# A Fine Fast Acquisition Scheme for a Communication and Navigation Fusion System
## 5 Simulation Results and Analysis
### Performance Analysis  
#### 5.2.1 Detection Performance  
The threshold in DD-MAX/TC-CACFAR method can be adjusted adaptively based on the noise power. However, the setting of multiple parameter T can still influence the detection performance. Therefore, the performance of DD-MAX/TC-CACFAR method corresponding to different T is firstly analyzed. Probability of correct rejection \(P_{\text{Bcr}}\) and probability of false alarm \(P_{\text{Bfa}}\) in H0-block versus different multiple parameter T are shown in Figure 10. \(P_{\text{Bcr}}\) and \(P_{\text{Bfa}}\) are not affected by SNR and the lower bound of T can be obtained based on the requirements of both. As the multiple parameter T increases, higher \(P_{\text{Bcr}}\) and lower \(P_{\text{Bfa}}\) can be realized. \(B=B_{\text{fBc}}\) and \(N_{\text{nc}}\) also have influence on \(P_{\text{Bcr}}\) and \(P_{\text{Bfa}}\). With T unchanged, an increase in B will cause the decrease of \(P_{\text{Bcr}}\) and an increase in \(N_{\text{nc}}\) will cause the increase of \(P_{\text{Bcr}}\). As a matter of fact, the choice of B mainly depends on the implementation of the receiver. The larger the B, the more hardware resources the receiver consumes. In CNFS positioning receiver, the default setting of B is 70. Though there are only two values of \(N_{\text{nc}}\) in Figure 11, we can draw the conclusion that \(N_{\text{nc}}\) has greater effect on \(P_{\text{Bcr}}\) and \(P_{\text{Bfa}}\). Positioning receiver can meet the requirement of \(P_{\text{Bcr}}\) and \(P_{\text{Bfa}}\) with smaller T when a larger value of \(N_{\text{nc}}\) is used. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline PRN code length & 10,230 \\ Available PRN code number & 64 \\ Code rate & 10.23 MHz \\ Navigation message data rate & 100 bps \\ Code phase search step & 0.5 chip \\ Frequency search space & \(-\)3 kHz to 3 kHz \\ Frequency search step in first dwell & 1000 Hz/T\({}_{\text{coh}}\) \\ Frequency search step in second dwell & 100 Hz/T\({}_{\text{coh}}\) \\ Block size & 70 \\ Block number & 2046 \\ CIT & 5 ms \\ NCT number & 2 \\ False alarm penalty time & 500 ms \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 11: \(P_{\text{Bcr}}\) and \(P_{\text{Bfa}}\) versus multiple parameter T.  
Figure 12 gives the influence of multiple parameter T on probability of detection \(\mathrm{P_{Bd}}\) and probability of error \(\mathrm{P_{Bm}}\) when \(\mathrm{SNR}=-36\) dB. The increase of T leads to the decrease of \(\mathrm{P_{Bd}}\) and the increase of \(\mathrm{P_{Bm}}\). NCT can improve the SNR of received signal. Therefore, \(\mathrm{P_{Bd}}\) can be effectively improved with larger \(\mathrm{N_{nc}}\). The receiver cannot meet the requirement of \(\mathrm{P_{Bd}}\geq 0.9\) if \(\mathrm{N_{nc}}=1\) when the SNR of received signal is \(-36\) dB. When the influence of T on \(\mathrm{P_{Bcr}}\) and \(\mathrm{P_{Bfa}}\) is taken into consideration at the same time, the value of T is limited in a certain range. Considering the situation of \(\mathrm{B}=70\) and \(\mathrm{N_{nc}}=2\), the value of T can be in the range of \((5,8)\) to meet the requirement of \(\mathrm{P_{Bd}}\geq 0.9\) and \(\mathrm{P_{Bcr}}\geq 0.99\). Though larger \(\mathrm{N_{nc}}\) leads to better detection performance, we cannot set the value of \(\mathrm{N_{nc}}\) as larger as possible because of the square loss of NCT. The influence of coherent integration, NCT, and SNR of the received signal is analyzed after. Three other different methods-- MAX/TC, DD/MAX, and TDCC method--are simulated here as the comparison [26; 30]. Detection performance of TDCC method is in terms of one cell in search space while the other three methods are in terms of one block. Therefore, the corresponding probabilities in the TDCC method are rewritten as Equation (40).