# Comparison of L1 and L5 Bands GNSS Signals Acquisition
## 4 Application to GPS and Galileo Signals
### Comparison of Galileo E1 and E5 Signals Acquisition  
The general parameters independent of the integration time that have been selected for Galileo signals are summarized in Table 14. For the Galileo signals, three cases are compared. E1 with a sampling frequency slightly higher 6 times the chipping rate in order to have a code step small enough to give the same losses as in the BPSK case [24]. However, this leads to long sequences (longer than the E5a or E5b). Therefore, E1 with a sampling frequency slightly higher than four times the chipping rate to cover the main lobes of the signals is then considered, but this requires some additional techniques to compensate the correlation shape [34; 35]. Finally, for E5a or E5b, a sampling frequency slightly higher than twice the chipping rate is considered, like the L5 signal. The E1 and E5 secondary codes are both 100 ms long even if the number of chips is different, therefore this value will be considered as coherent integration time when using non-coherent integration. Starting with the E1 signal, to be fair compared to the parameters selected for the GPS signals, a typical search space of \(\pm 4\) kHz is considered (since the Galileo satellites have a lower speed and a maximum range rate around 20% lower); and since the coherent integration time is fixed to 100 ms, the frequency step is \(2/(3T_{\rm C})=6.67\) Hz, implying \(2\times 4000/6.67\approx 1200\) frequency bins. The code step is one sample, giving 16,384 primary code bins for a sampling frequency of 4.096 MHz and 24,576 primary code bins for a sampling frequency of 6.144 MHz. Since the E1 secondary code is 25 chips long, the number of cells is 1200 \(\times\) 16,384 \(\times\) 25 = 491,520,000 and 1200 \(\times\) 24,576 \(\times\) 25 = 737,280,000 respectively. A global probability of false alarm of \(10^{-3}\) gives \(P_{\rm FA,C}=2.04\times 10^{-12}\) and \(P_{\rm FA,C}=1.36\times 10^{-12}\) respectively, and finally a typical probability of detection of 0.9 gives a required final SNR of 18.30 dB and 18.35 dB respectively. Then, as for the GPS, a case with assistance is also considered, where the current chip of the secondary code is known, and where the frequency search space is reduced to 213.3 Hz (80% of the 266.7 Hz of the GPS L1 C/A), giving 32 frequency bins. The same is done for the E5 signal, considering four cases, coherent integration limited to 100 ms or unlimited, and with or without assistance. As for GPS, the only difference in the assumptions is that the frequency search space is about 75% the one of the E1 signal, which gives 900 frequency bins without assistance (\(\pm 3000\) Hz), and 24 frequency bins with assistance (\(\pm 160\) Hz). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Signals** & \multicolumn{4}{c}{**No Assistance**} & **Assistance** \\ \cline{3-7}  & **-140 dBm** & **-145 dBm** & **-150 dBm** & **-140 dBm** & **-145 dBm** & **-150 dBm** \\ \hline Number of frequency bins in the search space & L1 C/A & 301 & 301 & 301 & 17 & 17 & 17 \\  & L5 NC & 225 & 225 & 225 & 13 & 13 & 13 \\  & L5 C & 169 & 529 & 1643 & 7 & 23 & 73 \\ \hline Number of frequency bins searched until detection & L1 C/A & 135.5 & 146.9 & 139.9 & 7.3 & 7.0 & 7.9 \\  & L5 NC & 100.5 & 109.4 & 104.3 & 5.1 & 4.9 & 5.6 \\ \hline Ratio of number of frequency bin in the search space & L5 NC versus L1 C/A & 0.75 & 0.75 & 0.75 & 0.76 & 0.76 & 0.76 \\  & L5 C verses L1 C/A & 0.56 & 1.76 & 5.46 & 0.41 & 1.35 & 4.29 \\ \hline Ratio of number of frequency bins searched until detection & L5 NC versus L1 C/A & 0.74 & 0.74 & 0.75 & 0.70 & 0.71 & 0.71 \\  & L5 C verses L1 C/A & 0.56 & 1.75 & 5.08 & 0.43 & 1.44 & 4.52 \\ \hline \end{tabular}
\end{table} 
Table 13: Theoretical and average of the measured number of frequency bins and their ratio between L5 and L1.