## 2 Modeling of Receiver Pulsed Environment Interference Effect Based on BER
### BER Formula under Pulse Signal Interference  
According to the typical working type of radar, three types of radar pulse signals are selected as interference signals, namely simple pulse, linear frequency modulation (LFM) pulse and bi-phase-coded pulse [40]. Among them, the carrier frequency, repetition period and pulse width of simple pulse are fixed. Square wave is usually used to modulate the amplitude of high-frequency carrier to generate simple pulse, as shown in (8). \[s(t)=A(t)\exp\{j[2\pi f_{c}t+\theta_{0}+\varphi(t)]\},t\in(0,T] \tag{8}\]  
where \(T\) is the pulse width, \(A(t)\) is the amplitude function, \(f_{c}\) is the carrier frequency, \(\theta_{0}\) is the initial phase and \(\varphi(t)\) is the phase function. The carrier frequency of LFM pulse changes linearly with time. The basic digital module can be used to generate continuous LFM signal, and then the square wave can be used to modulate the continuous LFM signal, as shown in (9). In the application field of radar measurement and positioning, the LFM signal can be used to obtain higher average transmission power and larger pulse width, so as to greatly increase the working coverage of radar. Moreover, due to the wide spectrum of LFM signal, it can also ensure that the radar system has high range resolution during ranging. \[F(t)=A(t)\cos(\omega_{c}t+\frac{1}{2}\cdot\mu\cdot t^{2}) \tag{9}\]  
where \(\omega_{c}\) is the carrier angular frequency, and \(\mu=\
icefrac{{d\omega}}{{dt}}\) is the chirp rate. The phase coded pulse has a fixed carrier frequency, and the absolute value of the phase is switched at a certain phase interval within the pulse duration. When the absolute value of the phase change in the pulse is two phases of opposite polarity, it is called bi-phase-coded pulse, as shown in (10). In radar positioning technology, bi-phase-coded pulse has been widely used in short-range communication because of its convenient phase synchronization extraction and narrow spectrum bandwidth [41]. Here, we choose the most commonly used binary code, the Barker code [22], which is meaningful only when the meaning of each code type is known. \[ \begin{split} x(t)=\sum_{n=0}^{N-1}x_{n}(t-n\tau_{c})\\ x_{n}(t)=\left\{\begin{array}{cc}\exp(j\phi_{n}),&0\leq t \leq\tau_{c}\\ 0,&\text{other}\end{array}\right.\end{split}  \tag{10}\]  
where \(n\tau_{c}\) is pulse width. The simulation flow of bi-phase-coded pulse is shown in Figure 2. Firstly, the RF signal source generates the high-frequency carrier. After quadrature modulation, the polarity of the RF signal is controlled through the encoded digital signal source to show the same change law as that of the Barker code. Finally, the continuous signal is converted into a pulse signal through the digital pulse module, and finally the bi-phase-coded pulse is output. In Figures 3-5, the time distribution and frequency domain characteristics of the simple pulse, LFM pulse and bi-phase-coded pulse are shown respectively. Based on above analysis, let us take a further step to consider the BER formula under pulse signal interference. Figure 6 shows a schematic diagram of the influence of the pulse signal on the receiver when the pulse width is smaller than the symbol period. The rectangular sequence in the figure represents the receiver symbol sequence, i.e., the gray rectangles represent the disturbed symbol, and the white rectangles represent the undisturbed symbol. Through in-depth analysis, the impact of the pulse signal on the symbol is significantly different from that of the GWN signal. The GWN signal is random  
Figure 4: LFM pulse characteristic diagram: (**a**) time distribution; (**b**) frequency domain. Figure 5: Bi-phase-coded pulse characteristic diagram: (**a**) time distribution; (**b**) frequency domain. Figure 3: Simple pulse characteristic diagram: (**a**) time distribution; (**b**) frequency domain. Figure 2: The simulation flow of bi-phase-coded pulse. in the time domain and interferes with every symbol.