## 3 Results and Discussion
### C/N\({}_{0}\) Level Sensitivity Study  
Another sensitivity study was conducted to investigate the impact of the GNSS signal C/N\({}_{0}\) level on the vertical _Ne_ measurements. The GNSS antenna gain for the incoming signals to the receiver on a small satellite can be unstable or below the anticipated level in some scenarios, such as, satellite attitude control error or failure, spacecraft (power system) in a low power mode, and degraded satellite antenna. Any anisotropy in the GNSS antenna gain will imply the tracking PRN C/N\({}_{0}\) will be different because the GNSS satellite signals come from different directions with different relative distances. Also, the power levels of GNSS signals transmitted by different GNSS constellations or different frequency bands from the same constellation are different. Moreover, ionospheric scintillations can impact the C/N\({}_{0}\) level as well. Therefore, it is important to characterize the effect of C/N\({}_{0}\) level on vertical _Ne_ retrieval.  
By adjusting the global power level offset in the GNSS simulator, different C/N\({}_{0}\) level tracked by the receiver can be effectively simulated with the isolation of other controlled variables. The result in Figure 8 ii is chosen as the reference (power level). Two scenarios of global power offset (applied to all PRNs) on the deputy satellite's antenna were simulated: (a) \(-\)3 dB and (b) \(-\)8 dB. The HIL simulation comparison used the default formation configuration based on the 8 March 2019 almanac.  
The simulation results show that the lower the C/N\({}_{0}\) is, the more the TEC measurement fluctuates. As a result, more measurement noise is introduced into the vertical _Ne_ retrieval. Figure 10a shows the vertical _Ne_ retrieval for PRN 1 using Galileo E1 andE5b TEC with a power offset of \(-\)3 dB, where the average absolute error is \(1.1302\times 10^{5}\) cm\({}^{-3}\) and the standard deviation of error is \(1.3706\times 10^{5}\) cm\({}^{-3}\). Figure 10b shows the same vertical _Ne_ retrieval except with a power offset of \(-\)8 dB, where the average absolute error is \(1.2387\times 10^{5}\) cm\({}^{-3}\) and the standard deviation of errors is \(1.5471\times 10^{5}\) cm\({}^{-3}\). By comparing to the reference result in Figure 8 ii, the absolute mean and standard deviation of _Ne_ measurement errors becomes larger when the signal power (C/N\({}_{0}\)) decreases.  
A comparison using the GPS constellation indicates a similar trend of decreasing accuracy that is in line with the Galileo comparison described above. Choosing the vertical _Ne_ retrieval results using GPS L1 and L2 TEC from PRN 7, the absolute mean and standard deviation of raw measurement errors for the reference power level scenario are \(5.6474\times 10^{4}\) cm\({}^{-3}\) and \(7.8486\times 10^{4}\) cm\({}^{-3}\), respectively. For the \(-\)3 dB power offset scenario, the absolute mean and standard deviation of _Ne_ measurement errors increase to \(5.7376\times 10^{4}\) cm\({}^{-3}\) and \(8.0685\times 10^{4}\) cm\({}^{-3}\), respectively. For the \(-\)8 dB power offset case,  
Figure 10: Vertical _Ne_ retrieval for PRN 1 using Galileo E1 and E5b TEC with different signal power offsets against Figure 8 ii (reference level): (a) \(-\)3 dB power offset (b) \(-\)8 dB power offset.  
the absolute mean and standard deviation of measurement errors further increase to \(9.4891\times 10^{4}\) cm\({}^{-3}\) and \(8.0909\times 10^{4}\) cm\({}^{-3}\), respectively.  
This sensitivity study demonstrates a correlation between the C/N\({}_{0}\) level and the vertical _Ne_ retrieval characteristics: When the C/N\({}_{0}\) is reduced, the _Ne_ retrieval accuracy is reduced and associated with more scattering in the _Ne_ measurements. During the antenna selection process for a LE satellite with a GNSS receiver, a link budget calculation including the C/N\({}_{0}\) is important in characterizing the ionospheric remote sensing capability.