# Atmospheric Effects on Satellite-Ground Free Space Uplink and Downlink Optical Transmissions
## 2 Uplink and Downlink Channels in Satellite-Ground FSO Communications
### Atmospheric Turbulence  
The diurnal cycle and the varying rates at which sunlight heats and cools the Earth cause significant variations in air temperature. The refractive index of air fluctuates arbitrarily as a result of random temperature changes, creating turbulence in Earth's atmosphere [20]. Turbulent cells, also known as eddies, will form as a result of turbulence and will vary in size and refractive index [18]. The distortion brought on by this phenomenon affects how light travels through the atmosphere. Consequently, a laser beam suffers distortions on a satellite-ground FSO link. Beam spreading (beyond that caused by pure diffraction), random changes in the location of the beam centroid (beam wander), and random redistribution of beam energy within a cross-section of the beam (irradiance fluctuations) are all effects of wavefront distortions in the optical wave caused by atmospheric turbulence [7]. When the magnitude of turbulence eddies exceeds the size of the beam, the phenomenon known as beam wander occurs. The beam will be randomly deflected from its propagation route, which causes link failure. On uplink, the transmitted laser beam is distorted by atmospheric turbulence near the transmitter, and hence, the laser beam, for a long period of propagation, suffers from free space diffraction. Therefore, along with scintillations, beam wander is a major concern for the uplink channel [7]. When the size of the eddies is less than the size of the beam, beam spreading is taken into consideration. In this scenario, the incoming beam will be separately diffracted and scattered, causing the received wavefront to be distorted [2]. The atmospheric turbulence close to the ground interferes with satellite-ground laser communications, but for most of the path, the beam largely travels over free space. As a result, the beam is quite broad when it encounters the atmospheric layer. Hence, scintillations and angle-of-arrival variations are the main issues with downlink propagation channels [7]. The scintillation index, which is a function of the refractive index structure parameter, is used to measure atmospheric scintillation. The refractive index structure parameter, denoted as \(\text{C}_{\text{n}}\)2 and developed by [PERSON], is an essential parameter for measuring the level of refractive index variation in atmospheric turbulence [18]. The refractive index structure is constant for horizontal paths but should be considered to vary throughout the propagation path for vertical links. The Hufnagel Valley model is a heuristic model that uses the refractive index parameter to characterize turbulence conditions. The model predicts that the refractive index structure parameter at altitude h can be expressed as follows [1]:  
\[\text{C}_{\text{n}}^{2}(\text{h})=0.00594\times\Big{(}\frac{\text{v}_{\text{ wind}}}{27}\Big{)}^{2}\Big{(}10^{-5}\times\text{h}\Big{)}^{10}\times\text{e}^{- \frac{\text{h}}{1000}}+2.7\times 10^{-16}\times\text{e}^{-\frac{\text{h}}{1500}}+ \text{A}\;\times\text{e}^{-\frac{\text{h}}{100}} \tag{5}\]  
where h is the height above sea level in meters, A is the nominal value of \(\text{C}_{\text{n}}\)2(0) at the ground in \(\text{m}^{-2/3}\) and \(\text{v}_{\text{wind}}\) is the rms wind speed in meters per second. Equation (5) clearly shows that the refractive index structure parameter depends on wind speed and altitude above sea level, which depend upon the spatial location of the receiver and the time of day. Hence, the spatial location of the receiver and the time of day play a vital role in the system design of FSO links for satellite-ground and ground-satellite channels. An essential FSO channel parameter that depends on \(C_{n}{}^{2}\) is the atmosphere's coherence length. Coherence length describes the spatial coherence characteristic of a light wave moving in an unsteady environment. The coherence length is typically in the 5 cm to 30 cm range.