On the Use of a Direct Radiative Transfer Equation Solver for Path Loss Calculation in Underwater Optical Wireless Channels

In this letter, we propose a fast numerical solution for the steady state radiative transfer equation based on the approach in [1] in order to calculate the optical path loss of light propagation suffering from attenuation due to the absorption and scattering in various water types. We apply an optimal 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. Finally, we extend the resulting radiance in 2-dimensional to 3-dimensional by the azimuthal symmetric assumption to compute the received optical power under the given receiver aperture and field of view. The accuracy and efficiency of the proposed scheme are validated by uniform RTE solver and Monte Carlo simulations.