An Improved Accurate Solver for the Time-Dependent RTE in Underwater Optical Wireless Communications

Underwater optical wireless communication (UOWC) has been widely advocated as a viable way to satisfy these high-speed links constraints in the marine medium through the use of the visible spectrum. Nevertheless, UOWC faces several limitations, such as the path-loss due to the absorption and scattering phenomena, caused by underwater particles. Thus, quantifying this path-loss is of paramount importance in the design of futuristic UOWC systems. To this end, several approaches have been used in this regard, namely the Beer-Lambert's law, Monte Carlo simulation, as well as radiative transfer equation (RTE). This last mentioned evaluates the optical path-loss of the light wave in an underwater channel in terms of the absorption and scattering coefficients as well as the scattering phase function (SPF). In this paper, an improved numerical solver to evaluate the time-dependent RTE for UOWC is proposed. The proposed numerical algorithm was improved based on the previously proposed ones, by making use of an improved finite difference scheme, a modified scattering angular discretization, as well as an enhancement of the quadrature method by involving a more accurate seven-point quadrature scheme in order to calculate the weight coefficients corresponding to the RTE integral term. Importantly, we applied the RTE solver to three different volume scattering functions, namely the single-term Henyey-Greenstein (HG) phase function, the two-term HG phase function, and the Fournier-Forand phase function, over both Harbor-I and Harbor-II water types. Based on the normalized received power evaluated through the proposed algorithm, the bit error rate performance of the UOWC system is investigated in terms of system and channel parameters. The enhanced algorithm gives a tightly close performance to its Monte Carlo counterpart by adjusting the numerical cumulative distribution function computation method as well as optimizing the number of scattering angles.