# Anti-Jamming Method and Implementation for GNSS Receiver Based on Array Antenna Rotation
## 5 Simulation Results and Analysis
### Effectiveness of Array Antenna Rotation Method  
Based on the above scenario and parameters, the Monte Carlo simulation was repeated for 3000 times [20] to identify the effectiveness of the array antenna rotation method. As the simulation repeated, the DOAs of the interferences and satellite signals changed randomly as shown in Table 3. The \(JSR\) was set to 60 dB per jammer. Ignoring the navigation signal DOA, Figure 8a shows the average residual interference-plus-noise power \(p_{inres,\text{min}}\) against the rotation angle and Figure 8b shows the corresponding average \(ICR\). Taking the \"4 jammer\" blue line for instance, the residual interference power reaches the minimum value while the optimal rotation angle is 15\({}^{\circ}\). At the same time, the \(ICR\) reaches the peak. The phenomenon is anastomotic with the analysis in Section 3. In order to make the figure clear, only the jammer number of 4-10 is given. The curves of more jammers are similar. They are analyzed later. Figure 8: Simulation results ignoring navigation signal DOA. (**a**) Residual interference-plus-noise power against rotation angle. (**b**) \(ICR\) against rotation angle. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline light speed & \(3\times 108\) m/s \\ carrier frequency & 1268.52 MHz \\ array geometry & four element central circular array \\ array element spacing & 1/2 wavelength \\ navigation signal power & \(-\)160 dBW \\ noise bandwidth & 20.48 MHz \\ interference type & wideband gaussian noise \\ jammer incident angles in elevation & 0\({}^{\circ}\)\(-\)15\({}^{\circ}\), uniform distribution \\ jammer incident angles in azimuth & 0\({}^{\circ}\)\(\sim\)360\({}^{\circ}\), uniform distribution \\ \(\Delta\Psi\) of jammer incident angles in azimuth & 90\({}^{\circ}\) \\ satellite signal incident angles in elevation & 15\({}^{\circ}\)\(\sim\)90\({}^{\circ}\), uniform distribution \\ satellite signal incident angles in azimuth & 0\({}^{\circ}\)\(\sim\)360\({}^{\circ}\), uniform distribution \\ number of interferences & 4–30 \\ implementation of anti-jamming algorithm & Sampling Matrix Inversion \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters. Considering the navigation signals, the proposed method was applied to the classic PI algorithm and MVDR algorithm. According to Equation (6), the numerical result of the anti-jamming output equivalent \(CNR\) is shown in Figure 9. The black dashed line represents the receiver's acquisition threshold. As can be noted in Figure 9, at the initial state for 4 jammers, the output \(CNR\) is around 23 dBHz, which does not satisfy the signal acquisition. As the antenna rotates, there is a segment for which the output \(CNR\) surpasses the threshold. In this segment, the receiver is available. Thus, the receiver can tolerate an interference intensity of at least a 60 dB \(JSR\). Furthermore, the index of the receiver's anti-jamming capability is defined as follows: the receiver's maximum tolerated interference power keeps the signal \(CNR\) greater than the receiver's acquisition threshold. Assume that the \(CNR\) has a certain probability greater than the threshold. The probability here is the receiver availability and the interference power is recorded in the single-interference \(JSR\). Assume the receiver's acquisition threshold has a \(CNR\) of 28 dBHz [21], the availability threshold is 95%, the interference number is 4\(\sim\)30, and the azimuth is \(\Delta\Psi=90^{\circ}\). According to the incident direction statistics of terrestrial jammers relative to airborne GNSS receivers, the incident angle of jammers and satellite signals are listed in Table 3. Monte Carlo simulation is repeated 3000 times and the results are shown in Figure 10.  
Figure 10a,b depicts the receiver's anti-jamming ability. As analyzed in Section 2, the anti-jamming ability varies due to the antenna attitude (represented by rotation angle).