceiver parameters and water type. The authors then used this formula to determine the maximum link distance for UVLC systems in different water types, including pure sea, clear ocean, coastal water, and harbor water. In Anous et al. (2018), the authors evaluated the performance of UVLC by calculating the received power and BER for inhomogeneous underwater links and provide numerical examples to illustrate their proposed models. They deduced a generalized path loss expression, as well as mathematical expressions of the received power for LoS and NLoS links between transmitters and receivers. Underwater visible light communication: recent advancements… Page 15 of 45 1617 2.4.1 Line of sight (LoS) LoS communication is a widely used and straightforward optical link (Arnon 2010). It requires perfect alignment between the transmitter and receiver (Tang et al. 2014). Achiev- ing precise alignment between the transmitter and receiver makes the LoS configuration demanding in terms of PAT (Miroshnikova et al. 2019), limiting the receiver beam cover- age to the receiving lens area. LoS links with low divergence angle light sources like laser diodes enable higher communication rates and longer distances (Ali and Jayakody 2023). However, maintaining alignment in turbulent underwater environments or with mobile nodes is challenging (Sun et al. 2020). Despite these challenges, LoS scenarios offer reli- able performance with high data rates, better BER performance, and improved system effi- ciency (Saeed et al. 2019). LoS connections may not always be feasible in practical systems. While static trans- mitters and receivers, like two sensor nodes on the ocean floor, can implement this link easily, it becomes more challenging for mobile platforms like underwater vehicles (Kong et al. 2018). In Elamassie et al. (2019), the authors discuss the LoS configuration. Simi- larly, in Zhang et al. (2015), Authors analyzed UWOC systems with precisely aligned LoS geometry. 2.4.2 Non‑line‑of‑sight (NLoS) The NLoS communication link in underwater optical communication is an indirect optical link that utilizes back-reflection at the water-air interface (Tang et al. 2013) or light scat- tering from water molecules and particles (Liu et al. 2015) to establish communication between the transmitter and receiver. This approach is beneficial in scenarios where obsta- cles or complex underwater environments hinder direct optical links, allowing for commu- nication even in NLoS conditions. NLoS communication presents a dynamic channel because the transmitted signal expe- riences multiple reflections, diffractions, and scattering in the environment before reaching the receiver. This dynamic behavior results in varying signal paths and signal strengths over time, leading to frequency-selective fading and time-varying channel characteristics (El-Fikky et al. Oct 2019; Mahmoud et al. 2021). The dynamic channel behavior of NLoS makes it a practical choice for real-world applications where reliable and efficient com- munication is required in challenging and complex environments. In Pan et al. (2021), the authors introduced a method for achieving high-fidelity NLoS free-space optical data trans- mission through turbid water. For dynamic scenarios with temporal coherence information, the researchers in Cai et al. (2021) performed 288 MC simulations for each group of chan- nel parameters. Anous et al. (2018) presented a point-to-multipoint NLoS link model for UVLC. The model involved a transmitter (Tx) and multiple receivers (Rx) located at different depths from the water-air interface. Sun et al. (2020) addressed the performance degradation of UWOC caused by oceanic turbulence. Their proposed solution utilized NLoS commu- nication using light-scattering to mitigate the impact of turbulence. In Sun et al. (2020), the authors presented a robust NLoS UWOC link that effectively operateed in highly tur- bid water conditions. They addressed the challenges encountered in UWOC, particularly emphasizing the need for a system that does not rely on precise PAT. To overcome this limitation, the system incorporated an ultraviolet laser to enhance light scattering and uti- lized a high-sensitivity photomultiplier tube. Remarkably, the NLoS link achieved a data 1617 Page 16 of 45 A. Elfikky et al. rate of 85 Mbps and a transmission distance of 30 cm using OOK modulation. Even when the alignment is LoSt, a data rate of 72 Mbps was still maintained, showcasing the system’s resilience and practicality in real-world underwater communication scenarios. Yildiz et al. (2022) proposed a cLosed-form NLoS UVLC channel model for semi-collimated Gaussian optical signals. Through experiments, they confirmed a 3 dB gain using reflecting water and a 2.8 dB gain with a man-made reflector at distances of 2 m or more. 3 Underwater visible light communication system The UVLC system, depicted in Fig. 3, comprises three main segments: transmitter com- ponents, the underwater medium channel, and receiver components. The transmitter com- ponents play pivotal roles in transmitting optical signals underwater and typically include elements such as light sources (commonly LEDs or laser diodes (LDs)), modulation techniques, and signal processing units. These components work collaboratively to pro- duce optical signals encoded with data. On the other hand, the receiver components are crucial for capturing these optical signals in the underwater channel. Key elements of the receiver components involve photodiodes, decoding modules, and signal-processing units. This integrated system facilitates effective communication through UVLC in underwater environments. 