# Comparison of L1 and L5 Bands GNSS Signals Acquisition
## 5 Conclusions  
This paper performed a very detailed comparison of the complexity of the acquisition of L1 and L5 bands signals, to determine which signal should be acquired first to then help the other, to verify the common thought that L5 band signals acquisition is more complex, and especially to quantify this ratio. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Parallel without Assistance**} & \multicolumn{4}{c}{**Serial with Assistance**} \\ \cline{2-9}
**Sensitivity** & \multicolumn{2}{c}{**Non-Coherent**} & \multicolumn{2}{c}{**Coherent Only**} & \multicolumn{2}{c}{**Non-Coherent**} & \multicolumn{2}{c}{**Coherent Only**} \\ \cline{2-9}  & **Average** & **Worst** & **Average** & **Worst** & **Average** & **Worst** & **Average** & **Worst** \\ \hline \(-140\) dBm & 31.4 & 31.4 & 31.4 & 31.4 & 7.9 & 7.9 & 2.3 & 2.9 \\ \(-145\) dBm & 31.4 & 31.5 & 31.4 & 32.0 & 7.9 & 8.1 & 2.8 & 2.9 \\ \(-150\) dBm & 32.5 & 32.6 & 18.2 & 13.8 & 8.1 & 8.2 & 3.1 & 3.2 \\ \(-155\) dBm & 31.2 & 33.2 & 15.9 & 14.4 & 8.2 & 8.2 & 3.1 & 3.1 \\ \(-160\) dBm & 33.3 & 33.0 & 14.8 & 13.8 & 8.2 & 8.4 & 3.1 & 3.1 \\ \hline \(-140\) dBm & 31.4 & 31.4 & 31.3 & 31.3 & 13.8 & 13.8 & 2.7 & 4.4 \\ \(-145\) dBm & 31.4 & 30.9 & 31.3 & 34.1 & 13.8 & 13.8 & 4.0 & 5.9 \\ \(-150\) dBm & 31.3 & 31.8 & 17.7 & 14.3 & 12.0 & 21.0 & 5.4 & 9.0 \\ \(-155\) dBm & 26.5 & 31.9 & 14.9 & 15.1 & 13.0 & 30.5 & 6.5 & 11.1 \\ \(-160\) dBm & 17.5 & 35.2 & 12.8 & 14.8 & 12.3 & 34.4 & 7.1 & 12.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 22: Final ratio of complexity (product of processing time ratio, memory ratio and frequency bins ratio) between the E5 and E1 signals obtained as the product of Tables 10 and 11. Top rows do not consider the input memory, while bottom rows consider the input memory. Figure 14: Ratio of complexity (product of processing time ratio and memory ratio) between the E5 signal and the E1 signal with a sampling frequency of 4.096 MHz. (**Left**) without assistance, (**right**) with assistance. Solid curves do not consider the input memory, while dashed curves consider the input memory. Such detailed comparison is needed because many parameters influence positively or negatively each band and each signal, such as the chipping rate, the sampling frequency, the carrier frequency, the length of the primary and secondary codes, the signal power, or the availability of a pilot channel; it is therefore difficult to make accurate estimation. In a first part, general expressions of the processing time and memory requirements have been presented and are summarized in Table 2. Such expressions are applicable for any GNSS signal, and depend on several parameters. Some parameters depend on the signal considered, such as the number of samples in one code period (which depends on the code length and sampling frequency), or the length of the secondary code; and some parameters do not depend on the signal considered but depend on the context and design, such as the number of non-coherent integrations or the number of bits used for the quantization. In a second part, the comparisons have been performed by evaluating the aforementioned expressions. An accurate estimation of the processing time and memory requirements has thus been done, providing all the details of the methodology, and considering many details (such as the search space that influences the probability of false alarm at the cell level and the signal-to-noise ratio required). In order to have a general view and not just one example, the following has been considered: Five sensitivities (from \(-140\) dBm to \(-160\) dBm with a step of \(5\) dBm); both unassisted and assisted case; and both coherent only integration (when applicable) and the use of non-coherent integration. Studies have been included to evaluate the impact of each element (Tables 7 and 18). For GPS, the L1 C/A and L5 signals have been compared.