# Distance Protection for Coexistence of 5G Base Station and Satellite Earth Station
## 2 Background Knowledge
### Basic Scenarios and Parameters
\right.\] (3)  
The off-axis/off-boresight angle, \(\varnothing\) i.e., the angle between the interference axis and direction of the main lobe (ES antenna orientation) of the FSS ES (ITU-R P.452-15 [15]) is given as  
\[\varnothing=\arccos(\cos(\alpha)\cos(\epsilon)\cos(\theta)+\sin(\alpha)\sin( \epsilon)) \tag{4}\]  
\[\epsilon=\frac{h_{ES}-h_{BS}}{d}-\frac{d}{2r} \tag{5}\]  
where \(\theta\): azimuth angle of the BS w.r.t the ES main lobe, \(\alpha\): ES elevation angle, \(r\): effective Earth radius = 8.5 \(\times\) 10\({}^{6}\) m, and \(\lambda\): wavelength. Since the ES antenna orientation is set to true north, areas closer to the main lobe of the ES antenna receive higher antenna gain. The ES is considered to be at the center (0,0), and the X-, Y-axis values are the BS coordinates. Figure 4 shows the ES antenna gain versus the BSs locations. The path losses from all possible BS locations to the ES are next considered. To calculate the path loss, we adopt the 3D propagation model proposed by the 3 GPP in [14], which is often referred to as the 3 GPP new radio (NR) model. This model is compliant with earlier channel models, e.g., 3D SCM model [21] and IMT-advanced [22] up to 6 GHz. It also supports comparisons across the frequency bands over the range of 0.5-100 GHz and various scenarios, including RMa, UMi, and UMa. The model in [14] considers 3D propagation distance; therefore, both the BS and ES antenna heights significantly affect  
Figure 4: FSS ES antenna gain orientations. the actual path loss values. In cellular network simulations, the path losses in rural areas are always much lower than those in urban areas; this is, mainly, because the altitudes of the Tx and receive (Rx) antennas are the same for all scenarios. However, the ES and BS antenna heights are both different in the RMa, UMa, and UMi. The altitude differences between the ES and BS antennas are the largest in these three scenarios. The path loss for RMa is slightly higher than those of the UMa and UMi scenarios. Figure 5 shows the signal propagation losses from all possible BS locations (X, Y) at the ES (0, 0). In practice, the LOS and NLOS scenarios are combined in the real environment, and the NLOS path is often the dominant loss component in urban areas. Therefore, we combine the LOS and NLOS path losses using a random mechanism and the LOS probability as shown in Algorithm 1, which is a function of the distance, as specified in the 3 GPP model. In obtaining the BS antenna gain, the g-NodeB antenna follows the 3 GPP NR model [14], where the antenna elements are uniformly distributed in N columns with horizontal spacing of \(\Delta H\) and in M rows with vertical spacing of \(\Delta V\). For a single antenna element radiation pattern, the BS antenna gain is calculated as:  
* Horizontal pattern: \[A_{E,\ H}(\varphi)=-\text{min}\left[12\left(\frac{\varphi}{\varphi_{3\ dB}} \right)^{2},A_{m}\right]\] (6)
* Vertical pattern: \[A_{E,\ V}(\theta)=-\text{min}\left[12\left(\frac{\theta-90}{\theta_{3\ dB}} \right)^{2},SLA_{V}\right]\] (7)  
Figure 5: Path loss propagation model. * Single antenna element pattern: \[A_{E}(\varphi,\theta)=G_{E,Max}-min\{-[A_{E,H}(\varphi)+A_{E,V}(\theta)],\ A_{m}\}\] (8) where \(\varphi_{3 dB}=65^{\circ}\): horizontal 3-dB beamwidth, \(A_{m}=30\) dB: front-to-back ratio, \(\theta_{3 dB}=65^{\circ}\): vertical 3-dB beamwidth, and \(SLA_{V}=30\) dB: side-lobe level limit. However, a planar uniform rectangular array (URA) antenna pattern uses the procedure illustrated below:
* Array factor: \[AF(\varphi,\theta,\varphi_{beam},\theta_{beam})=10*\log_{10}[1+\rho(|a\cdot w^{ T}|^{2})]\] (9) where \(w=[w_{1,1},w_{1,2},\,\ldots,w_{m,m}]\), \(\mathrm{m}=\sqrt{N_{c}},w_{py}=e^{2\pi}\Big{(}(p-1)\frac{\Delta V}{\lambda} \Psi_{p}+(r-1)\frac{\Delta H}{\lambda}\Psi_{r}\Big{)}\), \(\left\{ \begin{array}{l}\Psi_{P}=\cos(\theta)-\cos(\theta_{beam})\\ \Psi_{P}=\sin(\theta)\sin(\varphi)-\sin(\theta_{beam})\sin(\varphi_{beam}) \end{array}