# Design and Research of Photonic Reservoir Computing for Optical Channel Equalization
## 2 Design of Photonic Reservoir Computing and Verification System
The splitting ratio of DC is represented using a splitting ratio coefficient, with the equation as follows:  
\[R_{dc}=\frac{P_{out1}}{P_{in1}} \tag{6}\]  
where \(P_{out1}\) represents the output power at the through port of DC, while \(P_{in1}\) represents the input power. In the readout layer, photodiodes (PDs) are used to convert the optical signal output from the reservoir into current signals. These current signals are then converted into voltage signals by a transimpedance amplifier (TIA) array. Subsequently, analog-to-digital converters (ADCs) are employed to sample and discretize the voltage signals before they are sent to a computer for weight training. Ultimately, the trained weights produce an equalized signal. The transfer equation for PD is as follows:  
Figure 2: The structure of a 12-node optical reservoir computing structure. \[ \begin{bmatrix}I_{out1}\\ I_{out2}\\ \vdots\\ I_{out7}\end{bmatrix} =\alpha \begin{bmatrix}\left|E_{rl\_out1}\right|^{2}\\ \left|E_{rl\_out2}\right|^{2}\\ \vdots\\ \left|E_{rl\_out7}\right|^{2}\end{bmatrix} + \begin{bmatrix}I_{noise1}\\ I_{noise2}\\ \vdots\\ I_{noise7}\end{bmatrix}  \tag{7}\]  
where \(I_{out1}\), \(I_{out2}\), \(\ldots\), \(I_{out7}\) represent the output current of PDs. \(I_{noise1}\), \(I_{noise2}\), \(\ldots\), \(I_{noise7}\) are noises generated by PDs during photoelectric conversion. These noises follow a Gaussian distribution. The square-law relationship between optical intensity and current in PDs is crucial for implementing nonlinear activation functions. The IMDD system for channel noise equalization verification is shown in Figure 3. A continuous-wave (CW) laser generates continuous light with a center wavelength of 1550 nm. The polarization controller (PC) can manipulate the polarization state within this link. Random bit sequences are generated using the Mason rotation method, and the on-off keying (OOK) modulation scheme is employed. The modulator utilizes a differential Mach Zehnder modulator (MZM). The modulated signal is then transmitted through standard single-mode fiber (SSMF), where it undergoes distortion due to noise in the channel. The erbium-doped fiber amplifier (EDFA) and variable optical attenuator (VOA) are utilized to control the optical power input into the PhRC, maintaining it at 20 dBm. The distorted signal is used as the input for the PhRC, where equalization is performed using the bit error rate (BER) of the equalized signal as the basis for judging equalization performance. The simulation system is implemented utilizing Python 3.8.0 as its foundational platform, featuring a distorted signal comprising a 25 Gb/s OOK signal that is generated through the transmission over a 20 km SSMF. The key parameters involved in the verification system and PhRC during the simulation are shown in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Device Name** & **Parameter** & **Value** & **Units** \\ \hline \multirow{2}{*}{CW laser} & line width & \(10^{6}\) & Hz \\  & average power & 0.01 & W \\ \hline \multirow{4}{*}{MZM} & insertion loss & 6 & dB \\  & extinction ration & 20 & dB \\  & rise time & \(8.929\times 10^{-12}\) & s \\  & \(\pi\) phase change voltage & 2.1 & V \\ \hline \multirow{4}{*}{SSMF} & dispersion coefficient & \(16\times 10^{-6}\) & s/m\({}^{2}\) \\  & nonlinear index & \(2.6\times 10^{-20}\) & m\({}^{2}\)/W \\ \cline{1-1}  & group reference index & 1.47 & / \\ \cline{1-1}  & attenuation & 0.2 & dB/km \\ \hline GC & insertion loss & 5 & dB \\ \hline DC & insertion loss & 0.5 & dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of key devices. Figure 3: Verification system for distortion equalization performance of photonic reservoir computing. Due to the limitations of the simulation equipment, the symbol length of the input signal is 214, with 16 samples per symbol. Therefore, the BER is obtained based on the probability density function (PDF). After validating various distribution functions, it is determined that the PDF of each received symbol conforms to a Gaussian distribution.