**3.6. Total attenuation**

Atmospheric attenuation of FSO system is typically dominated by haze, fog and is also dependent on rain. The total attenuation is a combination of atmospheric attenuation in the atmosphere and geometric loss. Total attenuation for FSO system is actually very simple at a high level (leaving out optical efficiencies, detector noises, etc.). The total attenuation is given by the following [34]:

$$\frac{P\_r}{P\_t} = \frac{d\_2^2}{\prod\_{l\_1} + \text{(\text{\textdegree L}\_l\text{\textdegree}}} \times \exp\text{(-\beta L \text{ \textdegree L}\_l\text{)},\tag{34}$$

where,

ω(l)2= ωo

is the initial beam waist at

In which

ωo

The effective waist,

center will be equal:

, its path length

over an area of

**3.5. Geometric Losses (GL)**

L

π(Lθ

term.

θ

Where:

While the parameter Λ is given by:

184 Contemporary Issues in Wireless Communications

ωeff (l

As seen in other turbulence figure of merits,

L BE= 20

transmitter power, *P*r is spread over an area of *π*(*Lθ*)

be determined by the formula stated as [2]:

*d*2 is the diameter receiver aperture (unit: m);

beam path. Evidently, due to the fact that

<sup>2</sup> <sup>+</sup> ( <sup>2</sup>L

> L= 0,

strength of turbulence and beam path. Particularly, *T* for horizontal path, one gets:

σi

kω2(l

> ωeff (l

The geometric path loss for an FSO link depends on the beam-width of the optical transmitter

of the optical transmitter *θ*, its path length *L* and the area of the receiver aperture Ar. The

area of the receiver aperture to the surface area of the transmitter beam at the receiver. Since the transmit beams spread constantly with increasing range at a rate determined by the divergence, geometric loss depends primarily on the divergence as well as the range and can

> d2 2

d<sup>1</sup> + (Lθ

ωeff (l)>ω(l

log 10(ω(l) / ωeff (l

and the area of the receiver aperture

geometric loss=

2 Λ

caused by the turbulence. As seen in other turbulence figure of merits,

T= 1.33

> Λ <sup>=</sup> <sup>2</sup>L

kωo )<sup>2</sup> (m2

T

) (29)

T

depends on the

: is the additional spreading of the beam

5/6 (30)

) (31)

)<sup>2</sup> depends on the turbulence strength and

) beam will experience a loss that at beam

)) (32)

Pt

is spread

*.* The transmitter power,

2/4. Geometric loss is the ratio of the surface

) <sup>2</sup> (33)

), describes the variation of the beam irradiance averaged over long

Ar

)<sup>2</sup> / 4. The geometric path loss for an FSO link depends on the beam-width

*P*t is the transmitted power (unit: mW);

*P*r is the received power (unit: mW);

*θ* is the beam divergence (unit: mrad);

*β* is the total scattering coefficient (unit: km-1).

According to Eq. (34), the variables which can be controlled are the aperture size, the beam divergence and the link range. The scattering coefficient is uncontrollable in an outdoor environment. In real atmospheric situations, for availabilities at 99.9% or better, the system designer can choose to use huge transmitter laser powers, design large receiver apertures, design small transmitter apertures and employ small beam divergence. Another variable that can control is link range, which must be of a short distance to ensure that the atmospheric attenuation is not dominant in the total attenuation [35].

The strength of scintillation can be measured in terms of the variance of the beam amplitude or irradiance *σ*<sup>i</sup> given by the following:

$$
\sigma\_1^2 = 1.23 \, C\_n^2 \, k^{7/6} \, L \quad^{11/6} \tag{35}
$$

Here, *k*=*2π*/*λ* is the wave number and this expression suggests that longer wavelengths experience a smaller variance, and Cn 2 is a refractive index structure parameter. Equation (35) is valid for the condition of weak turbulence mathematically corresponding to *σ<sup>i</sup>* 2<1. Expres‐ sions of lognormal field amplitude variance depend on the nature of the electromagnetic wave traveling in the turbulence and on the link geometry.

In this chapter, we do not take into account the atmospheric turbulence, because its influence in Yemeni climate could be negligible. That means the effect of the turbulence is too small contrary to visibility and geometric loss. Therefore, we have taken into account only the total attenuation depending on visibility, and geometric loss.

An FSO communication system is influenced by atmospheric attenuation, which limits their performance and reliability. The atmospheric attenuated by fog, haze, rainfall, and scintillation has a harmful effect on FSO system. The majority of the scattering occurred on the laser beam is Mie scattering. This scattering is due to the fog and haze aerosols existed at the atmosphere and can be calculated through visibility. FSO attenuation at thick fog can reach values of hundreds dB. Thick fog reduces the visibility range to less than 50 m, and it can affect on the performance of FSO link for distances. The rain scattering (non-selective scattering) is inde‐ pendent on wavelength, and it does not introduce significant attenuation in wireless infrared links, it affects mainly on microwave and radio systems that transmit energy at longer wavelengths. There are three effects on turbulence: scintillation, laser beam spreading and laser beam wander. Scintillation is due to variation in the refractive index of air. If the light is traveled by scintillation, it will experience intensity fluctuations. The geometric loss depends on FSO components design such as beam divergence, aperture diameter of both transmitter and receiver. The total attenuation depends on atmospheric attenuation and geometric loss. To reduce total attenuation, the effect of geometric loss and atmospheric attenuation is small, as FSO system must be designed. The following section explores the simulation results of geometric loss and total attenuations for Yemeni climate.