3.1 Underwater optical transmitter the optical transmitter employs various components to transmit optical signals in under- water environments. The main component is the optical source, which can be LED or LD. In Abd El-Mottaleb et al. (2024), a LD source emitting light at a wavelength of 532 nm is utilized for optical signal generation. The LED light source, characterized by a larger diver- gence angle and reduced alignment requirements, proves highly suitable for underwater mobile networks (Liu et al. 2023). LEDs, available in various types like blue, white, RGB, or UV, are selected according to specific application requirements. Signal processing tech- niques are also employed in UVLC transmitters to enhance signal quality, including equali- zation, error correction coding, filtering, and adaptive modulation. Lenses play a crucial role in shaping and directing the emitted light, improving the efficiency of light transmis- sion through water by focusing the light beam. The beam width of the light source can significantly affect temporal spreading in UWOC systems (Romdhane and Kaddoum 2022). When the light source beam width is Information Encoder Modulator Underwater Photodiode Demodulator Dimming Driving Channel Control Circuit LED Decoder Fig. 3 Comprehensive overview of the UVLC system design illustrating the integration of both transmitter and receiver components, along with the underwater communication channel Underwater visible light communication: recent advancements… Page 17 of 45 1617 larger, the emitted photons are more spread out over a wider area, leading to a higher prob- ability of scattering interactions with water molecules and particles. This scattering process causes the photons to take longer and more varied paths to reach the receiver, resulting in the temporal spreading of the optical pulse. As a consequence, the received pulse becomes broader and may overlap with neighboring pulses, leading to potential signal distortions and degradation in data transmission. On the other hand (Fletcher et al. 2015), the narrow- beam light source offers several advantages over wide-beam, including an increased light transmission range, a reduced temporal spread of signals, and enhanced filtering options to reduce background light interference. These benefits result in improved communication performance, especially in challenging underwater environments. Narrow-beam laser com- munication enables more efficient and reliable data transmission, making it a promising approach for underwater communication systems. The authors in [?] presented a study on the use of LED-based UWOC for collabora- tive work between small mobile platforms in highly turbid natural water environments. The study demonstrated the use of a green LED-based UWOC system with a bandwidth of up to 3.4 MHz and explores the effects of the turbid water channel on the receiving signal amplitude and frequency selection. The authors in Li et al. (2019) demonstrated a transmit- ter setup consisting of a lens group and a blue-emitting silicon substrate LED with a peak emission wavelength of 458 nm. By conducting underwater transmission over a distance of 1.2 m, the system achieved a data rate of over 1 Gbps. In Shen et al. (2019), a blue LED was employed as a transmitter to generate signals with pulse position modulation (PPM) ranging from 8-PPM to 64-PPM at a slot frequency of 5 MHz. The performance of these signals was evaluated after a 46 m underwater transmission. In Arvanitakis et al. (2020), researchers successfully achieved high-speed underwater optical wireless data communications using OFDM modulation. By employing 6 series- connected LED arrays with high output power, they achieved impressive data rates of 2.34 Gbps and 1.32 Gbps over distances of 3 m and 4.5 m, respectively. The study in Han et al. (2019) demonstrated freeform lens-LED array performance in diverse transmission orien- tations, achieving a 19 Mbps data rate over an 8 m distance in a 20 m × 20 m × 14 m tank. Different freeform lenses can be used to tailor transmitting illumination for specific UWOC applications. In Cossu et al. (2018), authors tested an UOWC system with common LEDs, achieving 10 Mbps Manchester-coded signal transmission over a 10 m distance in marine environments. In Chen et al. (2020), a blue LD was used as the light source, and a single-photon ava- lanche diode (SPAD) receiver was used in the UWOC system. The blue LD offered high power and low divergence, enabling communication up to a maximum distance of 144 m. In Shen et al. (2016), a system was developed using a 450-nm LD and a Si avalanche pho- todetector. The system achieved high-speed UWOC with data rates up to 2 Gbps over a 12 m channel and 1.5 Gbps over a record 20 m channel. In Fei et al. (2018), an experimental UWOC system achieved high data rates at 450 nm. Data rates of 16.6 Gbps over 5 m, 13.2 Gbps over 35 m, and 6.6 Gbps over 55 m tap water were achieved with a single LD. Using a single-mode pigtailed green-light LD and 32-quadrature amplitude modulation (QAM) Orthogonal Frequency Division Multiplexing (OFDM), Chen et al. (2017) achieved high- speed transmissions. They achieved a data rate of 5.3 Gbps and 5.5 Gbps over a 5 m air channel and a 21 m water channel. Liu et al. (2017), utilized a 520 nm green LD to demon- strate a data rate of up to 2.70 Gbps over a 34.5 m underwater transmission distance using the NRZ-OOK modulation scheme. Huang et al. (2018) demonstrated a visible-light com- munication (VLC) link in a seawater environment utilizing a GaN blue laser diode (BLD). They achieved impressive data rates of 14.8 Gbps and 4 Gbps over distances of 1.7 m and 1617 Page 18 of 45 A. Elfikky et al. 10.2 m, respectively. Wu et al. (2017) demonstrated a UWOC link using a 450-nm blue GaN LD modulated by 16-QAM-OFDM. They achieved bit rates of 5.2 Gbps and 12.4 Gbps over transmission distances of 10.2 m and 1.7 m, respectively, in tap water. 