## 4 Results
### High-Sensitivity Acquisition Latency
#### 4.2.2 Tests Results Using the OCXO  
We also tested the acquisition using an OCXO. The OCXO did not require any CFO correction. The OCXO was accurately tuned using a trimmer when used for the first time, and required no further adjustments. When using an OCXO, the receiver was configured according to Table 13. The Doppler search space of \(\pm\)50 Hz accounts for possible inaccuracies in the estimation of the Doppler frequency and in the OCXO calibration.  
As shown in Table 13, when using the OCXO, stage 1 takes 7.1 s to complete. Considering that the largest Doppler shift rate experienced by a static receiver is about 1 Hz/s [48], the Doppler shift in the received signal may vary by up to 7.1 Hz when transitioning from stage 1 to stage 2. This change is larger than acquisition Doppler search step, which is set to 5 Hz. Consequently, if the second acquisition stage is not utilized, the Doppler frequency of the received signal might not align with the Doppler frequency estimated during acquisition upon initiation of the tracking process.  
To mitigate this issue, the two-stage acquisition process was employed also for the OCXO. As explained in Section 3.5, stage 2 captures new samples from the analog front-end, increasing the total acquisition latency, but reducing the latency from sample capture to the initiation of the tracking process. In this case, stage 2 was configured to perform a Doppler search of \(\pm\)10 Hz around the Doppler frequency detected in Stage 1. In this way, stage 2 reduces the time required to transition from sample capture to tracking down to 1.5 s. This ensures that when the receiver begins tracking the detected signals, the Doppler frequency of the detected signals remains close to the Doppler frequency estimated during acquisition. This approach is expected to increase the probability of successfully tracking the detected signals.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Stage** & **Doppler Search Space** & **Measured Latency** \\ \hline \multirow{3}{*}{Stage 1} & \(\pm\)50 Hz around the Doppler frequency & Initial part of sample capture: 100 ms \\  & predicted using assistance data, in steps & 7 non-coherent iterations: 7 s \\  & of 5 Hz & Total: 7.1 s \\ \hline \multirow{3}{*}{Stage 2} & \(\pm\)10 Hz around the Doppler frequency & Initial part of sample capture: 100 ms \\  & estimated in step 1, in steps of 5 Hz & 7 non-coherent iterations: 1.4 s \\ \cline{1-1}  & & Total: 1.5 s \\ \hline \hline \end{tabular}
\end{table}
Table 13: Acquisition latency using an OCXO.  
The receiver was tested using the configuration shown in Table 13, successfully acquiring and tracking weak Galileo E1b/c signals and detecting the telemetry preambles. However, we did not perform tests to quantify the impact of enabling or disabling the second acquisition stage when using the OCXO. Detailed lists of weak signals that were successfully acquired and tracked by the receiver, utilizing an OCXO, are provided in Section 4.3.  
Due to the manual estimation and correction of the CFO induced by the TCXOs being inconvenient, we switched to using an OCXO, configuring the receiver as outlined in Table 13 for subsequent tests. Nevertheless, it would be desirable to improve the acquisition algorithm to eliminate the need for manual CFO compensation. Achieving this would make the use of TCXOs practical in the proposed receiver, as TCXOs enable the detection of weak GNSS signals with a \(C/N_{0}\) as low as 20 dB-Hz.