# GNSS Signal Distortion Estimation: A Comparative Analysis of L5 Signal from GPS II and GPS III
## 3 Results Analysis
### Signal Analysis  
This section first verifies the feasibility and accuracy of the model and algorithm from the time-domain waveform and the power spectrum density (PSD). On this basis, the digital and analog impulse responses of GPS II and GPS III signals are estimated and analyzed in detail. Finally, the ranging error reference of the signal under the estimated navigation payload transmission channel is given to the user receivers. Measurements of all GPS BIIF and GPS III satellites were performed with NTSC's 40 m high-gain antenna at the ground station of Hao-ping, to serve as data for analysis of signal distortion. The signal sampling rate was set to 250 MHz, and the accumulated average was 100 code periods. To verify the accuracy of the model and estimation algorithm, this study first compares the differences between the measured data and model calculations from power spectra and time-domain waveforms. BIIF-5 and BIII-2 are considered as examples of GPS II and GPS III, respectively. Figures 4-7 compare the measured signal and model estimation results from the time and frequency domains, respectively. Regardless of it being a GPS II or a GPS III signal, the figure indicates that the power spectrum and the time-domain waveform estimated by the model are completely consistent with the measured signal. The above results directly demonstrate the effectiveness and accuracy of the models and algorithms in this work. A significant carrier leakage due to digital distortion can be observed at integer multiples of the power spectrum in Figure 5, which was present in all BIIF satellites. However, referring to Figure 7, this phenomenon was absent in GPS III satellites. From the power spectrum, it is evident that the digital distortion of the GPS III satellite transmission channel was significantly improved. The digital distortion was further calculated according to the joint estimation method. Table 1 summarizes the L5 digital distortion for the latest data from all launched GPS IIF and GPS III satellites. Figure 4: BIIF-5 L5-Cd time-domain waveform. Figure 5: BIIF-5 L5 PSD. Figure 6: BIII-2 L5-Cd time-domain waveform. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c} \hline \hline
**Satellite** & **BIIF-4** & **BIIF-2** & **BIIF-3** & **BIIF-4** & **BIIF-5** & **BIIF-6** & **BIIIF-7** & **BIIF-4** & **BIIF-9** & **BIIIF-10** & **BIIIF-11** & **BIIIF-12** & **CFS** & **CFS** & **CFS** & **CFS** & **CFS** \\ \hline Date & -32 & -21 & -30 & -20 & -30 & -30 & -20 & -20 & -10 & -20 & -10 & -20 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\ Fixed & -11 & -20 & -20 & -20 & -50 & -60 & -50 & -40 & -20 & -10 & -40 & -30 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Navigation payload transmission channel digital distortion. It can be seen from Table 1 that all BIIF satellites had different degrees of digital distortion. The BIIF-1 satellite had the highest digital distortion of the L5 data signal, reaching 3.2% chips; BIIF-9 and BIIF-11 satellites had the lowest at 1% chips. For the L5 pilot signal, digital distortion in the BIIF-6 satellite was the highest, reaching 6% chips, whereas that in the BIIF-10 satellite was the smallest, at 1% chips. In addition, the BIIF-1, BIIF-3, and BIIF-5-12 satellites had inconsistent digital distortions of data and the pilot signal, with a maximum difference of 3% chips. Data and pilot inconsistencies indicate an imbalance in the quadrature modulation I/Q branch. Although the digital distortion of GPS II was small and tolerable, GPS III had negligible digital distortion compared with GPS II, consistent with the PSD. After the digital distortion was calculated accurately, the satellite analog impulse response could be estimated. Figures 8-11 show the amplitude and group delay characteristics of the navigation payload analog channel. Figure 8: BIIF-5 amplitude characteristic. Figure 7: BIII-2 L5 PSD. Figure 11: BIII-2 group delay characteristic. Figure 10: BIIF-5 group delay characteristic. Figure 9: BIII-2 amplitude characteristic.