# Navigation in GEO, HEO, and Lunar Trajectory Using Multi-GNSS Sidelobe Signals
## 3 Results  
### C/N\({}_{0}\)  
\(C/N_{0}\) is a critical parameter for spaceborne navigation since sidelobe signals are mostly received. \(C/N_{0}\) of GEO, HEO, and lunar trajectory are shown in Figure 7. In our paper, \(C/N_{0}\) was calculated using Equation (2), in which the transmission distances between  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**System Orbit**} & **GPS** & \multicolumn{2}{c}{**BDS**} & \multirow{2}{*}{**Galileo**} & \multirow{2}{*}{**GLONASS**} \\  & **MEO** & & & & & \\ \hline Earth block angle [deg] & 13.84 & 13.21 & 8.70 & 12.28 & 14.50 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Earth block angles of different system orbit.  
GNSS satellites and spacecraft were computed using the orbits described in Tables 1 and 3, Tables 4 and 5. Note that we showed \(C/N_{0}\) of each visible GNSS satellite here. A GNSS satellite was visible once the signal was not blocked by the Earth and the \(C/N_{0}\) was beyond the receiver sensitivity. As the spacecraft moves along its orbit, the received signals were marked as blue or grey dots for mainlobe or sidelobe signals, respectively. The red curve in Figure 7b refers to altitudes of HEO; the red curves in Figure 7c,d refer to altitudes of lunar trajectory. Obviously, the altitude of GEO was basically the same during the simulation period, so it was not shown here. Numbers of observations from mainlobe and sidelobe signals were collected in Table 7. The simulation period of GEO, HEO, and lunar trajectory was 24, 24, and 76.2 h, respectively. The sampling rate of the three types of spacecraft was 30 s.  
For the GEO spacecraft, 3 GEO and 3 IGSO satellites of BDS-3 were constantly visible. Mainlobe signal variation was between 35 and 46 dB-Hz; sidelobe signals mostly ranged between 16-32 dB-Hz. Numbers of GEO observations showed that almost 92.4% of the received signals were sidelobe signals, which is reasonable, since the altitude of GEO was higher than most of the GNSS satellites.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Mainlobe Signal** & **Sidelobe Signal** \\ \hline GEO & 18,502 & 226,155 \\ HEO & 29,143 & 186,635 \\ Lunar trajectory (20 dB-Hz) & 18,977 & 68,864 \\ Lunar trajectory (15 dB-Hz) & 20,299 & 133,767 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Number of observations from mainlobe and sidelobe signals.  
Figure 7: \(C/N_{0}\) of mainlobe and sidelobe signals for three types of spacecraft: **(a)** GEO; **(b)** HEO; **(c)** Lunar trajectory (20 dH-Hz); **(d)** Lunar trajectory (15 dH-Hz).  
For the HEO spacecraft, the highest \(C/N_{0}\) appeared at perigee, which was as strong as 65 dB-Hz. When the spacecraft moved towards apogee, \(C/N_{0}\) was reduced because sidelobe signals were received. In total, 86.5% of the received signals were from sidelobe signals. HEO spaceborne antenna received more mainlobe signals than that of GEO. This was due to the low altitude near the perigee, where mostly mainlobe signals were received.  
For lunar trajectory, when receiver sensitivity was set as 20 dB-Hz, 78.4% of the received signals were sidelobe signals. Due to the long transmission loss, \(C/N_{0}\) of most signals were below receiver thresholds. When receiver sensitivity increased to 15 dB-Hz, the received signals increased by 6.5% and 94.2% for mainlobe and sidelobe signals respectively, which will bring significant improvement in signal visibility.