3.2 Underwater optical receiver Optical receivers play a crucial role in UVLC systems. They are responsible for detect- ing and decoding the optical signals transmitted through water. In UVLC, optical receiv- ers typically consist of photodetectors, amplifiers, and signal-processing components. Photodetectors convert the received optical signals into electrical signals, which are then amplified to enhance the signal-to-noise ratio (SNR). Signal processing techniques such as filtering, equalization, and decoding are applied to extract the transmitted information accurately. The design and performance of optical receivers are critical for achieving reli- able and high-speed data transmission in UVLC systems. Table 4 presents a concise overview of studies conducted across various years, offering insights into the evolution and capabilities of photodetectors in UVLC. The primary goal of the photodetector is to maximize the collection of transmitted photons, particularly in the presence of channel attenuation in UVLC. One of the key factors for achieving this is the aperture size of the photodetector (Gussen et al. 2016). Having a larger aperture is desirable as it allows the capture of more photons (Fu et al. 2019). One approach to increas- ing the aperture size is by utilizing an array of lenses positioned in front of the photodetec- tor; this arrangement helps to effectively enlarge the overall aperture size (Mahmoud et al. 2021). Additionally, it is important to use a photodetector with high sensitivity to ensure efficient detection of the collected photons. The results in Jiang et al. (2020) demonstrated that employing a SPAD as the detector can extend the transmission range. Also, the study by Yang et al. (2022) utilized a SPAD as a receiver. The main photodetector types are: PIN photodiodes (PIN PDs), avalanche photodiodes (APD), photomultiplier tubes (PMT) and silicon photo-multipliers (SiPMs). PIN PDs oper- ate at a low bias voltage typically ranging from 2 to 5 V, providing advantages such as fast response times and cost-effectiveness, although they lack internal gain (Zedini et al. 2019). APDs are designed to achieve internal gain through avalanche multiplication in a high electric field region known as the avalanche region. They share a similar semiconduc- tor structure with PIN PDs. PMTs consist of three main components: a photocathode, a series of electron multipli- ers called dynodes, and an electron collector known as the anode. PMTs amplify the initial Table 4 Summary of Ref Year Photodetectors Bit rate photodetectors for UVLC Fei et al. (2018) 2018 PIN PDs 16.6 Gbps Gökçe et al. (2018) 2018 APD Zedini et al. (2019) 2019 PIN PDs Wang et al. (2019) 2019 APD 500 Mbps Tsai et al. (2019) 2019 APD 30 Gbps Zhang et al. (2020) 2020 SiPMs 1 Gbps Ning et al. (2021) 2021 PMT 150 Mbps Xu et al. (2022) 2022 APD 200 Mbps Hong et al. (2022) 2022 SiPMs 2 Gbps Underwater visible light communication: recent advancements… Page 19 of 45 1617 signal by triggering the emission of electrons from the photocathode and accelerating and multiplying them as they pass through the dynodes. This cascade effect results in an excep- tional sensitivity, low noise levels, and rapid response times. Due to its high sensitivity and large receiver gain, a PMT receiver could extend UWOC systems transmission distance in the deep ocean (Nakamura et al. 2019). The PMT receiver presents a promising solution for long-distance UWOC. It is well- suited for efficient signal detection and transmission in challenging underwater environ- ments (Ning et al. 2021). SiPMs consists of an array of APDs operating in Geiger mode (Essalih et al. 2020). The output currents of individual APDs are summed to produce a total output current. SiPMs offer compact size, low operating voltage, high photon detec- tion efficiency, and excellent timing resolution, making them advantageous compared to traditional PMTs. In Nakamura et al. (2019), authors achieved over 1 Gbps NRZ-OOK UWOC transmission using a wideband PMT. The PMT’s large gain, exceeding 103, led to a significant improvement in receiver sensitivity of approximately 17 dB compared to an APD receiver. They utilized a PMT module from Hamamatsu Photonics K.K. as the receiver in their 1 Gbps class NRZ-OOK UWOC experiments. The PMT’s maximum cath- ode radiant sensitivity is centered around 450 nm, with a sensitivity spectrum covering approximately 550 nm (green). 4 Underwater visible light communication modulation techniques The signal can be modulated in frequency, phase, or amplitude. Choosing the best modula- tion can improve the reliability of the system and enhance the data rate. When constructing a communication system, one of the most important decisions that must be made is the selection of a modulation technique. Direct modulation or modulation done with an exter- nal modulator are both valid methods for performing modulation (Kaushal and Kaddoum 2016; Mohsan et al. 2023). Quadrature Amplitude Modulation-Carrierless Amplitude Phase Modulation (QAM-CAP) combines QAM for amplitude modulation and Carrier- less Amplitude Phase (CAP) modulation for phase modulation. This combination increases data transmission by transmitting multiple bits per symbol. Its higher spectrum efficiency and channel impairment resilience make it appropriate for high-speed and dependable data transmission in UVLC (Rajalakshmi et al. 2023). In the external modulation, the light from a laser that is outputting a constant power is routed through a device called an external modulator, which is powered by a voltage, to create a modulated optical power at the output of the external modulator. These systems are able to draw the maximum amount of power from their respective sources. This exter- nal modulation method can be used with high-power light sources to increase the transmis- sion distance and make it possible for underwater mobile devices like AUVs and subma- rines to communicate to each other (Wang et al. 2022). In most of studies, intensity modulation direct-detection (IM/DD) is used in UVLC, where modulation is mostly done by changing the intensity of the output (Ali et al. 2022). IM uses changes in the intensity of an optical wave to change the data being sent (Kumar et al. 2022). NRZ-OOK is the most popular modulation technique in UWOC due to its ease of use. PPM is more energy-efficient than OOK. PPM may detect harsh signals at the receiver without dynamic thresholding, unlike OOK. Pulse Wave Modulation (PWM) provides superior spectrum efficiency, less peak power, and better Intersymbol Interfer- ence (ISI) resistance than PPM. However, for L-ary PWM with M = log2 L requires more 1617 Page 20 of 45 A. Elfikky et al. power, which offsets these benefits (Gabriel et al. 2012). Unlike OOK, the need for higher data rates leads to the utilization of multi-level modulations such as Pulse Amplitude Mod- ulation (PAM), where the bandwidth efficiency of M-ary PAM with (M > 2) surpasses that