# Chapter 4

# Propagation Model

“*Definition of free space propagation: In a homogeneous space comparable to the vacuum, the radiated energy of an isotropic source propagates at light speed and uniformly spread over the surface of a sphere whose radius increases with time*.”*Fundamentals of Radio Propagation*,Jacques Deygout, Eyrolles, Paris, 1994

# 4.1. Introduction

The aim of this chapter is to give a description of a baseband wireless optical link. First, we compare the modeling of the system to a radio system. Then, we describe the disruptive noises and define the electrical signal-to-noise ratio (SNR). Finally, an analysis of the diffuse channel is performed and different calculation models are presented.

# 4.2. Baseband equivalent model

In this section, the radio propagation principles are first remembered and compared to those of free-space optical ones. Finally, a baseband free-space optical link model is presented.

## 4.2.1. *Radio propagation model*

We can define a real signal *f* (*t*), located in a narrow frequency band around a carrier frequency *f*_{0}. When the frequency band occupied by *f*(*t*) is small compared to *f*_{0}, the signal can be called narrowband signal or passband signal. It can be written in terms of its complex envelope in the following form:

where *f*_{0} is the carrier frequency, *a*_{f}(*t*) is the complex envelope of the signal, ...