## 3 Analysis Method of iNterference on DME  
### Metric of Interference on DME  
A DME signal flowchart is shown in Figure 4 during the process of the whole work. There are \(n\) (\(n>1\)) aircraft installed DME interrogator transmit interrogations to the ground transponder at the same time; moreover, JTIDS is in the same electromagnetic environment as DME. All interrogations transmitted from different DME interrogators form an interrogation pulse-stream with pulse density \(\lambda_{i}\). Since the initial time and PRF of interrogations are all different, it is unavoidably for pulses in the interrogation pulse-stream to collide with each other. Thus intra-system interference occurs. JTIDS signal is called inter-system interference as far as DME is concerned because they belong to different systems. The density of valid request pulse changes from \(\lambda_{i}\) to \(\lambda_{i2t}\) after interfered by intra-system interference and JTIDS during the transmission from interrogator to transponder. A period named as dead time immediately following the decoding of a valid interrogation during which a received interrogation will not cause a reply to be generated, dead time is intended to prevent the transponder from replying to echoes resulting from multi-path effects. The subsequent pulse will not be received during dead time, the collision between subsequent pulse and dead time is a part of intra-system interference, then the density of valid request pulse changes from \(\lambda_{i2t}\) to \(\lambda_{r}\) after overlapping with dead time.  
Figure 3: The frequency distribution for DME and JTIDS.  
Figure 2: The time distribution of a JTIDS slot.  
Transponder transmits identification pulse pairs every 40 s at the speed of 1350 ppps besides transmitting request pulses, the maximum period of identification pulse transmitting is 5 s, so the average valid density of identification pulse \(\lambda_{id}=\frac{5}{50}\times 1350=169\) ppps. Moreover, identification pulse has priority over request pulse to transmit, that is to say, if the time of identification pulse overlaps with request pulse, then request pulse is thought to be interfered and cannot be received by interrogator, so identification pulse is inter-system interference source too. Reply consisting of identification and request pulses not interfered whose valid density is \(\lambda_{t}\) are transmitted from transponder to interrogators, which can be interfered by JTIDS again, the density of valid request pulse is \(\lambda_{t2i}\) when they arrive at interrogators. The density of valid request pulse change from \(\lambda_{i}\) to \(\lambda_{t2i}\) after a whole working process, so the ratio of replies received to the total of transmitted interrogations by the interrogators named as reply efficiency \(R_{e}\) can be thought to be indicator for capability of DME. \(R_{e}\) can be calculated as follows:  
\[R_{e}=\frac{\lambda_{t2i}}{\lambda_{i}}=\frac{\lambda_{r}}{\lambda_{i}}\cdot \frac{\lambda_{t}}{\lambda_{r}}\cdot\frac{\lambda_{t2i}}{\lambda_{t}}=P\left( I\right)\cdot P\left(D\right)\cdot P\left(R\right) \tag{2}\]  
where \(I\) denotes the event that valid interrogations are received by transponder, \(D\) is the event that valid interrogations are not interfered by identification pulses, and \(R\) is the event that reply transmitted from transponder which is not interfered by JTIDS. The probabilities of these events are \(P(I)\), \(P(D)\) and \(P(R)\), respectively.