A Direct Radiative Transfer Equation Solver for Path Loss Calculation of Underwater Optical Wireless Channels

In this letter, we propose a fast numerical solution for the steady state radiative transfer equation in order to calculate the path loss due to light absorption and scattering in various type of underwater channels. In the proposed scheme, we apply a direct non-uniform method to discretize the angular space and an upwind type finite difference method to discretize the spatial space. A Gauss-Seidel iterative method is then applied to solve the fully discretized system of linear equations. The accuracy and efficiency of the proposed scheme is validated by Monte Carlo simulations. Index Terms Radiative transfer equation, underwater optical path loss, finite difference method, Gauss-Seidel iteration.