of OOK. This is because PAM is a multi-level scheme in which symbols are modulated using M different intensity levels. Two common modulation techniques employed in UVLC are Single Carrier Modula- tion (SCM) and Multi-Carrier Modulation (MCM). Table 5 provides a comprehensive summary of modulation techniques in UVLC. SCM involves using a single carrier fre- quency to transmit the entire information, utilizing the full available bandwidth for signal transmission. On the other hand, MCM is a modulation technique where the information is divided and transmitted over multiple carrier frequencies simultaneously. One popular MCM scheme is OFDM, which divides the available bandwidth into several sub-channels. Each sub-channel carries a portion of the data, and these sub-channels are designed to be orthogonal to each other to prevent interference. MCM, like OFDM, offers advantages in utilizing the available bandwidth effectively by dividing it into smaller sub-channels. This enables higher data rates and improved spectral efficiency (SE) compared to SCM. Dis- sanayake and Armstrong (2013) conducted a comparison between ACO-OFDM and DCO- OFDM modulation techniques. The modulation technique referred to as hybrid OOK and ACO-OFDM (Asymmetrically Clipped Optical Orthogonal Frequency Division Multiplex- ing) was investigated in Yang et al. (2016). 4.1 Non‑return‑to‑zero on‑off keying (NRZ‑OOK) OOK is a type of modulation method that is often used in VLC. The main benefit of OOK is that it is easy to use. On the other hand, its spectrum efficiency, working data rate, and dimming control range are all rather low. Figure 4 shows the OOK as a series of rectangular pulses. Each pulse lasts for a time period of Ts. It is done by giving bits ’1’ and ’0’ the optical power intensity values POn,OOK and POff ,OOK , respectively. The system’s bandwidth is equal to the data rate, BWOOK = Rb. The average power Pavg can be written as: Table 5 Summary of modulation techniques for UVLC Modulation techniques Modulation type Ref Single Carrier OOK Ali and Jayakody (2023), Anous et al. (2017) and Amalia et al. Modulation (SCM) (2020) NRZ-OOK Chen et al. (2020), Wang et al. (2019) and Zhao et al. (2020) PPM Amalia et al. (2020), Shen et al. (2018) and Shen et al. (2019) DPIM Sahnoun et al. (2017) PAM Amalia et al. (2020), Kong et al. (2018) and Elamassie and Uysal (2019) QAM-CAP Rajalakshmi et al. (2023) and Zhao et al. (2020) CAP Xu et al. (2022) and Niu et al. (2022) Multi-Carrier DCO-OFDM Hu (2019), Hameed et al. (2022) and Essalih et al. (2020) Modulation (MCM) ACO-OFDM Tokgoz et al. (2019), Lian et al. (2019) and Essalih et al. (2020) ADO-OFDM Wei et al. (2021) QAM-OFDM Huang et al. (2018), Oubei et al. (2015) and Guo et al. (2020) Underwater visible light communication: recent advancements… Page 21 of 45 1617 Fig. 4 NRZ-OOK modulation signal (Essalih 2021) POn,OOK + POff ,OOK Pavg,ook = , (12) 2 In Li et al. (2021), UWOC system used a 450 nm blue laser source and was modulated with a 1.25 Gbps NRZ-OOK format. The use of PAM and Frequency-Domain Equaliza- tion (FDE) at the receiver is introduced in Khalighi et al. (2020),where the paper utilize SiPMs for photodetection and proposes suitable processing methods for PAM modulation and demodulation, taking into account the quantum-noise-limited receiver when a SiPM is used. 4.1.1 Pulse modulation There are several types of pulse modulation techniques used in UVLC. In the PPM, the data is modulated by varying the position of the transmitted pulses within a fixed time period (Elsayed and Yousif 2020). Each pulse represents a specific digital value or symbol. The position of the pulse within the time period is used to convey the digital information. For example, in a 4-level PPM, the timing of the pulse can be shifted to four different posi- tions within the time period to represent four different symbols as seen in Fig. 5. PPM with a traditional M-ary PPM whose symbol has k bits (log2 M ) (Mohammed et al. 2022), with M “slots” allocated to each symbol. PPM has a worse bandwidth efficiency than OOK to attain the same data rate since its bandwidth is BWPPM = MRb ∕k and the average transmit optical power is Fig. 5 PPM modulation with M = 4 (Essalih 2021) 1617 Page 22 of 45 A. Elfikky et al. 1 Pavg,PPM = ((M − 1)POff ,PPM + POn,PPM ), (13) M where (M-1) slots are “Off” and one is “On”, The optical power for “On” and “Off” states is POn,PPM and POff ,PPM. Digital Pulse Interval Modulation (DPIM) is a different kind of modulation that has a lot going for it. Since each frame in DPIM starts with only a short pulse, the receiver archi- tecture may be kept relatively simple, allowing for a higher transmission data rate (Sah- noun et al. 2017). Another modulation technique is PAM, where the data is modulated by varying the amplitude of the transmitted pulses. The number of intensity levels in PAM is determined by the bit depth. For example, if the PAM system has a bit depth of 2 bits, there will be 22 = 4 intensity levels, ranging from the minimum to the maximum amplitude that can be represented as seen in Fig. 6. PAM modulates symbols with M intensity levels. The OOK is a PAM scheme with M = 2, the power ( Pm) of a PAM can be expressed as Essalih (2021) 2mPavg Pm,PAM = + POff ,PAM , (14) M−1 where Pavg represents the average power of the signal, and M is the total number of levels. There are other various pulse modulation techniques utilized in UVLC. The PWM var- ies the width of the pulses while keeping the amplitude constant, where the width of the pulse represents the data. The variable Rate Multi Pulse Modulation (VR-MPPM) com- bines variable rate and multi-pulse modulation. The variable Pulse Position Modulation (VPPM), where the position of pulses is varied to represent different digital values, allows for efficient use of the available bandwidth. In the Differential Pulse Width Modulation (DPWM); the difference in pulse widths between successive pulses represents data. The Multiple Pulse Amplitude and Position Modulation (MPAPM) combines variations in both pulse amplitude and position to modulate the data. The Overlapping Pulse Position Modu- lation (OPPM) allows pulses to overlap in