## 4 Interference Analysis
### Parameter Definitions and Relevant Equations
#### 4.1.2 Relevant Equations  
This subsection lists the fundamental equations that relate most of the key parameters listed above. These relations are used to calculate the different carrier-to-interference parameters. The power flux density (or power density) at a distance r from a point power source P is the total power emitted by the source divided by the surface area of a sphere with radius r centered at P. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Details (Nominal Values, Units,...)** \\ \hline R & distance between ES and GEO & 40,973 km \\  & satellite system & \\ PFD & Power flux density at a distance d & \\  & from the antenna & \(\mathrm{W/m^{2}}\) \\ G & Antenna gain in dBi & ES: G\({}_{\mathrm{ES}}\) = 47.5 dBi \\  & & \(\mathrm{MVDS:GMvDS}\) = 41.5 dBi \\ P & Transmission power & \(\mathrm{P_{ES}}\) = 5 dBW \\  & & \(\mathrm{P_{MVDS}}\) = 10 dBW \\ EIRP & Effective isotropic radiated power & \(\mathrm{ES:EIRP_{ES}}\) = 52.5 dBi \\  & & \(\mathrm{MVDS:EIRP_{MVDS}}\) = 25.6 dBi \\  & Carrier-to-noise-density ratio & dB-Hz \\  & Carrier-to-noise ratio & dB \\  & Energy per bit to noise power & \\  & spectral density & dB-Hz \\ R & Data rate & Mbps \\ FSL & Free-space path loss & dB \\ L\({}_{\mathrm{ABS}}\) & Atmospheric and ionospheric & 0 dB \\  & losses & \\ \(\mathrm{G}\) & Figure of merit of a & ES : \(\left(\frac{\mathrm{G}}{\mathrm{T}}\right)_{\mathrm{ES}}\) = 24 dB/K \\  & communication system & \(\mathrm{MVDS:}\) : \(\left(\frac{\mathrm{G}}{\mathrm{T}}\right)_{\mathrm{MVDS}}\) = 5.6 dB/K \\ G(\(\theta\)) & Off-axis gain of the Earth station & dBi \\  & antenna & dB \\ \(\Theta\) & Off-axis angle & Degree \\  & Carrier-to-adjacent satellite & dB \\  & interference ratio & dB \\ \(\left[\frac{\mathrm{G}}{\mathrm{ACT}}\right]\) & Carrier-to-adjacent-carrier & dB \\  & interference ratio & dB \\ \(\left[\frac{\mathrm{C}}{\mathrm{M}}\right]\) & Carrier-to-intermodulation & dB \\  & interference ratio & dB \\  & Carrier-to-cross-polarization & \\ \(\left[\frac{\mathrm{C}}{\mathrm{M}}\right]\) & Interference ratio & dB \\  & Carrier-to-MVDS side lobe & dB \\ \(\left[\frac{\mathrm{G}}{\mathrm{T}}\right]\) & interference & dB \\ Fr & Satellite power fraction & \\  & Input backoff for the entire & \\ IBO, IBOi & satellite system and the input & \(-\)4 dB \\  & backoff of an individual carrier & \\  & Output backoff for the entire & \\ OBO, OBOi & satellite system and the output & \(-\)4 dB \\  & backoff of an individual carrier & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._The PFD is given in terms of EIRP and \(d\), the distance from the transmitting antenna to the point where PFD is measured, as shown in Equation (1):  
\[\mathrm{PFD}=\frac{\mathrm{EIRP}}{4\pi\mathrm{d}^{2}} \tag{1}\]  
The EIRP can be deduced from the output power of the system (ES or satellite) using Equation (2):  
\[\mathrm{EIRP}=\mathrm{G}+\mathrm{P} \tag{2}\]  
The PFD can be calculated from the \(IBO\) using Equation (3):  
\[\mathrm{IBOi}=\mathrm{SFD}-\mathrm{PFD} \tag{3}\]  
where SFD is the satellite flux density, typically provided in the satellite's specifications. The PFD at the satellite level can be calculated using Equation (4):  
\[\mathrm{PFD}=\mathrm{EIRP}_{\mathrm{ES}}-\mathrm{FSL}_{\mathrm{up}}-\mathrm{ L}_{\mathrm{ABS}}+\mathrm{G}_{\mathrm{I}} \tag{4}\]  
where \(\mathrm{FSL}_{\mathrm{up}}\) is the free-space path loss on the uplink, \(L_{ABS}\) represents atmospheric losses, and \(G_{\mathrm{I}}\) signifies the satellite gain. IBO and OBO are system specifications managing the trade-off between the power efficiency and linearity of the satellite's high-power amplifier (HPA), as well as the HPA at the Earth station. The satellite's Fr is related to IBO and OBO by Equation (5):  
\[\mathrm{Fr}=\mathrm{IBO}-\mathrm{IBOi}=\mathrm{OBO}-\mathrm{OBOi} \tag{5}\]  
\(\left[\frac{\mathrm{E}_{\mathrm{b}}}{\mathrm{N}_{0}}\right]\) is a fundamental and crucial parameter in digital communication systems.