# Impact Evaluation of DME Beacons on BeiDou B2a Signal Reception Performance
## 3 Interference Evaluation Model
### Effective Carrier-to-Noise Ratio Degradation
#### 3.2.1 Single DME Signal Interference  
For the case where \(P_{k}\leq P_{th}\), as shown in Figure 4, we have the following:  
When the received signal power remains below the blanking threshold, the PB maintains inactive status, resulting in \(PDC_{i}=0\). The width of the equivalent rectangular pulse can be obtained by directly integrating the signal:  
\[P_{eq}=\int_{-\infty}^{\infty}e^{-\alpha t^{2}}dt. \tag{5}\]  
The equivalent rectangular pulse width of a single pulse is 2.6 us.  
The DME pulse transmits 2700 pulse pairs per second (\(\lambda_{\text{PRR}}=2700\)), and the equivalent pulse signal power per second is  
Figure 3: The structure of a general civil aviation BDS receiver.  
According to the RTCA calculations, the thermal noise power spectral density of the GNSS receiver \(N_{0}\) was \(-200\) dBW [13]. For the B2a signal receiver, the bandwidth \(BW\) was \(20\) MHz [6], where \(R_{i}\) can be expressed as  
\[Ri_{i}=\frac{P_{k}\times dc_{i}}{N_{0}\times BW}. \tag{7}\]  
For another case where \(P_{k}\geq P_{thr}\), as shown in Figure 5, we have the following:  
It must be noted that \(dc_{i}\) and \(R_{i}\) follow Formulas (6) and (7). Since the PB was triggered, the equivalent rectangular pulse width could not be determined through integration. For the pulse width of the blanking part, the power of a single pulse pair was made equal to the threshold:  
\[P_{k}e^{-\alpha t^{2}}=P_{thr}. \tag{8}\]  
It can be calculated that  
\[t=\pm\sqrt{\frac{\ln(P_{k}/P_{th})}{\alpha}}. \tag{9}\]  
After pulse blanking, the signal only retains residual components beyond the eliminated main lobe, as shown in the red shaded part in Figure 5. The area of the equivalent rectangular pulse in the figure is equal to the area of the signal residual part. The equivalent  
Figure 4: Blanking of a weak pulse signal.  
Figure 5: Blanking of a strong pulse signal.  
rectangular pulse width of the residual signal can be obtained from the complementary error function (ERCF):  
\[P_{eq}=\frac{\text{erfc}(w\sqrt{\alpha})}{\sqrt{\alpha}}, \tag{10}\]  
where \(w\) is half of the pulse blanking width, which is equal to \(t\) in value. Subsequently, the equivalent rectangular pulse width was used to calculate the value of \(PDC\):  
\[PDC_{i}=P_{eq}\times\lambda_{PRR}. \tag{11}\]  
The performance of the PB was directly related to the selection of the pulse blanking threshold. According to RTCA validation, the receiver achieved better overall performance when \(P_{th}=-120\) dBW [13], and this value has been implemented in practical receivers. Additionally, the calculated total continuous aviation RFI power spectral density was \(I_{0,WB}=-197.5\) dBW/Hz [13]. By incorporating these parameters, the \((C/N_{0})_{\text{deg}}\) values under different interference power levels for a single DME signal were obtained, as illustrated in Figure 6.  
The \(PDC\) remained a zero value before the PB was triggered. However, both \(R_{i}\) and \((C/N_{0})_{\text{deg}}\) exhibited increases progressively as the interfering signal persisted and \(P_{k}\) gradually increased. \(R_{i}\) and \((C/N_{0})_{\text{deg}}\) reached the maximum value when \(P_{k}\) equaled \(P_{th}\). When \(\text{P}_{k}>\text{P}_{\text{th}}\), \(PDC\) began to show positive values due to the blanking effect of PB, while \(R_{i}\) and \((C/N_{0})_{\text{deg}}\) decreased as the interference signals diminished. However, when \(P_{k}\) became excessively large, the overactive blanking effect led to a significant reduction in the B2a signal power, while the \((C/N_{0})_{\text{deg}}\) gradually res  
Figure 6: The impact of the DME signal received power on \(PDC\) (a), \(R_{i}\) (b), and \((C/N_{0})_{\text{deg}}\) (c).