## 4 Results
### High-Sensitivity Acquisition Latency
#### 4.2.1 Tests Results Using the TCXO  
When using the TCXO, a significant CFO was observed in the received signals. To determine the required Doppler search space for acquisition, the authors used the receiver to perform a coarse estimation of the CFO. To perform this estimation, the receiver operated in normal-sensitivity mode to predict the Doppler frequency of the tracked satellites. It then compared this prediction to the measured Doppler frequency, and averaged the error. Three different instances of TCXOs were tested. Each TCXO was tested multiple times over the course of a week. Table 10 shows the minimum and maximum estimated CFO values in the E1 frequency band for each TCXO over that week. The measurements shown in Table 10 indicate a frequency stability of approx. 56 ppb, 99 ppb, and 170 ppb for TCXO 1, TCXO 2, and TCXO 3, respectively. A certain variation in the detected CFO is expected, given that the stability of the TCXO can be influenced by environmental factors including temperature, voltage and load variations, as well as long term frequency drift [47]. However, the CFOs induced by TCXOs 2 and 3 were higher than expected. The TCXOs were mounted on a custom-made PCB, which was attached to the RFFE and exposed to the environment. The exploration of the underlying reasons behind the observed frequency stability fluctuations in the TCXOs lies beyond the scope of this study, as this paper is focused on GNSS. The large CFO observed in TCXO 2 and TCXO 3 required the use of a large Doppler search space in the acquisition. To mitigate the CFO, we implemented a crude two-step CFO estimation and correction process in the software. The first step required taking the receiver outdoors and using the receiver in normal-sensitivity mode. The receiver estimated \begin{table}
\begin{tabular}{c c} \hline \hline
**TCXO** & **Measured CFO in the E1 Frequency Band** \\ \hline TCXO 1 & \(-\)61 Hz to 89 Hz \\ \hline TCXO 2 & 109 Hz to 156 Hz \\ \hline TCXO 2 & \(-\)273 Hz to \(-\)185 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 10: CFO in the E1 frequency band when using a TXCO. \begin{table}
\begin{tabular}{c c} \hline \hline
**Step** & **Description** \\ \hline Step 1 & \multicolumn{2}{c}{Configure the Doppler search space of the two-stage acquisition process.} \\ \hline Step 2 & \multicolumn{2}{c}{Apply weak Galileo E1b/c signals to the receiver, aiming for a \(C/N_{0}\) ratio that is} \\  & approximately 20 dB-Hz \\ \hline Step 3 & \multicolumn{2}{c}{Verify that the receiver acquires and initiates tracking of the weak signals, successfully} \\  & detecting the telemetry preambles. Measure the acquisition latency. \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Acquisition latency: test procedure. the CFO during tracking using the method described above. In the second step, the receiver was tested in high-sensitivity mode, and the estimated CFO was corrected by adjusting the tuning frequency in the E1/L1 and the E5a/L5 frequency bands accordingly. When using the TCXO, the two-stage acquisition process was set as follows: the Doppler search space for the first acquisition stage was configured to accommodate Doppler prediction inaccuracies and the CFO observed in the L1/E1 frequency band, but it was limited to \(\pm\)100 Hz to limit memory usage and to prevent a large TTFF. The Doppler search space for the second stage was set to be small enough to minimize the latency from sample capture to the beginning of the tracking process, ensuring successful tracking of the detected signals. Additionally, the following constraint was considered: in the worst-case scenario, the change in the Doppler frequency of the received signal during the time it takes to go from stage 1 to stage 2 should not exceed the Doppler search space set for the stage 2. As explained in Section 3.5, failure to adhere to this constraint could result in the inability of the second stage to identify the signal detected during the first stage.