# Data-Aided and Non-Data-Aided SNR Estimators for CPM Signals in Ka-Band Satellite Communications
## 2 Channel Model of Ka-Band Satellite Communication  
### Attenuation Factor  
Many factors in the atmosphere cause the additional decline of the signal in the Ka-band satellite communication, precipitation, water vapor, clouds, oxygen, and flickers. The most important factor is rain attenuation, which is related to frequency, weather conditions, and system availability. These factors can be considered in the satellite communication link by modifying the free space propagation formula. Signal fading caused by rainfall is the most serious propagation loss in Ka-band satellite communication. Measured data show that rain attenuation is a function of carrier frequency and system feasibility. In the case of large elevation [22], \(L_{r}\) can be expressed as  
\[L_{r}=C_{1}\exp(\delta_{1}f)+C_{2}\exp(\delta_{2}f)-(C_{1}+C_{2})\qquad\quad( \mathrm{dB}) \tag{1}\]  
where \(C_{1}\), \(C_{2}\), \(\delta_{1}\), and \(\delta_{2}\) are the functions of the system availability, and \(f\) is the carrier frequency. When the elevation is small, the formula can be simplified as  
\[L_{r}(\theta)=L_{r}(\theta_{0})\sin\theta/\sin\theta_{0}\qquad\quad(\mathrm{ dB}), \tag{2}\]  
where \(\theta\) is the elevation of the earth station, and \(\theta_{0}\) is the reference elevation. Atmospheric absorption includes mainly oxygen and water vapor absorption. The International Telecommunication Union Radio communications sector (ITU-R) provides the expression of oxygen absorption loss under a slant path as follows  
\[L_{\mathrm{o}}=\frac{h_{o}\gamma_{o}}{\sin\theta}\qquad\quad(\mathrm{dB}), \tag{3}\]  
where \(h_{o}\) is the effective height of dry air, \(\gamma_{o}\) is the oxygen loss coefficient, and \(\theta\) is the elevation. ITU-R also gives the expression of water vapor absorption loss  
\[L_{w}=\frac{h_{w}\gamma_{w}}{\sin\theta}\qquad\quad(\mathrm{dB}), \tag{4}\]  
where \(h_{w}\) is the effective height of water vapor, \(\gamma_{w}\) is the water vapor loss coefficient, and \(\theta\) is the elevation. The size of cloud attenuation is related to the content and temperature of liquid water. ITU-R gives the expression of cloud attenuation  
\[L\mathrm{c}=\frac{0.4095h}{i(1+\left(\frac{2+r}{l}\right)^{2})\sin\theta} \qquad\quad(\mathrm{dB}) \tag{5}\]  
where \(h\) refers to the cloud layer thickness, \(r\) and \(i\) are the real and imaginary parts of the dielectric constant of water, respectively, and \(\theta\) is the elevation. The refractive index of the propagation path rises randomly with position and time. A flicker exhibits rapid fluctuation when the radio waves pass through the atmosphere, causing fast fluctuation of the amplitude and phase of the radio wave. A flicker can attenuate and enhance the electric wave signal. ITU-R suggests that the total attenuation value \(L_{t}\) can be expressed as  
\[L_{t}=L_{\mathrm{o}}+L_{w}+L_{c}+\sqrt{{L_{r}}^{2}+{L_{s}}^{2}}\quad(\mathrm{ dB}). \tag{6}\]The free space propagation formula in the design of the Ka-band satellite communication system should be amended with the additional attenuation caused by rainfall, atmosphere, cloud, and flicker. It can be expressed as  
\[P_{R}=(P_{T}A_{T}A_{R}/c^{2}l^{2})\cdot(f^{2}/L_{t})=(P_{T}A_{T}A_{R}/c^{2}l^{2}) \cdot m(f,p)\qquad(w), \tag{7}\]  
where \(P_{R}\) and \(P_{T}\) are the average power of the receiver and transmitter, respectively, \((w)\) is the unit, \(f\) is the carrier frequency, \(l\) is the distance from satellite to earth terminal, \(c\) is the speed of light in vacuum, \(A_{R}\) and \(A_{T}\) are the effective contact areas of receiving antenna and transmitting antenna, respectively, \(L_{t}\) is the total attenuation for link, and \(p\) refers to system unavailability. Formula (7) shows that the multiplicative factor \(m(f,p)=f^{2}/L_{t}\) increases with the increase of \(f\). \(L_{t}\) increases rapidly with the increase of \(f\) and the feasibility of the system. \(m(f,p)\) decreases with the increase of \(f\).