## 4 Results and Discussion
### Analysis of JTIDS Interference and DME Mode on RE  
DME is interfered by inter-system and intra-system interference at the same time, as has been discussed above, the probability of inter-system interference are \(P(D)\) and \(P(R)\), and \(P(R)\) is the probability of intra-system interference. Some simulation parameters are the same as mentioned above, others are shown as follows:  
* When DME operates in mode Y, \(\tau_{m\_i,j}\) = 39.5 \(\upmu\)s, \(\tau_{m\_r}\) = 33.5 \(\upmu\)s and \(t_{d}\) = 66 \(\upmu\)s.
* JTIDS signal duration: \(\tau_{f}\) = 5.772 ms.
* Number of aircraft: variation from 5 to 400 every 15.
* \(f_{f}\) = 0 means that there is no JTIDS interference, \(f_{f}\) = 128 means that JTIDS is in present.  
When the number of aircraft varies from 5 to 400 with 15 spacing, DME RE based on Equation (17) is illustrated in Figure 6, where mode X and Y indicate that DME operates in mode X and Y, respectively. The numbers on the curve marks are DME transponder reply rate accordingly.  
Figure 6 shows that DME reply efficiency decreases obviously when interfered by JTIDS compared to no JTIDS interference, the decrease value is about 5% when there are 5 aircraft. However, RE decreases smaller as the number of aircraft increases, the decrease value is about 2% when the number of aircraft is 395. The reason is that inter-system interference is basically unchanged when the number of aircraft changes, but intra-system interference increases with the number of aircraft. Intra-system interference is small when there are small numbers of aircraft, so inter-system interference is the main interference. But as the number of aircraft increases, the main interference is converted  
Figure 5: Number of aircraft vs. reply efficiency.  
Figure 6: Reply efficiency in different modes vs. number of aircraft.  
from inter-system interference to intra-system interference. As a result, the difference of RE between JTIDS in present and JTIDS in absent becomes smaller and smaller as the number of aircraft increases.  
Since the calculation for reply efficiency is based on pulse collision, and DME signal duration in mode Y is larger than that in mode X from Table 1, the collision probability in mode Y is larger than that in mode X according to Equations (13)-(15); as a result, reply efficiency in mode Y is smaller than that in mode X just as shown in Figure 6. Moreover, we can see that the difference of reply efficiency between mode X and Y increases with the number of aircraft, and yet the differences is not always increases in fact. According to Equation (17), the difference \(\Delta R_{e}\) can be calculated as follows:  
\[\Delta R_{e}=R_{eX}-R_{eY}=\frac{e^{-\lambda_{i}\times 1.5095\times 10^{-5} \times 0.9434}}{\lambda_{i}\times 7.3526\times 10^{-5}+1}-\frac{e^{-\lambda_{i} \times 3.8463\times 10^{-5}\times 0.9404}}{\lambda_{i}\times 1.0273\times 10^{-4}+1} \tag{18}\]  
where \(R_{eX}\) and \(R_{eY}\) are reply efficiencies in mode X and Y, respectively. If the limitations of pulse density \(\lambda_{i}\) are not considered, \(\Delta R_{e}\) with respect to the number of aircraft is shown in Figure 7. It can be seen that if the number of aircraft is less than about 500, \(\Delta R_{e}\) increases with the number of aircraft, and yet if the number is more than 500, \(\Delta R_{e}\) decreases. In the present practice, DME capacity is usually less than 200 owning to the limitations of reply efficiency and reply rate.