# Analysis of Multi-Antenna GNSS Receiver Performance under Jamming Attacks
## 4 Field-Test Results and Discussion
### Measurement Domain Analysis  
The measurements generated by the interference free reference antenna data acts as reference measurements in this case. Differences between these measurements and those generated after beamforming were compared for PM and MPDR. The resulting time series plot of the pseudorange and carrier phase measurement errors are shown in Figure 13 and the corresponding statistics are provided in Tables 7 and 8. Pseudorange biases up to 2 m were observed in both PM and MPDR beamformers. The biases observed are different for different PRNs. Carrier phase biases are minimal (less than 1 mm) with the MPDR beamformer for all PRNs, which agrees with the simulation results. With PM, different biases were observed for different PRNs as seen from Figure 13a and they reach 1.1 cm for some PRNs. The results with PM also agree with simulation results where different biases were observed for different PRNs.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Single Antenna with Interference**} & \multicolumn{3}{c}{**PM**} & \multicolumn{3}{c}{**MPDR**} \\ \cline{2-10}
**PRN** & **RMSE Doppler** & **PLI** & **C/N\({}_{0}\)** & **RMSE Doppler** & **PLI** & **C/N\({}_{0}\)** & **RMSE Doppler** & **PLI** & **C/N\({}_{0}\)** \\  & **(Hz)** & **PLI** & **(dB-Hz)** & **(Hz)** & **(dB-Hz)** & **(Hz)** & **(Hz)** & **PLI** & **(dB-Hz)** \\ \hline PRN 1 & 0.98 & 0.98 & 34.1 & 0.43 & 0.99 & 44.9 & 0.66 & 0.99 & 46.5 \\ PRN 4 & 0.97 & 0.98 & 36.7 & 0.45 & 0.99 & 44.7 & 0.49 & 0.99 & 48.1 \\ PRN 11 & 0.91 & 0.97 & 37.6 & 0.45 & 0.99 & 46.8 & 0.31 & 0.99 & 49.1 \\ PRN 13 & 0.89 & 0.97 & 37.5 & 0.45 & 0.99 & 48.2 & 0.28 & 0.99 & 50.9 \\ PRN 15 & 0.92 & 0.97 & 33.8 & 0.85 & 0.99 & 43.4 & 0.64 & 0.99 & 48.6 \\ PRN 17 & 0.92 & 0.97 & 38.2 & 0.28 & 0.99 & 45.5 & 0.47 & 0.99 & 47.7 \\ PRN 28 & 0.92 & 0.97 & 38.7 & 0.23 & 0.99 & 47.7 & 0.34 & 0.99 & 49.8 \\ PRN 30 & 0.98 & 0.99 & 41.1 & 0.60 & 0.99 & 44.7 & 0.29 & 0.99 & 52.7 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Tracking performance of different PRNs, PM and MPDR in the presence of chirp interference.  
Figure 12: Tracking performance of PRN 4 with PM and MPDR using actual data with chirp interference.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**PRN**} & \multicolumn{2}{c}{**PM**} & \multicolumn{2}{c}{**MPDR**} \\ \cline{2-5}  & **Mean (m)** & **Standard Deviation (m)** & **Mean (m)** & **Standard Deviation (m)** \\ \hline PRN 1 & \(-1.42\) & 1.94 & \(-1.71\) & 2.92 \\ PRN 4 & 0.34 & 1.32 & 0.26 & 2.40 \\ PRN 11 & 0.22 & 1.49 & 1.27 & 2.42 \\ PRN 13 & 0.48 & 1.33 & 0.47 & 2.38 \\ PRN 15 & \(-1.05\) & 3.31 & \(-0.55\) & 3.21 \\ PRN 17 & \(-0.06\) & 1.48 & 0.24 & 2.01 \\ PRN 28 & \(-0.01\) & 0.69 & 0.29 & 1.11 \\ PRN 30 & \(-0.69\) & 1.31 & 1.12 & 1.35 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Pseudorange measurement errors for PM and MPDR in the presence of chirp interference.  
Figure 13: Pseudorange and carrier phase measurements with actual data with chirp interference for (a) PM; and (b) MPDR.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**PRN**} & \multicolumn{2}{c}{**PM**} & \multicolumn{2}{c}{**MPDR**} \\ \cline{2-5}  & **Mean (mm)** & **Standard Deviation (mm)** & **Mean (mm)** & **Standard Deviation (mm)** \\ \hline PRN 1 & \(-7.3\) & 2.0 & 0.3 & 1.6 \\ PRN 4 & 7.1 & 1.7 & 0.9 & 2.0 \\ PRN 11 & \(-10.9\) & 3.8 & 0.2 & 1.4 \\ PRN 13 & \(-5.0\) & 1.3 & \(-0.8\) & 1.3 \\ PRN 15 & \(-2.3\) & 1.8 & 1.0 & 1.7 \\ PRN 17 & 8.2 & 1.9 & 0.5 & 2.1 \\ PRN 28 & 1.6 & 0.8 & 0.9 & 1.1 \\ PRN 30 & 2.3 & 1.1 & 0.5 & 1.5 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Carrier phase measurement errors using PM and MPDR with chirp interference.