# Intelligent Simulation Technology Based on RCS Imaging
## 2 Target Drone Simulation Principle
### Doppler Signal Generation  
Assuming that the target is an ideal target, i.e., the target size is considerably smaller than the radar resolution unit, the transmitted signal can be expressed as:  
\[s(t)=A\cos(\omega_{0}t+\phi) \tag{16}\]  
where \(A\) represents the amplitude of the transmitted signal, \(\omega_{0}\) represents the angular frequency of the transmitted wave signal, and \(\phi\) represents the initial phase. Subsequently, the echo signal received from the moving target can be expressed as:  
\[s_{d}(t)=ks(t-t_{d})=kA\cos[\omega_{0}(t-t_{d})+\phi] \tag{17}\]  
where \(k\) represents the attenuation coefficient and \(t_{d}\) represents the time delay of the radar signal from the transmission to reception. Figure 4: Schematic diagram of Luneberg lens. If the target is stationary, the time delay represented by \(t_{d}\) has a constant value of 2R/c. If the target moves with a certain speed, the distance R changes with the change of time t, namely:  
\[R(t)=R_{0}-v_{d}t_{d} \tag{18}\]  
The phase difference can be expressed as:  
\[\varphi=-\omega_{0}t_{d}=-\omega_{0}\frac{2}{c}(R_{0}-v_{d}t)=-2\pi\frac{2}{ \lambda}(R_{0}-v_{d}t) \tag{19}\]  
The derivative of the phase difference can be obtained as:  
\[f_{d}=\frac{1}{2\pi}\frac{d\varphi}{dt}=\frac{2}{\lambda}v_{d} \tag{20}\]  
At this point, the speed of the moving target is:  
\[v_{d}=\frac{f_{d}\lambda}{2} \tag{21}\]  
Similarly, if the target is stationary, \(t_{d}\) in Equation (2) has a constant value. Consequently, \(s_{d}(t)\) is a fixed value. However, the environment around the target is not static when the target is measured. As an example, if the wind blows the trees, the leaves will produce vibration, and flowing rivers will produce a large amount of clutter interference, which will affect the Doppler frequency deviation. In this paper, the oscillation circuit is used to simulate the Doppler frequency corresponding to the velocity. Here, Figure 4(a) shows the schematic diagram of a capacitor-based three-point LC oscillation circuit. The oscillation frequency is \(f_{0}=1/(2\pi\sqrt{LC})\), where \(C=C_{1}C_{2}/C_{1}+C_{2}\). Although the oscillating waveform produced by this circuit structure is utility, it is difficult to adjust the frequency of the generated oscillating waveform. Therefore, this circuit is only suitable for a high fixed frequency. The most widely used sinusoidal oscillators are LC and RC oscillator circuit structures. In the sinusoidal oscillation circuit shown in Figure 4(b), the oscillation frequency is \(f_{0}=1/(2\pi RC)\). The oscillation waveform output by this circuit structure has a stable frequency and no distortions. The amplitude of the output waveform can be stabilized by adding negative feedback, which makes it suitable for applications requiring an adjustable frequency. To evaluate the performance of the Doppler frequency simulator, a 10 GHz frequency test system is designed for experimental verification, as shown in Figure 6. A speed of 0-200 km/h is simulated, divided into six levels: 0 km/h, 12.5 km/h, 25 km/h, 50 km/h, 100 km/h and 200 km/h. According to Equation (6), the corresponding analog frequencies  
Figure 5: Two types of oscillating circuits. can be calculated at 0, 230 Hz, 460 Hz, 925 Hz, 1.96 kHz, and 4 kHz. The voltage of the 4 kHz oscillation circuit is \(\pm\)9 V, R1 and R2 are equal to 62.82 k\(\Omega\), C\({}_{3}\) and C\({}_{4}\) are equal to 0.01 uF, R7 is 18 k\(\Omega\), R4 is 10 k\(\Omega\) and R8 is equal to 3 k\(\Omega\). The two diodes constitute a nonlinear network, which can render the amplifier of the circuit stable over 3 repetitions [28]. This prevents the distortion of the output waveform and ensures its stability. The opamp uses LF356n. Since it is a single-stage common emitter amplifier circuit, the output voltages of the transistor \(VT_{U_{0}}\) and \(VT_{U_{i}}\) are 180\({}^{\circ}\) in phase. When the output voltage passes through the RC network, it becomes the feedback voltage, and then sends this to the input end.