time. By carefully managing the overlapping positions, it is possible to increase the data transmission rate and improve the overall sys- tem performance. In Chi and Shi (2018), the authors conducted a comparative analysis of three advanced modulation formats (CAP, OFDM, and DFT-S OFDM) in UVLC systems. Their experi- mental findings revealed that single carrier modulations (CAP and DFT-S OFDM) out- perform OFDM, achieving impressive data rates of up to 3 Gbps over a 1.2 m underwater Fig. 6 PAM modulation with M = 4 (Essalih 2021) Underwater visible light communication: recent advancements… Page 23 of 45 1617 transmission. Authors in Ibrahimy et al. (2020) examined the performance of UVLC sys- tems with various modulations and wavelengths. They compared the BER performance of different modulations, including OOK-NRZ, On-Off Keying Return Zero (OOK-RZ), 8-PPM, and 8-PAM, at wavelengths of 450 nm, 480 nm, and 500 nm. The simulation results indicated that a wavelength of 500 nm offers the best signal-to-noise ratio (SNR) performance with a value of 13.1147 dB. Furthermore, the combination of 8-PPM with a 500 nm wavelength produces the lowest BER value of 1.8922 × 10−10, which is smaller than the BER value of optical wireless communication (OWC) at 10−9. Here, we summarize the pros and cons of the employed modulation techniques that are used for analyzing the BER performance in UVLC systems: OOK modulation is simple but energy and bandwidth inefficient. PPM is power-efficient but with poor bandwidth utilization and time synchronization obligations among the transceivers that increse the system complexity. PWM is spectrum efficient and can endure Inter Channel Interference (ICI) impair- ment, but at a high-power consumption cost. DPIM is much more spectrum-efficient than both PPM and PWM, with simple detec- tion and low complexity, but it is susceptible to time jitter, and errors can spread dur- ing the decoding process. However, the time interval utilization of DPIM, rather than amplitude and position, simplifies the transmitter design and results in power efficiency (Mi and Dong 2016). PAM is a simple, bandwidth-efficient, and cost-effective modulation scheme with ease of detection, but it is susceptible to noise and provides poor performance at high data rates. PAM require half the bandwidth of OOK to achieve the same data rates but at a higher optical power cost (Kong et al. 2018). Subcarrier Intensity Modulation (SIM) is also a spectrum-efficient but power-ineffi- cient technique, where the data is encoded in the intensity variations of subcarrier sig- nals inside the core optical carrier signal (Guler et al. 2021). Phase Shift Keying (PSK) is highly effective for achieving higher data rates and main- taining good Bit Error Rate (BER) performance. However, it is known to be power- inefficient. Cochenour et al. (2007). Polarization Shift Keying (PolSK) is a good choice to cope with underwater turbu- lence-induced fading, but it yields poor data rates (Cox et al. 2009). QAM is spectrum-efficient, but the implementation cost and complexity are very high and not suitable for UVLC systems (Oubei et al. 2015; Wang et al. 2019). There are some viable options in the literature to increase the spectrum efficiency of UVLC systems. First, a larger constellation size can yield improved spectrum efficiency, but this causes high Peak-to-Average Power Ratios (PAPRs) with nonlinear distortions and causes the optical amplifiers to operate outside their linear regime, and thus the BER performance decreases (Rappaport 2010; Ghassemlooy et al. 2013). Second, OFDM efficiently utilizes the available bandwidth by dividing it into numerous orthogonal subcarriers. For higher data rate transmission, it effectively mitigates ISI, and can dynamically adapt to chang- ing channel conditions by adjusting the modulation and coding schemes of individual sub- carriers (Armstrong 2009). However, it exhibits a high PAPR, which can lead to nonlin- ear distortions in optical amplifiers, and is also sensitive to noise (Shieh and Djordjevic 2010). Third, the diversity schemes, either Repetition Coding (RC) or Spatial Multiplexing (SMX), provide reliability and higher data rates that can yield improved BER performance and mitigate underwater turbulence-induced scintillations (Jamali et al. 2016; Chauhan 1617 Page 24 of 45 A. Elfikky et al. et al. 2022). Unlike time and frequency diversity, which needs time and bandwidth expan- sion, space diversity is a favorable choice that provides optimal spectrum efficiency by exploiting all the transmitter and/or receiver antennas (Goldsmith 2005), but this comes at the expense of higher computational as well as hardware complexity and more power con- sumption due to all active optical chains per unit processing time (Di Renzo et al. 2014). Thus, SMX and RC may not be practically feasible for UVLC systems where energy effi- ciency is of great concern. Space-Domain Index Modulation (SD-IM): Space diversity concepts can be exploited differently (Di Renzo et al. 2014; Mesleh et al. 2008) to achieve higher SE and simplify the transceiver design, providing power-efficient UVLC systems. This scheme is called SD-IM or simply spatial modulation (SM) (Elsayed and Yousif 2020), where other than the con- ventional signal constellation, some extra bits can be transmitted using antenna indices in space. This concept was successfully applied to the optical domain as well (Mesleh et al. 2011), called Optical Spatial Modulation (OSM). The work in Fath et al. (2010) proved that OSM outperforms OOK, PPM, and PAM both in terms of bandwidth and power effi- ciency. Instead of activating all transmitter antennas, only one (or few) antennas are acti- vated for signal transmission that can yield spatial gains using only one (or few) active optical chains, with the following benefits, such as higher data rates (Di Renzo et al. 2014), improved SE (Hussein et al. 2018), higher power efficiency (Stavridis et al. 2013), reduced detection complexity (Jeganathan et al. 2008), simple transceiver design due to one (or few) active antennas, and simple detection algorithm (Yang et al. 2014), No need for inter- antenna synchronization (IAS) (Di Renzo et al. 2014), compatibility with massive multiple- input multiple-output (MIMO) (Basnayaka et al. 2015). Multipath optical signal propaga- tion yields a delayed version of transmitted signals reaching the receiver. Such a significant delay gives rise to ICI. High ICI requires a complex receiver algorithm, which increases the overall system complexity (Goldsmith 2005). SM technique completely avoids ICI. For Nt transmit antennas in space and constellation signal modulation order M, the SE of SM is log2 (Nt ) + log2 (M) bits/sec/Hz per channel use, where the first term is used as a spatial index and the second term as the signal constellation. On the receiver side, the Maximum Likelihood (ML) detector (Liu et al. 2019) can easily detect the indices of both the active transmit antenna and the M-ary symbol differentiating the channel prints due to different spatial channel paths. One special case of SM is Space Shift Keying (SSK), where antenna indices are used as the only means to transfer the information (Jeganathan et al. 2009; Abaza et al. 2015). For no signal constellation with M = 1, SE yields log2 (Nt ), and this elimination of ampli- tude and phase modulation (APM) provides SSK with remarkable advantages over SM. First, the detection complexity is lowered, but the performance remains almost the same as that for SM. Second, the transceiver requirement is reduced significantly. Third, due to the reduced complexities of transceivers, the power consumption is reduced, and SSK may prove to be a strong candidate for UVLC systems. Other variants of SM are Generalized SM (GSM) (Wang et al. 2012; Alaka et al. 2015), Quadrature SM (QSM) (Mesleh et al. 2014; Bhowal and Kshetrimayum 2020), General- ized SSK (GSSK) (Jeganathan et al. 2008; Popoola et al. 2013), Quadrature SSK (QSSK) (Mesleh et al. 2014), etc., where either more than one antennas are active or in-phase and quadrature components are used independently to help further increase the energy efficiency (EE) and SE of the UVLC systems. The space modulation technique has been recently used to analyze UVLC system performance. The BER performance of the UVLC system employing SM-MIMO is studied in a weak turbulence channel (Huang et al. 2018). An approximate analytical expression for average BER expressions is derived for the Underwater visible light communication: recent advancements… Page 25 of 45 1617 SM-MIMO system in the presence of absorption, scattering, and turbulence-induced fad- ing. Huang et al. (2018) investigated SM-MIMO with flag dual amplitude PPM via channel impulse response (CIR) for harbor and coastal water and proposed a novel adaptive Power Allocation Algorithm (PAA) to minimize the average BER. This algorithm obtained even better BER performance than the MIMO while reducing the receiver complexity. Bhowal and Kshetrimayum (2020) proposed an improved quadrature spatial modulation scheme, thereby improving the UVLC system BER performance in weak oceanic turbulence. It is observed that Optically Improved Quadrature Spatial Modulation (OIQSM) yields a SNR gain of at least 5.5 dB over the conventional optical spatial modulation scheme for the BER value between 10−2 and 10−4. Unlike OSM, the number of transmit lasers need not be a power of 2 in OIQSM, unlike OSM, which is also beneficial. The increased SNR gains using OIQSM will improve BER performance in UVLC systems. Future work and challenges to improve UVLC system performance include exploring the potential of SD-IM modulation technique. SD-IM has shown promise in enhancing SE and EE while achieving higher data rates for UVLC networks. By utilizing a single (or very few) optical chain(s), SD-IM enables interference avoidance, simplifies IAS, and incurs minimal deployment costs. Thus, SD-IM can provide a compelling compromise and trade-off between SE and EE for optical IoUT. They can be very compatible if deployed with massive MIMO (Elsayed et al. 2024; Li et al. 2023), however, channel estimation may be a tricky task (Palitharathna et al. 2022). Moreover, due to the existence of multi- ple transmitters, spatial correlation impacts on system performance need to be explored. To facilitate multiple users in UVLC networks, the employment of SD-IM with NOMA can be an area to explore further (Palitharathna et al. 2022, 2021). Activation of only one transmitter per unit of time can give a bit of decreased SE that can be facilitated using more than one transmitter, ensuring that the index separation should be greater than the spatial coherence length. Thus, exploring other variants, like GSSK, GSM, QSSK, QSM, etc., can help in further improving the UVLC system performance. 5 UVLC channel modeling To design efficient transmission techniques for UVLC, it is important to have an accurate characterization and model of the optical channel. This includes understanding the various physical phenomena that affect the propagation of light underwater, such as absorption, and scattering. By accurately modeling the optical channel, it is possible to optimize the design of transmission techniques to improve the performance of the system. Underwater channel modeling is a complex and challenging task due to the dynamic and unpredictable nature of underwater environments (Boluda-Ruiz et al. 2020). As a result, researchers con- tinuously work to improve the accuracy and fidelity of these models to enhance the perfor- mance and reliability of underwater optical communication systems. For UVLC channel modeling, commonly used methods include the Beer–Lambert law, analytical RTE model, and Monte Carlo ray tracing (MCRT) simulations (Ghonim et al. 2021). Table 6 presents a summary of different approaches used in channel modeling for UVLC. Each modeling approach has its unique advantages and disadvantages. The authors in Jamali et al. (2018) used a general channel model that incorporates absorption, scatter- ing, and turbulence effects to analytically study the BER performance of UVLC systems with binary pulse position modulation (BPPM). The approach proposed by Li et al. (2018) 1617 Page 26 of 45 A. Elfikky et al. Table 6 Summary of the channel modeling approaches Modeling Approach Advantages