## 4 Monte Carlo Simulation
### MCS Implementation Results--A Quick Preview
Second, in both use cases, the \(f^{\prime}s\) profiles (Equations (74) and (77)) for all seawater types are distinguishable in general. Also, in Figure 17, we can observe that the \(f\) curves depict a DGF-fitted profile with Rytov variance around 100; this means that both regimes indicate the dominance of the scattering loss component regardless of the related IOP impairment (single scattering, scintillation, turbulence, etc.). The impact of doubling the \(w\) in both use cases is noticeable. It is worthwhile reminding the reader here that the profile of f (i.e., received scattered photons vs. time) represents \(h_{opt}(t)\), which is the received optical pulse (Section 2.1). To deduce the impulse response function of the seawater channel \(h_{c}(t)\), we need to execute a deconvolution (not the convolution) operation:  
\[h_{c}(t)=h_{p}(t)*h_{opt}(t)\] deconvolution (82)  
Third, Table 3 indicates the ascending of the scattering level across the seawater types. Hence, we expect the lowest \(f(h_{opt}(t))\) peaks. Figure 17 reflects this guiding turbid scattering. Nevertheless, there is a crossing in the harbor and turbid profiles for the scenario of (\(L\), \(w\)) = (4 m, 0.6) for both computational regimes, HG-SPF and FURS. This issue could be attributed to the computation-handling bug in handling the histogram bins of the collected MCS results. Such computational bugs are attributed to the near values of the albedo for the harbor and turbid waters. Fourth, while the impact of \(w\) on the maximum number of the received photons is not prominent across the water types, it impacts the \(f\)'s profile tail spread, which proportionally increases by higher \(w\) and \(L\). Fifth, the UOWC light attenuation in different water types is depicted in Figure 18. The main observation we can conclude is that the general attenuation curves are as expected, i.e., higher \(L\), and more light attenuation (i.e., less received photons) regardless of the \(w\). Furthermore, we can detect that turbid and harbor waters have less inclination than clear and coastal waters. Such behaviour can be attributed to scattering being more dominant than absorption in turbid and harbor waters than in clear and coastal waters. Sixth, the MCS code can produce the impact of the photon propagation along the z-direction in seawater by capturing snapshots of the scattered photon distributions on the (x,y) planes. To achieve this, we must ensure that the initial photon positions are created as tiled _dnarray_ with a size equal to the transmitted photons (\(K\)). Each unit of the tiled array should be a copy of a position equal to \(np\_array\)([0, 0, 0], \(dtype\) = \(np\_float64\)) and a z-direction equal to \(np\_array\)([0, 0, 1], \(dtype\) = \(np\_float64\)). Figures 17 and 18 are part of the foundations that must be provided in MCS work. To further analyse the result of MCS programme runs, we need to (1) conclude the profile of \(h_{c}(t)\) using a deconvolution of \(h_{opt}(t)\) with \(h_{p}(t)\) as we stated earlier and (2) compare the frequency response bandwidth of \(h_{p}(t)\), \(h_{opt}(t)\), and \(h_{c}(t)\) to show the impact of the \(h_{c}(t)\) on \(h_{p}(t)\) bandwidth. Typically, it is expected that \(h_{opt}(t)\) has a narrower bandwidth compared to that of \(h_{p}(t)\) and \(h_{c}(t)\). The signal bandwidth narrowing might not be easy to conclude; then, drawing the eye diagram for \(h_{opt}(t)\) creates a complementary diagram to complete the description of the impact on \(h_{p}(t)\). The eye diagrams of \(h_{opt}(t)\) allow us to compute the Q-Factor, which is equivalent to the optical SNR. Deducing the Q-Factor helps us to compute the BER. To obtain a series of Q-Factor values, we need to execute many runs with different \(K\) values for the same \(L\), or we can fix the \(K\) value with different \(L\) values.