## 2 QPSK-Oriented All-Optical Matching System and Noise Analysis
### Noise in the QPSK-Oriented All-Optical Matching System  
In the QPSK-oriented all-optical matching system, noise comes from two main sources: input noise and amplifier noise. The input noise refers to the noise accumulated in the input QPSK signal before entering the system. This noise causes fluctuations in the amplitude and phase shift of the  
Figure 1: QPSK-oriented all-optical matching system in [16]. QPSK signal, thereby reducing the quality of the signal. The sources of the input noise are as follows:  
**(1) Optical transmitter:** In practical applications, due to the limitations of devices such as lasers and modulators, the transmitted signal in the optical transmitter is not ideal. Despite the stabilization of all operating conditions, including bias, light reflections, and temperature, the laser output light intensity and phase can fluctuate, resulting in relative intensity noise (RIN), which limits the achievable signal-to-noise ratio (SNR) of the emitted signal. **(2) Optical transmission:** When signals are transmitted through optical fibers, they are affected by nonlinear effects and dispersion. For communication systems using wavelength-division multiplexing technology, during optical transmission, nonlinear effects, such as FWM and XPM, and mode dispersion occur between lights of different frequencies, thereby reducing the quality of the signals. The single-mode transmitted optical signals are affected by the material, waveguide, and polarization mode dispersion in the optical fiber. In addition, during long-distance transmission, the amplifiers in the transmission link introduce noise. In the all-optical matching system, the composition of the input noise is complex. In coherent optical communication systems, the generalized signal-to-noise ratio (OSNR) is commonly employed to unify the optical signal-to-noise ratio (OSNR) with impairments (dispersion and nonlinear effects), as expressed in Equation (1). Here, \(P_{NL}\) can be estimated using the Gaussian noise model [27]. In the field of optical transmission, a lot of research focuses on the GSNR [28; 29]. When the input noise is dominated by amplified spontaneous emission (ASE) noise and thermal noise, it can be described using an additive Gaussian white noise (AWGN) model. In this study, we consider such input noise conditions and thus utilize the NoiseWhiteGaussOpt module in VPItransmissionMaker to simulate input noise. We use the OSNR to quantify the impact of input noise, which is expressed in Equation (2), where \(P_{in}\) is the power of the input signal and \(P_{noise}\) is the power of the Gaussian white noise. Figure 2 shows the changes in the constellation diagram of the QPSK optical signal under different input OSNRs. By keeping the power of the input signal constant, the input OSNR can be reduced by increasing the power of the Gaussian white noise. As the input OSNR decreases, the amplitude and phase fluctuations of the QPSK optical signal increase. Therefore, we can assume that under this condition, phase noise is also included. \[GSNR\left(dB\right)=10\log(P_{in}/(P_{ASE}+P_{NL})) \tag{1}\]  
\[OSNR_{input}\left(dB\right)=10\log(P_{in}/P_{noise}) \tag{2}\]  
The noise from the amplifiers also affects the performance of the system. To meet the power requirements of the input signal for various modules, multiple EDFAs are employed  
Figure 2: QPSK optical signal constellation diagram under different input OSNR levels: (**a**) ideal scenarios, (**b**) input OSNR = 10 dB, (**c**) input OSNR = 6 dB, (**d**) input OSNR = 2 dB. in the QPSK-oriented all-optical matching system to amplify the optical signal, which introduces amplifier noise, including shot noise, beat noise, ASE noise, and frequency-difference noise. Among the four types of noise generated by EDFAs, ASE noise is considered a type of shot noise because of the spontaneous emission process of the optical amplifier. In addition, because it arises from the quantum properties of photons, it is also considered a type of quantum noise.