# A Fine Fast Acquisition Scheme for a Communication and Navigation Fusion System
## 5 Simulation Results and Analysis
### Performance Analysis
#### 5.2.1 Detection Performance
\[\mathrm{P_{Bd}}=\frac{1}{\mathrm{P_{Bd}}}\int_{\mathrm{R}}^{\infty} \mathrm{f_{Y}(y)}\sum_{i=1}^{\mathrm{B_{R}}\mathrm{f_{X}}}\left(\int_{0}^{ \mathrm{th}}\mathrm{f_{X}(x)}\right)^{i-1} \tag{40}\] \[\mathrm{P_{Bm}}=\left(\int_{0}^{\mathrm{th}}\mathrm{f_{X}(x)} \right)^{\mathrm{P_{B}}\mathrm{P_{B}}-1}\int_{0}^{\mathrm{th}}\mathrm{f_{Y}(y)}\] \[\mathrm{P_{Be}}=1-\mathrm{P_{Bd}}-\mathrm{P_{Bm}}\] \[\mathrm{P_{Bcr}}=\left(\int_{0}^{\mathrm{th}}\mathrm{f_{X}(x)} \right)^{\mathrm{P_{B}}\mathrm{P_{Bfa}}}=1-\mathrm{P_{Bcr}}\]  
All probabilities \(\mathrm{P_{Bd}}\), \(\mathrm{P_{Bm}}\), \(\mathrm{P_{Be}}\), \(\mathrm{P_{Bcr}}\), and \(\mathrm{P_{Bfa}}\) are rewritten as \(\mathrm{P_{d}}\), \(\mathrm{P_{m}}\), \(\mathrm{P_{e}}\), \(\mathrm{P_{cr}}\), and \(\mathrm{P_{fa}}\) for clear description in the following analysis. Figure 13 gives the ROC curves of these four methods. Because of the TC criterion, TDCC method has the worst ROC curves compared with the other three methods. TC criterion test every cell one by one, so \(\mathrm{P_{d}}\) decrease seriously when \(\mathrm{P_{fa}}\) is high enough. All methods except MAX/TC use double dwell technique, which can effectively reduce \(\mathrm{P_{fa}}\) by performing tests twice. However, this double dwell structure cannot compensate the weakness of TC criterion used in TDCC method. When the received signal has a higher SNR, the detection performance can be effectively improved using double dwell structure. However, this technique also causes lower \(\mathrm{P_{d}}\) when the SNR of received signal is low enough. DD/MAX method adds double dwell technique in MAX/TC method. Figure 12: \(\mathrm{P_{Bd}}\) and \(\mathrm{P_{Bm}}\) versus multiple parameter T.  
Therefore, DD/MAX method has better performance than MAX/TC method. However, DD/MAX has lower \(\rm P_{d}\) when \(\rm P_{fa}\) is high enough compared with MAX/TC method. DD-MAX/TC-CACFAR gives better performance than DD/MAX method because of the CACFAR technique and the coarse-to-fine structure utilized. Equation (4) indicates that smaller frequency estimation error leads to smaller attenuation. The first dwell of these two methods has similar detection performance while the second dwell of the DD-MAX/TC-CACFAR method has smaller integration gain loss, which is about 2 dB according to the parameters described above. Figure 14 shows the \(\rm P_{d}\), \(\rm P_{m}\), and \(\rm P_{fa}\) of these methods versus SNR. The two figures realize different SNR by two approaches. Figure 14a changes signal power while Figure 14b changes noise power. \(\rm P_{fa}\) remains 0.001 in Figure 14a for the comparison of \(\rm P_{d}\) and \(\rm P_{m}\) under different SNR environments. The DD-MAX/TC-CACFAR method has higher \(\rm P_{d}\) compared with the other three method. Figure 14b shows the advantage of the CACFAR technique utilized in DD-MAX/TC-CACFAR method. The detection threshold in DD-MAX/TC-CACFAR and TDCC method adaptively changed based on the noise power, which ensures the constant \(\rm P_{fa}\) when noise power changes. Therefore, \(\rm P_{fa}\) of DD-MAX/TC-CACFAR and TDCC method remains the value of 0.001. The fixed threshold used in the other two methods cause the huge change of \(\rm P_{fa}\). DD/MAX and MAX/TC methods can have smaller \(\rm P_{fa}\) than that of DD-MAX/TC-CACFAR method and TDCC method in this situation. However, this decrease of \(\rm P_{fa}\) causes the decrease of \(\rm P_{d}\). Therefore, a constant false alarm is especially important when the noise power fluctuates. Figure 15 shows the influence of coherent and non-coherent integration. Both can effectively improve the \(\rm P_{d}\). On the other hand, the frequency error loss and square loss of CIT and NCT becomes bigger as with large CIT and NCT. The effect becomes smaller when CIT or NCT is large enough. In practical applications, the choice of CIT and NCT requires consideration of other factors such as the sensitivity requirements, receiver hardware resources, and data bit transition. Figure 13: ROC curves.