# Research on the Compound Jamming Method against FDA-MIMO Beamforming
## 5 Simulation Analysis
### Beamforming Gain Analysis  
Figure 5 is the FDA-MIMO non-adaptive beam antenna pattern. As can be seen from Figure 5, the desired target and the false target NFT1 and NFT2 were located at the peak position of the antenna pattern, and the false target can obtain the same gain as the desired target. The false targets EFT1 and EFT2 were located at the side lobe positions, and the gain at their positions was low, so the power at the false targets EFT1 and EFT2 will be greatly weakened after passing through the radar system. At the same angle, observed from the range dimension profile, the gain at the position of the false target EFT was reduced compared to that of the desired target, but it still had a higher beam gain. At the same range, observed from the angle dimension profile, the false target and the desired target had the same large angle dimension beam gain.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Carrier frequency & \(f_{0}=9\) GHz & Frequency offset & \(\Delta f=2.0\) kHz \\ Target location & \((15^{\circ},20\) km) & Pulse repetition period & \(T=0.1\) ms \\ Elements number & \(M=N=10\) & Number of range bin & 600 \\ Target time delay & \(\tau_{0}=0.05\) ms & Input SNR & \(SNR=20\) dB \\ EFT1 time delay & \(\tau_{1}=0.0733\) ms & NFT1 time delay & \(\tau_{1}=0.0733\) ms \\ EFT2 time delay & \(\tau_{2}=0.1233\) ms & NFT2 time delay & \(\tau_{2}=0.1233\) ms \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters setting table.  
Figure 5: _Cont._Figure 6 is the FDA-MIMO range-angle two-dimensional MVDR adaptive beam antenna pattern. As can be seen from Figure 6, the gain at the desired target was almost unchanged compared to the non-adaptive beam gain, and the false targets NFT1 and NFT2 were still at the peak position of the antenna pattern, which can obtain a higher beam gain as the desired target. The false targets EFT1 and EFT2 were located at the side lobe position of the range dimension, and their gain was significantly reduced compared to the non-adaptive beam. At the same angle, observed from the range dimension profile, the gain at the position of the false target EFT was greatly reduced compared to the gain at the desired target, and it formed a zero notch in the range dimension side lobes. At the same range, observed from the angle dimension profile, the false target also had the same angle dimension beam gain as the desired target, similar to the non-adaptive beam.  
Figure 5: FDA-MIMO non-adaptive beamforming gain. (**a**) Range-angle two-dimensional beamforming gain; (**b**) Range dimension; (**c**) Angle dimension.  
Figure 6: FDA-MIMO range-angle two-dimensional MVDR adaptive beamforming gain. (**a**) Range-angle two-dimensional beamforming gain; (**b**) Range dimension; (**c**) Angle dimension.  
Table 2 shows the values of the gain for the non-adaptive beam and the range-angle two-dimensional MVDR adaptive beam. As can be seen from Table 2, the gain values at the desired target and the false targets NFT1 and NFT2 under non-adaptive beamforming reached the maximum gain values, while the beam gain values at the false targets EFT1 and EFT2 were reduced by 20 dB. With the range-angle two-dimensional MVDR adaptive beamforming algorithm, the gain of the desired target and the false targets NFT1 and NFT2 remained almost unchanged, while the beam gains at the false targets EFT1 and EFT2 were reduced to \(-80\) dB, and they could no longer form an effective jamming effect.