## 3 Numerical Verification of Received Pulsed Environment Interference Model Based on BER
Set the SNR to 10 dB, we can figure out that the noise in the channel should be less than \(-60\) dBm if the output power is 100 W (50 dBm). For the signal bandwidth is 640 kHz, according to (24), the calculated noise density (ND) should be \(-118\) dBm/Hz. The SNR is used to characterize the relationship between signal and noise in the system. The expression is as follows:  
\[SNR(\rm dB)=P_{signal}-P_{noise} \tag{23}\]  
Figure 9: Schematic diagram of Friis transmission formula in free space. where \(P_{signal}\) is the signal power and \(P_{noise}\) is the noise power. The ND refers to the noise power corresponding to each Hertz frequency in the system operating frequency band, which reflects the noise energy level of 1 Hz bandwidth. The ND can be used to estimate the total noise power within the operating bandwidth of the system, as follows:  
Figure 8.0  
where \(P_{total}\) is the total noise power, and \(F_{S}\) is the Nyquist sampling frequency. In the radio receiver, it consists of heterodyne receiver and the demodulate module. Then the signal passes through the demodulation part, and the digital processor that includes the judging circuit and the code-switching module, and we use a decode module before exporting the signal out. In the pulse signal interference source, we establish the sources generating simple pulses, LFM pulses and bi-phase coded pulses respectively. By modifying the parameters of the pulses and observing the variation of the BER, the degree of interference of different pulses can be figured out. According to the simulation experiment based on the behavioral model, as is shown in Figures 10 and 11, the curve is drawn according to the Formula (15), which represents the ideal curve of the BER changing with the SIR under different duty cycles. The discrete points in the figure are the measured values obtained from the simulation experiment based on the above model. The measured values all fall on the theoretical curves obtained from the simulation, indicating that the measured results are consistent with the theoretical results, and verify the correctness of the model proposed in Section 2. At the same time, it can also be obtained from the curve that, according to the property in (17), i.e., the function value tends to 1 when the independent variable of the error function tends to 0, it is deduced that there is an upper bound for the BER. In this model, calculated according to the set parameters, at a 30% duty cycle, the upper bound of the BER is 0.364. When the SIR is the same, the higher the duty cycle of the interference pulse is, the higher BER can achieve, and the higher the corresponding upper bound of the BER can be. The above simulation results are consistent with the theoretical derivation results, further verifying the correctness of the theoretical derivation. Figure 8.1 Variation curve of receiver BER with SIR under pulse signal interference (linear form). As is shown in Figure 12, under the pulsed interference of different modulation, the relationship between the BER and the pulse duty cycle is simulated. As the SIR increases, interference to the receiver from simple pulse and bi-phase-coded pulse with the same pulse parameters is significant and there is a similar change in receiver BER. In contrast, with LFM pulse interference, the receiver BER is always at a low level. In other words, the interference of LFM pulses to the receiver is not apparent. The theoretical analysis of the reasons is as follows:  
The LFM pulse has no fixed carrier frequency, and the pulse signal energy is less distributed in the working frequency band of the receiver, so the interference to the receiver is not apparent. According to the spectrum distribution of the three pulse signals, the simple pulse energy is the most concentrated, mainly at the carrier frequency of the pulse signal. The spectrum of bi-phase-coded pulse widens to a certain extent due to phase  
Figure 8.2 Variation curve of receiver BER with SIR under pulse signal interference (logarithmic form).