# Jamming Analysis between Non-Cooperative Mega-Constellations Based on Satellite Network Capacity
## 2 System Model
### Main jamming Region  
The jamming effect between non-cooperative constellations is affected by the angle \(\theta\) between the jamming and jammed satellites. \(\theta\) is the angle between the jammed satellite's pointing antenna and the jamming satellite-jammed satellite connection line. For an arbitrary ISL, the jamming effect will decrease as \(\theta\) increases. Therefore, we mainly consider the jamming effect within a certain pinch range (e.g., \(\theta_{\text{max}}\)), i.e., the main jamming region (MJR). The MJR is the cone formed with \(\theta_{\text{max}}\) as the half-cone angle. The MJR in a geocentric rectangular coordinate system is shown in Figure 2. For jammed ISLs, the MJR is the region where the jamming satellites can effectively interfere with the target ISLs.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Notation** & **Description** \\ \hline \(\Psi_{A}\) & The jammed constellation \\ \hline \(\Psi_{B}\) & The jamming constellation \\ \hline \(A(i,j)\) & The \(j\)th satellite in the \(i\)th orbit \\ \hline \(\theta_{\text{max}}\) & The semi-cone angle of the main jamming region \\ \hline \(G_{t}\) & The transmitting antenna peak gain \\ \hline \(G_{r}\) & The receiving antenna peak gain \\ \hline \(L^{(i,j+1)}_{(i,j)}\) & The ISL from satellite \(A(i,j)\) to satellite \(A(i,j+1)\) \\ \hline \(R^{\
earrow}_{i,j,t}\) & The maximum transmission rate of ISL \(L^{(i,j+1)}_{(i,j)}\) with no jamming \\ \hline \(R^{\searrow}_{i,j,t}\) & The maximum transmission rate of ISL \(L^{(i,j-1)}_{(i,j)}\) with no jamming \\ \hline \(R^{\searrow}_{i,j,t}\) & The maximum transmission rate of ISL \(L^{(i-1,j)}_{(i,j)}\) with no jamming \\ \hline \(R^{\
earrow}_{i,j,t}\) & The maximum transmission rate of ISL \(L^{(i+1,j)}_{(i,j)}\) with no jamming \\ \hline \(d_{i,j,t}\) & The distance between \(A(i,j)\) and \(A(i,j+1)\) at time slot \(t\) \\ \hline \(R^{\
earrow}_{i,j,t}\) & The maximum transmission rate of ISL \(L^{(i,j+1)}_{(i,j)}\) under jamming \\ \hline \(\bar{R}^{\
earrow}_{i,j,t}\) & The maximum transmission rate of ISL \(L^{(i,j-1)}_{(i,j)}\) under jamming \\ \hline \(\bar{R}^{\searrow}_{i,j,t}\) & The maximum transmission rate of ISL \(L^{(i-1,j)}_{(i,j)}\) under jamming \\ \hline \(\bar{R}^{\searrow}_{i,j,t}\) & The maximum transmission rate of ISL \(L^{(i+1,j)}_{(i,j)}\) under jamming \\ \hline \(R^{(i,j+1)}_{(i,j)}\) & The maximum transmission rate of intra-plane ISLIn mega-constellations, \(A(i,j)\) denotes the \(j\)th satellite in the \(i\)th orbit. The MJR is constructed as follows: take \(A(i,j)\) in the jammed constellation \(\Psi_{A}\) as the vertex, take the jammed ISL \(L_{(i,j)}^{(i,j+1)}\) as the central vertical line and form a cone with \(\theta_{\max}\) as the semi-cone angle. The region where the cone intersects the orbits of jamming constellation \(\Psi_{B}\) is defined as the MJR. The satellites in the MJR are the corresponding jamming satellites of \(L_{(i,j)}^{(i,j+1)}\). According to the above definition, we can construct the MJR for each ISL in \(\Psi_{A}\). For ISLs in the same orbit, if \(\theta_{\max}\) is small enough, the MJRs of each ISL will not overlap. Taking a single ISL as an example, we analyze the influence of the jamming parameters on the transmission rate.