**Abstract**

The radiative transfer equation (RTE) is a theoretical framework that can be used for predicting and interpreting underwater light fields in terms of the constituents of natural water bodies. However, the RTE is a complex integrodifferential equation and deriving exact solutions for it is a difficult task. In this chapter, we aim to present some details regarding Monte Carlo simulations and how this method may be applied to solve the RTE numerically. By solving the RTE, one may accurately predict the received power and estimate the channel bandwidth and several other measurable parameters with regard to multiple water conditions. Simulations will also be presented.

**Keywords:** RTE, underwater, optical, wireless, channel, propagation, photons, UOWC

### **1. Introduction**

When compared with free space optical (FSO) communication channel, the underwater optical wireless communication (UOWC) shows unique characteristics. Because of this, the channel models usually used in FSO are not suited for UOWC, and different channel models must be developed to describe the different photon interactions under play.

Mobley [1] classified the optical properties of water into two different groups, inherent optical properties (IOPs) and apparent optical properties (AOPs). The two major IOPs that will attenuate light propagation in UOWC are absorption and scattering. Hence, any attempt in modeling the UOWC channel will need to consider absorption and scattering effects within specific link configurations.

Several theoretical models were employed by researchers to model the UOWC channel, being the Beer-Lambert law the most employed due to its simplicity [2]. Despite its simplicity, the Beer-Lambert law contains two implicit assumptions: that the transmitter and receiver are perfectly aligned and that all scattered photons are lost. The assumption that all photons that undergo scattering are lost will severely underestimate the received optical power, especially in water environments where scattering is the dominant IOP.

Another theoretical model for modeling the underwater channel is the radiative transfer equation (RTE) [3]. The RTE simply says that as a beam of radiation travels through a medium, in this case water, it will lose energy to absorption, gain energy by emission, and redistribute energy by scattering. Yet, as the RTE is an

integrodifferential equation involving different independent variables, an exact analytical solution is hard to find. In view of this, solving the RTE numerically is a preferred approach, being the most popular one the Monte Carlo simulation.
