## 3 Numerical Verification of Received Pulsed Environment Interference Model Based on BER  
In order to verify the theoretical results proposed in Section 2, we establish a simulation model of the BDS interfered by pulse signal, which is shown in Figure 7. Based on the frame shown in Figure 7, we can divide the whole system into five parts, the pulsed signal interference source, the radio transmitter, the channel, the radio receiver and BER calculation module. Based on the system model in Figure 7, the behavioral model and model parameters of each module are established in the Advanced Design System (ADS) platform, as shown in Figure 8. By adjusting the functional parameters in the behavioral model, different types of receivers can be simulated. Firstly, a complete BDS functional model is established, including radio transmitter, channel and radio receiver. BER is one of the important indexes to evaluate whether the receiver is disturbed. The BER of BDS receiver can be displayed by the BER calculation module. In the case of no interference, the main cause of BER is channel noise, when under pulsed signal interference environment, pulses with different parameter or modulation are radiated to the receiver, which is collected and post processed by the BDS receiver antenna together with the functional signal through different transmission channels. Changing the parameters of pulse signal and analyzing the BER by using the method proposed in this paper, the interference degree of BDS receiver under the pulsed signal interference environment with different parameters can be evaluated by observing the change trend of BDS BER. In the radio transmitter, we use a module to read the signal and code it with 16-bits pulse code modulation (PCM) then convert the output integer data to binary non-return-to  
Figure 8: Diagram of the behavioral model. Figure 7: Block diagram of the system model. zero code (NRZ). As the ideal rectangle bit flow has a very broad spectrum after modulation, we divide it to two routes and let it go through a low-pass filter, in order to narrow the bandwidth. We then set the stop frequency of the raised cosine low pass filter to Nyquist sampling frequency, and then modulate the signal by 4 QAM. The output signal is expressed in (19), which we can make it clear that the QAM output signal can be regarded as a signal that is controlled of its range and its phase. \[V_{3}(t)=V_{1}(t)\cos\omega_{c}t+V_{2}(t)\sin\omega_{c}t \tag{19}\]  
According to the Friis transmission formula proposed in [42], as shown in Figure 9 and formula (20), in the channel, if we use \(P_{t}\) as the transmit power, \(P_{r}\) as the received power, and converting it into a logarithmic form, then we get the system loss \(L_{\rm s}\) as (21). \[P_{r}=\frac{P_{t}\cdot G_{t}\cdot G_{r}\cdot\lambda^{2}}{\left(4\pi R\right)^ {2}} \tag{20}\]  
\[L_{s}=10\lg\left(\frac{P_{t}}{P_{r}}\right)=L_{p}-G_{t}-G_{r} \tag{21}\]  
\(L_{p}\) represents the loss of electromagnetic field in free space, which can be calculated by (22). \[L_{p}=\frac{(4\pi R)^{2}}{\lambda^{2}}=\frac{(4\pi Rf)^{2}}{\rm c^{2}}=32.45+20 \lg f(\rm MHz)+20\lg R(\rm km)(\rm Logarithmic\ representation) \tag{22}\]  
where \(G_{t}\) presents the transmit antenna gain, \(G_{r}\) presents the receiving antenna gain, \(f\) is the working frequency, \(R\) is the transmission distance. Except the loss module in the channel, we also need to consider the interference. The exterior interference for navigation receiver points to all kinds of noise picked up by the receive antenna, such as artificial interference, the atmospheric noise, jamming and the universe noise, etc. The interior interference indicates the devices' own noise, it is easy to filter out, so we do not consider about it generally. In this part, we add exterior interference to the system, which is similar to the GWN in the receiver's pass-band. Thus, the received power and the noise can be weighed by signal-to-noise ratio (SNR), as shown in (23).