Disadvantages Beer–Lambert’s Law Simple Inaccurate Analytical RTE Analytical results Very difficult derivation Numerical RTE Easy programming Low efficiency in case of errors Monte-Carlo Accurate in simulation environ- Low errors ment modeled the impulse response in UOWC channels, providing a better understanding of the behavior of the channel and improving the accuracy of numerical fitting in most cases. The study on channel modeling, as detailed in Miramirkhani and Uysal (2018), delved into the in-depth modeling and characterization of channels in the context of UVLC. The investigation involved the analysis of multiple underwater scenarios, each with varying transmitter and receiver specifications and depths, providing a detailed characterization of channel parameters for each unique scenario. The results in Zhang et al. (2020) suggested that a Single-Input Multi-Output (SIMO) channel model could be employed in both turbu- lent and highly turbid UWOC. The study by Ghazy et al. (2019) proposed the utilization of angular MIMO (A-MIMO) as an alternative architecture for MIMO UWOCs, instead of conventional underwater MIMO systems(C-MIMO). The authors in Fu et al. (2023) proposed an improved-order successive interference cancellation (I-OSIC) algorithm that integrates partition space-time block coding (STBC) to address sub-channel correlation in underwater optical massive MIMO systems. 5.1 Dynamic channel model The underwater environment is inherently dynamic (Elfikky et al. 2023) and this dyna- mism arises from multiple interrelated factors. Firstly, water, as the medium for underwater communication, is in perpetual currents, and turbulence driven by wind and environmental elements contributes to this ceaseless movement (Ali and Jayakody 2023). Consequently, the behavior of underwater communication signals can be significantly influenced by the fluid nature of water (Wang et al. 2016). Secondly, the underwater propagation medium is not uniform; it exhibits variations in salinity (Ata et al. 2021), temperature [?], and pres- sure. These factors are not constant and can lead to signal refraction, absorption, and scat- tering, introducing dynamic complexities (Pan et al. 2022). Additionally, marine life plays a substantial role in this dynamism. The presence of fish and marine mammals can lead to unpredictability as their movements cause turbulence and signal scattering diminishes the quality of the transmission signal (Li et al. 2019). Moreover, underwater conditions change rapidly due to various factors, including weather, seasonal variations (Uitz et al. 2010), and geological events, further contributing to the dynamic nature of the underwa- ter environment (Uitz et al. 2006). Finally, noise (Lin et al. 2022; Morra et al. 2013)and interference sources in the underwater realm are pervasive, arising from industrial activi- ties and electronic equipment. Understanding and accommodating these dynamic factors is essential for establishing reliable underwater communication systems in this ever-changing environment (Li et al. 2019). Additionally, it is crucial to remain updated on advancements in channel modeling techniques. Underwater visible light communication: recent advancements… Page 27 of 45 1617 Emphasizing the dynamic nature of the underwater environment is critical for accurate modeling and effective communication (Mahmoud et al. 2021; Romdhane and Kaddoum 2022). Neglecting this dynamism can lead to misleading outcomes. Advanced simulation techniques are essential for capturing the complexities of the dynamic underwater channel. Additionally, integrating Machine Learning (ML) can facilitate the detection and under- standing of behaviors of this dynamic nature (Salama et al. 2023; Romdhane and Kaddoum 2022). Accurate modeling and data analysis are vital for improving underwater communi- cation performance in real-world scenarios. The authors in Miramirkhani and Uysal (2018) presented a detailed investigation into the channel modeling and characterization for UVLC using advanced ray tracing tech- niques. The study took into account several factors such as sea surface and bottom reflec- tion characteristics, water properties, and the presence of human and man-made objects to analyze the effects of shadowing and blockage. The analysis considered various trans- mitter/receiver specifications and depths from the sea surface, obtaining channel impulse responses and characterizing key channel parameters such as DC gain, path loss, and delay spread. The authors in Elamassie et al. (2018) developed a cLoSed-form path loss expres- sion based on transceiver parameters and water type, which can be used to determine the maximum achievable link distance for UVLC systems with a specified BER. Numerical results are provided for different water types, including pure sea, clear ocean, coastal water, and harbor water. In Ijeh et al. (2021), the authors investigated transmitter-receiver param- eter optimization for a vertical UWOC link under misalignment conditions. The study investigated the optimization of the transmitter and receiver parameters to improve the link performance in terms of outage probability without the need for MC simulations. 5.2 The Beer–Lambert law The attenuation of light during its propagation through water can be captured by the Beer–Lambert law, which is used as a standard and basic mathematical model to repre- sent the underwater channel. This approach relies on a decay function that exponentially decreases and is commonly used to obtain optical path loss, which is given by Mobley et al. (1993), Giles and Bankman (2005) I = Io e−c(𝜆)z , (15) where, the intensity of light, denoted as I, is a measure of light strength after it has propa- gated a distance z through water. Io represents the initial intensity of light before it enters the water. The attenuation coefficient of water, c(𝜆), is wavelength-dependent, influencing the absorption of light as it travels through the medium. While the Beer–Lambert law provides a simple and intuitive way to estimate light attenuation, it does not take into account the complex interactions between light and water molecules, and may not be accurate in all underwater scenarios. The Beer–Lambert law is based on an unrealistic assumption that all the scattered photons are LoSt. In practice, after multiple scattering events, some of the scattered photons can still reach the receiver. This means that the Beer–Lambert law may underestimate the received power, especially in scenarios dominated by scattering (Li et al. 2015). The path loss formula by Elamassie et al. (2019) introduces modifications to the well-known Beer–Lambert formula. The mod- ification introduces an additional term in the Beer–Lambert formula, accounting for scat- tered rays received by the detector. The proposed expression explicitly includes the beam 1617 Page 28 of 45 A. Elfikky et al. divergence angle, receiver aperture diameter, and extinction coefficient (related to water type), making it applicable to a wider range of water types. 