# SATCOM Earth Station Arrays Anti-Jamming Based on MVDR Algorithm
## 4 Simulation Analysis
### Jamming Suppression Performance in Actual Satellite Communication  
When there is jamming in the downlink(as shown in Figure 8), assuming that the jamming frequency is the same as the satellite downlink signal frequency, the signal/jamming power at the input of the satellite communication earth station receiver is without the polarization mismatch loss of the receiving and transmitting antennas, the receiving antenna pointing loss and the transmitting antenna pointing loss [26] can be expressed as  
\[[P]=[E]+[G(\theta)]-[L_{FS}]-[L_{RF}]-[L_{A}] \tag{28}\]  
where \([E]\) is the effective isotropic radiated power (EIRP) of the satellite/jamming source, \([G(\theta)]\) is the gain of the antenna for the satellite signal/jamming, \([L_{RF}]\) is the loss of the feeder, \([L_{A}]\) is the atmospheric absorption loss, and \([L_{FS}]\) is the free space propagation loss of the satellite signal/jamming, which can be expressed as  
\[[L_{FS}]=92.44+20\text{lg}z(\text{km})+20\text{lg}f(\text{GHz}) \tag{29}\]  
where \(z\) is the propagation distance of the signal/jamming, and \(f\) is the frequency of the signal/jamming. Figure 8: A satellite communication system with the downlink jamming. Figure 7: Output SINR versus PFD. The distance between the satellite and the earth station can be calculated as  
\[z_{s}=42164\times\sqrt{1.023-0.303\cos e\cos\Delta g}\quad(\rm km) \tag{30}\]  
where \(e\) is the latitude of the earth station, and \(\Delta g\) is the difference between the longitude of the earth station and the longitude of the satellite sub-point. The noise power is  
\[[N]=10\rm lg(\textit{kTB}) \tag{31}\]  
where \(k\) = 1.38 \(\times\) 10 \(-\) 23 J/k is the Boltzmann constant, \(T\) is the equivalent noise temperature of the earth station receiving system, and \(B\) is the noise bandwidth. The power flux density at a distance of \(z\) from the transmitting antenna can be expressed as  
\[[F]=[E]-20\rm lgz(m)-10.99 \tag{32}\]  
After experimental simulation and literature review, SINR enhancement effects of 5 MVDR algorithms are shown in Table 1. In order to test the effectiveness of the proposed algorithm in the actual satellite communication system, the following experiments are carried out. Assuming that the satellite in this experiment is a geostationary orbit communication satellite, and the specific parameters of the satellite, earth station, and jamming source are shown in Table 2. The distance between the satellite and the earth station is \(z_{\rm s}\) = 37,045 km. The satellite signal flux density at the earth station antenna is \(-\)110.36 \(\rm dBW/m^{2}\), and the satellite signal power after passing through the earth station antenna is \(-\)119.98 dBW. The noise power is \(-\)131.28 dBW. In experiment 3, assuming that the incident angle of the jamming source is \(10^{\circ}\), the EIRP of the jamming source is set from \(-\)20 dBW to 10 dBW. From Figure 9, it can be seen that when the EIRP of the jamming source is \(-\)7.18 dBW and 5.37 dBW, the output SINR of the single antenna and the array based on the CBF algorithm is about 7 dB, reaching the SNR threshold of the earth station. Within the range of experimental data, the output SINR of the array based on the MVDR algorithm with diagonal loading is about 12 dB, exceeding the SNR threshold of the earth station. Therefore, when the EIRP of the jamming source is less than \(-\)7.18 dBW, the single antenna, \begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **SINR Improvement** \\ \hline CBF algorithm & 29 dB \\ SMI algorithm & 34.6 dB \\ Jamming signal separation method & 28 dB \\ Despread–respread method & 30.1 dB \\ DL algorithm & 36 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of different methods for anti-jamming effect.