# A Cumulant-Based Method for Acquiring GNSS Signals
## 4 Simulation and Experimental Results
### Real Galileo Signal Acquisition Results  
To improve the reception of Galileo satellite signals, we utilized the SiGe GN3S Sampler version 3, an upgraded version of this USB dongle that features a wideband receiving mode. This new version allows users to select different modes (narrowband for GPS or wideband for Galileo) to capture various satellite signals. The specific parameters for these different modes are listed in Table 3. For this experiment, we selected Mode 6 to capture the signal. Figure 13 shows the sky plot of Galileo satellites observed from the university campus at 5:05 PM. \begin{table}
\begin{tabular}{c c c} \hline
**PRN Number** & \multicolumn{2}{c}{**Elevation**} \\ \hline
12 & 46.6 \\
14 & 31.9 \\
15 & 19.3 \\
18 & 87.2 \\
21 & 26.3 \\
22 & 52.8 \\
24 & 34.1 \\
25 & 39.8 \\
31 & 9.1 \\ \hline \end{tabular}
\end{table} 
Table 1: GPS satellites elevation. Figure 12: (**a**) GPS PRN 12 signal acquisition results using the traditional method; (**b**) GPS PRN 12 signal acquisition results using the proposed method. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**PRN Number**} & \multicolumn{2}{c}{**Traditional Method**} & \multicolumn{2}{c}{**Proposed Method**} \\ \cline{2-5}  & **Code Offset** & **Doppler [Hz]** & **Code Offset** & **Doppler [Hz]** \\ \hline
12 & 4402 & 2723 & 4402 & 2723 \\
18 & 219 & 1974 & 219 & 1974 \\
21 & – & – & 3836 & \(-\)1039 \\
22 & 5235 & 3816 & 5235 & 3816 \\
24 & 2925 & \(-\)1382 & 2925 & \(-\)1382 \\
25 & 2152 & 4346 & 2152 & 4346 \\ \hline \end{tabular}
\end{table} 
Table 2: Acquisition results of GPS signal for the traditional and proposed methods (PRN21 is not detected using the traditional method). Table 4 provides a summary of the acquisition results using the traditional method and the proposed method, respectively. Again, the two methods acquire the same code phase and Doppler shift. Figure 13(a) illustrates the acquisition results for PRN 12 using the traditional method, while Figure 13(b) depicts the acquisition results for PRN 12 using the proposed method. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**PRN Number**} & \multicolumn{3}{c}{**Traditional Method**} & \multicolumn{3}{c}{**Proposed Method**} \\ \cline{2-5}  & **Code Offset** & **Doppler [Hz]** & **Code Offset** & **Doppler [Hz]** \\ \hline
12 & 26,618 & 503 & 26,618 & 503 \\
19 & 18,590 & 1145 & 18,590 & 1145 \\
20 & 2198 & 33 & 2198 & 33 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Acquisition results of the Galileo signal using the traditional and proposed methods. Figure 13: Sky plot showing the positions of visible Galileo satellites during the experiment. Each numbered point represents a satellite, with its position on the plot indicating its azimuth and elevation relative to the receiver’s location. The blue structures in the background represent the local environment and are not relevant to the satellite data. The center of the plot represents the zenith, while the edge represents the horizon. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Mode Number**} & \multirow{2}{*}{**Frequency Band**} & \multicolumn{2}{c}{**Sampling Frequency**} & \multicolumn{2}{c}{**Intermediate Frequency**} & \multirow{2}{*}{**Data Format**} \\ \hline
1 & Narrow & 16.368 MHz & 4.092 MHz & 2 bit real \\ \hline
2 & Narrow & 8.184 MHz & 0 MHz & 4 bit I/Q \\ \hline
3 & Narrow & 5.456 MHz & 1.364 MHz & 2 bit real \\ \hline
4 & Narrow & 4.092 MHz & 0 MHz & 4 bit I/Q \\ \hline
5 & Wide & 16.368 MHz & 4.092 MHz & 2 bit real \\ \hline
6 & Wide & 8.184 MHz & 0 MHz & 4 bit I/Q \\ \hline
7 & Wide & 5.456 MHz & 1.364 MHz & 2 bit real \\ \hline
8 & Wide & 4.092 MHz & 0 MHz & 4 bit I/Q \\ \hline \hline \end{tabular}
\end{table} 
Table 3: SiGe GN3S Sampler v3 specification parameters. Figure 15a,b presents enlarged local plots of the acquisition results for the Galileo PRN 19 E1-C channel signal using the traditional method and the proposed method, respectively.