## 5 Conclusions and Future Work  
This research defines the steps to develop a mathematical optical receiver design optimization technique. This approach involves applying the time-invariant feature of the optical receiver system to formulate an overall MGF design model. Hence, this model describes the underlying system signal lifecycle dynamics, which includes system attributes and processes. Consequently, such a design model aims to optimize the underlying system performance to overcome the limitations imposed by the existing signal impairments due to various potential processes. Our work demonstrates how the MGF modelling design furnishes a closed-form optical receiver filter equation (ORFE). The ORFE equation includes a transmitted optical signal \(s(t)\), propagation channel impulse response \(h_{c}(t)\), received optical pulse \(\lambda(t)\), photodetector efficiency \(\mu\), and photoelectron generation processes \(g\), which equals one for PIN  
Figure 10: Use Case III: The impact of the optimum filter on the Optical receiver system performance in terms of the Q-Factor (\(\propto\) SNR) and log(BER). photodetector, ISI, and AGTN noise associated with the amplifier circuitry. Also, this work explains the necessary steps to optimize the solution of ORFE. ORFE incorporates both the optical and receiver electronic domain boundaries of the UWOC system. The optical domain includes the optical attributes set \(\{s(t),h_{c}(t),\lambda(t)\}\) and the associated optical process set {optical digital signal modulation, propagation channel impulse response} of UWOC. The electronic domain contains the photoelectron conversion process and its attribute set \(\{\mu,g,N(t)\}\), the photodetector backend electronic circuitry process \(\{\sigma 2\text{nd}\}\), and the equalization and filtering process \(\{h_{f}(t)\}\). To show the reliability of our modelling design, we deployed three use cases covering simple and complex scenarios of linear optical receivers for the UWOC system. The validity of the proposed new optical receiver modelling design was based on results comparison with closely related published MCB works. Through this, we also identified one potential weakness of MCB optimization. In conclusion, our MGF modelling methodology is more reliable than the CB and MCB design approaches. Our new MGF design modelling approach preserves the limits between the general solution and optimum space due to the \(J\) optimization. So, their undershoots, depths, and variations are different rather than uniform for CB and MCB filters [10; 16]. Also, it is worth noting that the analytical solution of use case II for the white AGTN noise exhibits undershoot when including ISI. Such behavior indicates that the undershoot is an intrinsic behavior of the solution rather than curve interpolation by the curve fitting library. Here, we do not mean that the numerical solution will not be subjected to changes due to possible higher fitting polynomial values. From Figures 9 and 10, we can conclude that the proposed optimum filter \(h_{f}\) reduces O\({}_{\text{eye}}\) by nearly 10-15% for five times increase in optical pulse width (pw). This outcome indicates that the optimum \(h_{f}\) manages the power dispersion correctly. Similarly, suppose the changes in pw values are mapped as the transmitted pulse broadening due to ISI impairment sources like scattering and scintillation. In that case, we can conclude that the proposed optimum filter \(h_{f}\) efficiently deals with the seawater impairments projected by the seawater channel model. Conceptualization, I.F.E.R. and Y.A.-H.; Methodology, S.M.A. and N.M.B. ; Software, I.F.E.R., S.M.A. and N.M.B. ; Validation, I.F.E.R., N.M.B. and A.Z.B. ; Formal analysis, I.F.E.R. and Y.A.-H.; Investigation, I.F.E.R., S.M.A., Y.A.-H. and A.Z.B. ; Writing--original draft, I.F.E.R. ; Writing--review & editing, S.M.A., N.M.B., Y.A.-H. and A.Z.B. ; Visualization, I.F.E.R. All authors have read and agreed to the published version of the manuscript.