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

## TL;DR

This paper introduces an improved numerical solver for the time-dependent radiative transfer equation in underwater optical wireless communications, enhancing accuracy and efficiency over previous methods and validating with simulations.

## Contribution

The paper presents a novel, more accurate finite difference and quadrature scheme for solving the RTE, with modifications to scattering discretization and application to various phase functions.

## Key findings

- Enhanced solver closely matches Monte Carlo results
- Improved accuracy in calculating optical path-loss
- Optimized scattering angle discretization improves performance

## Abstract

In this paper, an improved numerical solver to evaluate the time-dependent radiative transfer equation (RTE) for underwater optical wireless communications (UOWC) is investigated. The RTE evaluates the optical path-loss of light wave in an underwater channel in terms of the inherent optical properties related to the environments, namely the absorption and scattering coefficients as well as the phase scattering function (PSF). The proposed numerical algorithm was improved based on the ones proposed in [1]-[4], by modifying the finite difference scheme proposed in [1] as well as an enhancement of the quadrature method proposed in [2] by involving a more accurate 7-points quadrature scheme in order to calculate the quadrature weight coefficients corresponding to the integral term of the RTE. Furthermore, the scattering angular discretization algorithm used in [3] and [4] was modified, based on which the receiver's field of view discretization was adapted correspondingly. Interestingly, the RTE solver has been applied to three volume scattering functions, namely: the single-term HG phase function, the two-term HG phase function [5], and the Fournier-Forand phase function [6], over 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 improved based on the simulations provided in [7], by adjusting the numerical cumulative distribution function computation method as well as optimizing the number of scattering angles. Matlab codes for the proposed RTE solver are presented in [8].