# Acquisition of Weak BDS Signal in the Lunar Environment
## 3 Results
### Observation Results
#### 3.1.1 Visible GNSS Satellites  
GNSS visibility for this lunar application has two constraints: (1) the line of sight is not obstructed by the Earth and (2) the \(C/N_{0}\) is greater than the threshold value of the receiver. The number of visible GNSS satellites for different GNSS system combinations at carrier-to-noise ratio thresholds of 15 and 10 dB-Hz, respectively, is given in Figure 7. At a threshold of 15 dB-Hz, the average number of visible satellites for BDS-3 and GPS are 1.7 and 2.0, respectively. However, these two values are 3.6 and 3.9, respectively, when the receiving threshold is reduced to 10 dB-Hz, which is to be expected. BDS-3 performs worse than GPS, which is understandable because the transmitting antenna of the BDS-3 satellite suppresses the side lobe gain, as seen in Figure 2. This is reflected by the fact that there is only one main lobe peak in the gain pattern, while on the contrary, the antenna gain patterns of different GPS blocks show several gain peaks. The average number of accessible GNSS satellites increases to 6.3 and 13.5 when the thresholds are 15 and 10 dB-Hz, respectively, for the joint use of four GNSS systems. In addition, it can be found that periodic signal interruptions occur during the simulation time period, i.e., the number of visible GNSS satellites is 0, which is due to the occlusion of the Moon. Therefore, satellites in circumlunar orbit still have difficulty maintaining a high number of available signals when using the signals of four GNSS systems. Other navigation sensors such as inertial measurement units (IMUs) can be used to provide navigation solutions when GNSS satellite signals are not available. The literature [38] describes the simulation of an onboard GNSS receiver using a loosely coupled inertial navigation system (INS) on several different lunar missions.  
Table 5 summarizes the signal availability with at least one satellite and four or more satellites. If the recepted threshold is 15 dB-Hz, the percentage of epochs where more than four satellites are visible to BDS-3 is only 4.82%, while this value increases to 67.86% for when at least one satellite is visible. After lowering the threshold to 10 dB-Hz, the value of at least four BDS-3 available signals reaches 66.33%, which indicates that the \(C/N_{0}\) of most of the signals is between 10 and 15 dB-Hz. The effect of using the combined GNSS system is evident, when both BDS-3 and GPS systems are available, for more than 60% of the simulation period, the number of visible satellites is at least four. However, when four GNSS systems are used simultaneously, the improvement is not significant; the advantage brought by the dual system receivers is already excellent considering the number of receiver channels.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & \(T_{coh}\) **(ms)** & \(T_{acc}\)1  \\ \hline NCOI & 200/400 & \(T/T_{coh}\) \\ CODI & 200/400 & \(T/T_{coh}-1\) \\ SBCOI & 200/400 & \(T/T_{coh}\) \\ SBCODI & 200/400 & \(T/T_{coh}-1\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Receiver parameters for each algorithm.  
Figure 8 displays the statistical distribution of signals from the main and side lobes within a one minute time interval. The number of main lobe signals received from BDS-3 is higher than GPS, while the number of side lobe signals is less, in agreement with the side lobe gain suppression revealed in Figure 2. Although the number of side lobe signals is higher than the main lobe, this difference is not as noticeable in the BDS-3 system. Therefore, a more sensitive receiver is still required to effectively receive the side lobe signals. Lowering the received threshold from 15 to 10 dB-Hz approximately doubles the number of side lobe signals, while the number of main lobe signals increases only slightly. This suggests that the majority of low \(