## 4 Monte Carlo Simulation
### MC Techniques for Photon Propagation in Turbid Medium
Every photon's journey is stored and utilised to determine received power, CIR, and other variables. The simulation begins by setting the inputs to their default values. Next, the photon launch starts in accordance with the distribution profile of the source, with a calculated angle of photon emission calculated by applying the source's radiation pattern probability distribution function. The photon's original location is specified via its coordinates \(x,~{}y,~{}z\) and the direction vector: \(\mu_{x}~{},~{}\mu_{y},\) and \(\mu_{z}\). After that, the photon will travel in a step size before  
Figure 13: MCS methods. becoming absorbed or scattered. The water's attenuation coefficient defines the photon's distance across any of the two following processes. Photons are regarded as gone if they go beyond the border. Part of the photon's energy will be absorbed, while other parts will be spread in various directions when it collides with another particle. When a photon arrives at the receiver, its position, weight, and distance travelled will be stored for further analysis. This operation continues until all the photons are released [48; 139]. According to the description of photon step size \(l\) in Equations (64)-(68), the distance travelled by the photon from its origin \(r_{0}\), which is expressed in Equation (61), can be calculated. Following that, it is critical to determine what the following event is. It can be decided using the single-scattering albedo \(w_{0}\). Because it represents the possibility that the photon will scatter rather than absorb, the \(w_{0}\) parameter is the likelihood of surviving photons. To carry it out, the AR approach is utilised, which involves picking a random value of \(q\) from a uniform distribution to define the following event type. The \(q\) can take any value of \(0\ \leq\ q\ \leq\ 1\). \[event= \begin{cases}absorption,\ for\ q\leq w_{0}\\ scattering,\ for\ q>w_{0}\end{cases} \]  
The term AR originates from two circumstances. The first one is that the photon will terminate when it absorbs, and its location is stored for future calculations. Secondly, when the photon scatters, the scattering angles should be determined to adjust the transmission path [66]. After the scattering event, the computation of one of the equations listed in Table 4 that represents the elected SPF regime helps to provide the value of \(\cos\theta_{k,m}\) to conclude the photon's new position using Equations (64) to (68) for individual photons and Equations (69) to (72) for the whole travelled distance of one-photon. To deduce the received photons' profile, we need to assess the level of details of the use case under consideration and, based on which, we elect one of the relevant equations from the Equations (43) and (44). However, unlike FSO channels, photons would hit a significantly greater amount of particles in an underwater environment. Hence, many scattering events play a big part in obtaining optical power compared with optical wireless communication channels [66]. Few measurements are available, with some originating from Petzold, due to the difficulty in distinguishing the scattered photons from the incident ones across small forward angles and the wide range of scattering amplitudes throughout the whole domain of scattering angles.