## 3 Second-Order Noise-Suppression Structure  
After phase compression in the PSA module, the input QPSK optical signal interferes with the local target-sequence optical signal, converting the symbol information originally in phase into amplitude information. The PSA module converts the phase noise into amplitude noise. Therefore, it is necessary to design a noise-suppression structure that can reamplify and reshape the signal amplitude to enhance the system's resistance to noise. To meet the system's 100 Gbaud rate requirement while enabling signal reshaping after interference to counteract mismatch noise and input noise effects, we adopted the second-order noise-suppression structure based on HNLF from [26] and optimized its parameters according to the system's nodal power level. When two high-power optical signals of different frequencies are injected into HNLF, a new optical signal is generated at another frequency due to the FWM effect of the fiber. This new optical signal is referred to as idler light, and the two input optical signals are called the signal and pump lights. However, there are many idler frequencies generated after the FWM effect; thus, the most appropriate idler frequency must be selected. As shown  
Figure 3: Mismatch noise in the signal after interference. in Figure 4, the pump light with frequency \(\omega_{0}\) and the signal light with frequency \(\omega_{0}+\Omega\) generate a new idler optical signal at frequency \(\omega_{0}-\Omega\) after the FWM effect. This idler optical signal carries the information in the signal light. The FWM of HNLF is the core of the noise-suppression structure. Assuming that the power of the pump light is \(P_{p}\) at a frequency \(\omega_{1}\) and the power of the signal light is \(P_{s}\) at a frequency \(\omega_{2}\), they generate a new idler optical signal at a frequency \(\omega_{3}=2\omega_{1}\pm\omega_{2}\). Considering the effects of SPM and XPM, the coupled nonlinear Schrodinger equations of the pump light, signal light, and idler optical signal are expressed as shown in Equations (4)-(6) [32]:  
\[\frac{\mathrm{d}A_{1}}{dz}=-\frac{1}{2}\alpha A_{1}+i\gamma\Big{(}2|A_{2}|^{2} +|A_{1}|^{2}+2|A_{3}|^{2}\Big{)}A_{1}+2i\gamma A_{2}A_{3}A_{1}^{*}e^{i\Delta Kz} \tag{4}\]  
\[\frac{\mathrm{d}A_{2}}{\mathrm{d}z}=-\frac{1}{2}\alpha A_{2}+i\gamma\Big{(}2|A _{1}|^{2}+|A_{2}|^{2}+2|A_{3}|^{2}\Big{)}A_{2}+i\gamma A_{1}^{2}A_{3}^{*}e^{- i\Delta Kz} \tag{5}\]  
\[\frac{\mathrm{d}A_{3}}{dz}=-\frac{1}{2}\alpha A_{3}+i\gamma\Big{(}2|A_{1}|^{2 }+2|A_{2}|^{2}+|A_{3}|^{2}\Big{)}A_{3}+i\gamma A_{1}^{2}A_{2}^{*}e^{-i\Delta Kz} \tag{6}\]  
where \(A_{i}(i=1,2,3)\) is the slowly varying amplitude of each signal pulse envelope, \(\alpha\) is the signal loss coefficient, \(\gamma\) is the nonlinear coefficient, and \(\Delta K\) is the phase matching factor. In the application of noise suppression based on FWM, the most important part is the change curve of the power of the idler optical signal following the signal light (the power transfer curve). The shape of the curve directly determines the noise-suppression performance of the structure. A stepped power transfer curve indicates better noise suppression. The following equations are derived from Equations (4)-(6):  
\[\frac{\mathrm{d}P_{1}}{dz}=-\alpha P_{1}-\alpha_{7}(P_{1}^{2}P_{2}P_{3})^{1/2}\sin\theta \tag{7}\]  
\[\frac{\mathrm{d}P_{2}}{dz}=-\alpha P_{2}+2\gamma(P_{1}^{2}P_{3})^{1/2}\sin\theta \tag{8}\]  
\[\frac{\mathrm{d}P_{3}}{dz}=-\alpha P_{3}+2\gamma(P_{1}^{2}P_{2}P_{3})^{1/2}\sin\theta \tag{9}\]  
\[\frac{\mathrm{d}\theta}{dz}=\Delta k_{0}+\gamma\{2P_{1}-P_{2}-P_{3}+[(P_{1}^{ 2}P_{2}/P_{3})^{1/2}+(P_{1}^{2}P_{2}/P_{3})^{1/2}-4(P_{2}P_{3})^{1/2}]\cos\theta\} \tag{10}\]  
where \(P_{1}\), \(P_{2}\), and \(P_{3}\) are the powers of the pump light, signal light, and idler optical signal, respectively, and \(\theta=\Delta k_{0}z+\Phi_{2}+\Phi_{3}-2\Phi_{1}\), where \(\Phi_{1}\), \(\Phi_{2}\), and \(\Phi_{3}\) are the phases of the pump light, signal light, and idler optical signal, respectively.