# Comparison of L1 and L5 Bands GNSS Signals Acquisition
## 4 Application to GPS and Galileo Signals
### Comparison of GPS L1 C/A and L5 Signals Acquisition  
#### 4.2.1 Determination of Acquisition Parameters  
The general parameters independent of the integration time that have been selected are summarized in Table 3 (the spreadsheets used to obtain the further tables are available in supplementary materials). The sampling frequencies are chosen to be as low as possible, because it is desired that the acquisition be as fast as possible, i.e., slightly above twice the chipping rate since these are BPSK signals (it is not exactly twice the chipping rate because the sampling frequency should never be a multiple of the chipping rate, else it would lead to a very bad accuracy in the estimation of the pseudo-ranges and position [33]). Starting with the L1 C/A signal, a typical search space of \(\pm 5\) kHz is considered [8], and since the coherent integration time is fixed to 20 ms, the frequency step is \(2/(3T_{\text{C}})=33.3\) Hz, implying \(2\times 5000/33.3\approx 300\) frequency bins. The code step is one sample, giving 2048 code bins. The number of cells is thus 300 \(\times\) 2048 = 614,400. A global probability of false alarm of \(10^{-3}\) is chosen to avoid false  
Figure 11: Evaluation of the coherent integration time and number of non-coherent accumulations: (**a**) When the coherent integration time is fixed, and the number of non-coherent accumulations is estimated; (**b**) When there is coherent integration only, and the coherent integration time is estimated. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Signal** & \(f_{\text{S}}\) & \(N_{\text{P}}\) & \(N_{\text{FFT}}\) & \(N_{\text{Z}}\) & \(N_{\text{D}}\) & \(N_{\text{S}}\) & \(B_{\text{R}}\) \\ \hline L1 C/A & 2.048 MHz & 2048 & 4096 & 0 & 20 & - & 16 \\ L5 & 20.48 MHz & 20,480 & 65,536 & 24,576 & - & 20 & 16 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters independent of the integration time selected for Global Positioning System (GPS) signals. alarms, which gives \(P_{\text{FA,C}}=1.63\times 10^{-9}\), and finally a typical probability of detection of 0.9 is chosen following [8], which gives a required final SNR of 17.15 dB. Since a case of assistance will be considered for the L5 signal, this same assistance should be considered for the L1 C/A signal to make a fair comparison. As mentioned previously, the assistance indicates the current chip of the secondary code (or a small range), and the information needed for this information (time, and receiver and satellites position) can also be used to reduce the frequency search space. Therefore, with assistance, counting an error of 60 Hz due to almanac inaccuracy and an uncertainty of 180 Hz for the receiver velocity (Doppler added by a receiver at 130 km/h in the direction of a satellite) [8], it will be assumed that the search space is reduced to 16 bins, corresponding to \(\pm\)266.7 Hz. The same is done for the L5 signal, considering four cases, coherent integration limited to 20 ms or unlimited, and with or without assistance. One difference in the assumptions is that since the L5 frequency is about 75% the one of the L1 frequency, the expected Doppler and the search space for an L5 signal should be reduced. This gives 225 frequency bins without assistance (\(\pm\)3750 Hz), and 12 frequency bins with assistance (\(\pm\)200 Hz). For the L5 signal, the assistance reduces the number of secondary code bin \(N_{\text{SCB}}\) and consequently the number of code bins \(N_{\text{CB}}\). For the application here, the best assistance is assumed, i.e., the current secondary code chip is known and \(N_{\text{SCB}}=1\) and \(N_{\text{CB}}=N_{\text{PCB}}\). Table 4 summarizes all this information. Note that to be very accurate, the number of frequency bins for the unlimited \(T_{\text{C}}\) case should be higher since \(N_{\text{FB}}=3f_{\text{SS}}T_{\text{C}}/2\), and an iterative calculation should be performed as mentioned previously. However, this would lead to a different required SNR for each sensitivity, which would be hard to synthesize.