# A Fine Fast Acquisition Scheme for a Communication and Navigation Fusion System
## 5 Simulation Results and Analysis
### Performance Analysis
#### 5.2.2 Acquisition Time Analysis  
The proposed SSR method uses ATI and CPPI to reduce search space number \(\mathrm{N_{S}}\) and block number \(\mathrm{N_{B}}\). The number of adjacent FSBSs is related to the signals received. Limited by the signal power transmitted by FSBS and the sensitivity of positioning receiver, the positioning receiver receives up to 7 signals from different base stations in general. The number of adjacent FSBSs is listed in Table 2. Compared with the situation without ATI, the search space number is reduced from 64 to at least 12. Figure 14: (a) \(\mathrm{P_{d}}\) and \(\mathrm{P_{m}}\) versus SNR (\(\mathrm{P_{fa}}=0.001\)) (noise power remains constant); (b) \(\mathrm{P_{d}}\) and \(\mathrm{P_{fa}}\) versus SNR (signal power remains constant). The code phase search step and the chip number in one period of PRN code indicates that the original size of code phase search space is 20,460. Chip duration is about 30 m. Maximum distance dbs between FSBSs is less than 1000 m due to the limitation of the signal power transmitted by FSBS and the sensitivity of positioning receiver. Therefore, the maximum relative code phase difference of signal transmitted by FSBSs positioning signal generator is less than 103 based on Equation (17). Considering the code phase in one positioning signal as the code phase baseline, the relative code phase differences of the signals transmitted by other generators are set to random numbers in this range. Based on the analysis in Section 3.1, the code phase search space size becomes 206. In this case, the new search space size is shown in Table 3 below. The block number is reduced from 2046 to 21. Monte Carlo simulations are utilized to evaluation the effect of proposed method on acquisition time. The effect of SSR method on acquisition time is shown in Figure 16. \"Tr1\", \"T1\", \"Tr0\", \"T0\", and \"Tacq\" in the legend indicate \(\overline{\text{T}}_{\text{r1}}\), \(\overline{\text{T}}_{\text{1}}\), \(\overline{\text{T}}_{\text{r0}}\), \(\overline{\text{T}}_{\text{0}}\), and \(\overline{\text{T}}_{\text{acq}}\) in Equations (31), (35), (37), and (39) in the following figures. Figure 16a gives the time taken for H1-SS, H0-SS and all search spaces with and without SSR method versus SNR. Figure 16b gives the comparison versus multiple parameter T. Because of the significant reduce of search space size and number, time taken for H1-SS, H0-SS, and MAT is effectively reduced. The MAT has about 10 times reduction. Different multiple parameter T leads to different acquisition time. When T is smaller than about 6, MAT is dominated by the P\({}_{\text{fa}}\). Therefore, MAT can be reduced as the T increases. MAT is dominated by large P\({}_{\text{m}}\) and small P\({}_{\text{d}}\) when T is bigger than 6. Acquisition time grows faster as the T becomes bigger. The choice of T requires consideration based on the detection performance in Figure 11, Figure 12 and the acquisition time in Figure 16b. In this paper, T is set to 5.5 to realize a reasonable probability of false alarm (P\({}_{\text{fa}}\) = 0.001) and acquisition time. Figure 17 shows the acquisition time of four methods versus SNR, which can be analyzed together with Figure 14. The changes in signal power in Figure 17a is realized by adjusting signal transmitting power of FSBS. Because the actual power of the noise of the received signal cannot be accurately controlled, so the changes of noise power in Figure 17b is realized by adding simulative noise with different power on received signal. Because of the constant P\({}_{\text{fa}}\) of all methods in Figure 17a, the changes of acquisition time versus SNR is dominated by P\({}_{\text{d}}\). Higher P\({}_{\text{d}}\) with higher SNR can decrease the acquisition time. MAT and the time taken for H1-SS and H0-SS of proposed method is the shortest compared with the other three methods. This advantage is realized based on the SSR method and DD-MAX/TC-CACFAR method described in Section 3.