5.3 Radiative transfer equation The underwater light propagation is completely described by the Radiative Transfer Equa- tion (RTE) (Mobley 1994). The RTE is used to model light propagation underwater since it effectively describes the energy conservation of a light wave crossing a scattering medium, which is given by Johnson et al. (2013), Illi et al. (2018) [ ] 1𝜕 + n ⋅ 𝛁 I(t, r, n) v 𝜕t ∫4𝜋 = 𝛽(r, n, n′ ) I(t, r, n′ ) dn′ (16) − cI(t, r, n) + E(t, r, n). where I represents the intensity of the electromagnetic wave at time t and position r , in the direction of unit vector n., 1v 𝜕t𝜕 represents the time derivative of the intensity divided by the wave velocity v., n ⋅ 𝛁 represents the dot product of the direction vector n with the gradient operator 𝛁, signifying the spatial derivative along n, 𝛽(r, n, 𝐧 ) is the Volume Scattering Function (VSF), representing the probability of scattering from direction n to direction 𝐧′ at position r , I(r, n, 𝐧 ) represents the intensity of the electromagnetic wave scattered from direction n to direction 𝐧′ at position r , ∫4𝜋 denotes the integration over all possible direc- tions, cI(t, r, n) represents the scattering term, which is the product of the extinction coef- ficient c,which is the summation of the absorption coefficient, scattering coefficient, and intensity I at time t and position r in the direction n., E(t, r, n) represents directed light source radiance at time t and position r in the direction n. 5.3.1 Analytical RTE The RTE presents a complex integro-differential equation involving time and space, mak- ing it difficult to find precise analytical solutions (Li et al. 2015). Although some approxi- mate analytical solutions have been suggested in recent years, they heavily depend on simplifying assumptions. Nonetheless, achieving an exact analytical solution for many practical applications of UVLC remains exceedingly challenging. Cochenour et al. (2008) utilized the Small Angle Approximation (SAA) as a simplifying assumption to address the complexities of solving the RTE. The SAA relies on specific assumptions about the behav- ior of light scattering in the medium. Analytical RTE models can provide more accurate results than the Beer–Lambert law, but they can be computationally intensive and may require simplifying assumptions (John- son et al. 2013). Solutions to the RTE using analytical methods are only possible for a restricted set of geometries (Li et al. 2018). Analytical RTE models are more complex and utilize mathematical equations to describe how light interacts with water molecules. These models consider properties like absorption and scattering coefficients to simulate light behavior in various underwater environments. As a result, numerical methods are often preferred over analytical solutions for solving the RTE. Researchers typically focus on two numerical approaches: numerical methods and MC methods. Jaruwatanadilok (2008) Underwater visible light communication: recent advancements… Page 29 of 45 1617 has applied the vector radiative transfer theory to gain valuable insights into the impulse response, channel performance, attenuation, and optical characteristics of UWOC chan- nels. These insightful models have been employed to assess the feasibility and performance of UWOC systems, taking into account important factors like absorption, scattering, and signal degradation. 5.3.2 Numerical RTE The numerical solutions of the RTE can be achieved through two main approaches: proba- bilistic and deterministic methods Li et al. (2015). Among these, the MC simulation is frequently utilized as a probabilistic method to solve the RTE numerically. Li et al. (2015) developed a quick and efficient numerical solver for the RTE to calcu- late the UOWC system received power. Simulations showed that the suggested technique estimated received power with accuracy comparable to MC simulations and the uniform solver while drastically lowering computational time. They achieved this by converting the general time-dependent three-dimensional (3D) RTE into a two-dimensional (2D) RTE as follows: n⃗ ⋅ ∇L(⃗r, n⃗ ) = −cL(⃗r, n⃗ )+ (17) ∫2𝜋 𝛽(⃗n, n⃗ )L(⃗r, n⃗ )d⃗n + E(⃗r, n⃗ ), where L(⃗r, n⃗ ) represents the radiance at position ⃗r and direction n⃗ , n⃗ ⋅ ∇ is the dot product of the direction vector n⃗ with the gradient operator ∇, c is a coefficient representing the absorption of radiance. The term ∫2𝜋 𝛽(⃗n, n⃗ )L(⃗r, n⃗ )d⃗n represents the integral of the scat- tering phase function 𝛽 over all possible directions n⃗ ′, accounting for the scattering of radi- ance from direction n⃗ ′ to n⃗. Illi et al. (2018) proposed an enhanced numerical framework to evaluate the time- dependent RTE for UOWC systems, predicting optical path-loss and evaluating BER performance. The authors of Illi et al. (2019) proposed an improved numerical solver for time-dependent RTE in UOWC, considering three scattering functions for Harbor-I and Harbor-II water types. The algorithm generated the normalized received power and ana- lyzed BER performance for different parameters, performing similarly to MC by optimiz- ing angles and computation. 5.4 Monte Carlo The MC numerical simulation method is employed to calculate the received power in underwater optical communication systems (Cox and Muth 2014)

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