# The Design of a Long-Distance Signal Transmission System in a Bistatic RCS Testing System
## 2 System Principle and Simulation
### System Simulation  
In the previous section, we concluded through theoretical derivation that the system fundamentally meets the phase stability requirements. In this stage, we used Matlab 2020a to conduct simulations to gain an intuitive understanding of the waveform and phase variations at each node of the system as well as observe the impact of various component parameters on system gain and waveform. Firstly, we set the simulation parameters for the system. Since the carrier used in the photoelectric conversion is typically a laser with a wavelength of 1550 nm, which corresponds to a frequency of approximately \(f_{c}=1.9\times 10^{5}\) GHz, and the frequency range of the modulated electrical signal is \(f_{m}=1\)-40 GHz, it follows that in practical applications, \(\omega_{m}\ll\omega_{c}\). Thus, for the modulating signal, we set the parameters as follows: amplitude \(A_{m}=1V\), frequency \(\omega_{m}=1\), and initial phase \(\varphi_{m}=0\). For the optical carrier signal, we set the amplitude \(E_{0}=10V\), carrier signal frequency \(\omega_{c}=100\) to satisfy the condition \(\omega_{m}\ll\omega_{c}\) for amplitude modulation, and carrier signal initial phase \(\varphi_{c}=0\). The half-wave voltage of a LiNbO\({}_{3}\) MZM is generally between 3 and 10 V. A lower half-wave voltage can enhance the performance of the MZM by increasing the modulation speed, reducing the heat generation, and lowering the drive voltage requirements, thereby improving overall efficiency. However, MZMs with lower half-wave voltages require more complex fabrication processes and incur higher production costs. After comprehensive consideration, the half-wave voltage of the MZM was set to \(V_{\pi}=6V\), which is also the voltage used for the actual product. Thus, the modulation index \(m=(\pi/2V_{\pi})A_{m}=\pi/12\). The insertion loss is \(\alpha_{m}=0.5\). A waveform comparison between the modulated signal \(S_{m}(t)\) and the modulating signal \(S_{r}(t)\) is shown in Figure 7.  
In the figure above, the blue and green curves represent the complete modulated signal \(S_{m}(t)\) and the signal \(S_{m}(t)\) with only the DC and first-order components retained, respectively. The red curve represents the modulating signal \(S_{r}(t)\). It is evident from the figure that the envelopes of the blue and green curves almost entirely match the red curve. Unlike traditional amplitude modulation, the envelope of the modulated signal is no longer perfectly aligned with the phase of the modulated signal but instead undergoes a phase inversion. This is due to the inherent principles of the MZM, as shown in Equation (9). Comparing the blue and green curves shows that they overlap almost completely, with only slight differences around the peaks, confirming the approximation mentioned in Equation (9) that \"In the case of small signal modulation, only the DC component and the first-order component are considered\". Figure 6: Bessel function values for \(m=\pi/12\). Regarding the case where the modulation index is increased to \(m=1\), a comparison between the true values and the approximate values is shown in Figure 8. At this point, there is a significant difference between the true and approximate values, and neither envelope matches the modulated signal anymore, indicating that the intensity modulation of a single push-pull MZM is only applicable when the modulating signal amplitude is less than the half-wave voltage of the modulator. Therefore, in practical applications, it is essential to control the amplitude of the modulating signal. For the optical fiber in the system, the simulation parameters were set as follows: the attenuation coefficient of the fiber \(\alpha=0.3\) dB/km, the refractive index \(n=1.45\), the operating wavelength \(\lambda=1550\) nm, and the dispersion coefficient \(D=17\) ps\(/(\)nm\(\cdot\)km\()\). The length was set to \(l=500\) m, and a rough calculation revealed that the group delay is \(\tau_{0}=2420\) ns. For the photodetector, the responsivity is a positive number that is always less than 1.