## 4 Result and Discussion
At the normalized input signal of 0.1, the model accuracy falls below 50%. According to our simulation results, the ONN accuracy reduces when the signal amplitude is less than 0.4. This happens because when the signal amplitude is too low, the ASE noise from the EDFA and the thermal and shot noises from the PD become dominant, causing the ONN to fail in performing classification and prediction. When the signal amplitude is larger than 0.4, the ASE and PD noises will not be the dominating factors, and we can observe that the ONN accuracy is -1 when signal amplitude is between 0.6 and 1.0. To solve this issue, the electro-optic nonlinear activation function discussed in Figure 5 above is included into the ONN model. This enhances the capability of the ONN model to handle nonlinear problems. Figure 8: BER performances of ONN and ANN used for classifying the distorted PAM4 signal without the activation function. Figure 9: Accuracy and loss performance of different normalized input signal amplitudes without activation function. Figure 10 shows the modified ONN model with electro-optic nonlinear activation functions. In this architecture, each output port of the first Reck mesh will be connected to an electro-optic nonlinear activation function. The output of the electro-optic nonlinear activation function will then be connected to the input port of the second Reck mesh, and subsequently will be connected to a PD. Furthermore, the fusion of the activation function and the fully connected layer can be considered as a two-layer fully connected ONN, interconnected through activation functions  
In the modified ONN, the parameters of the electro-optic nonlinear activation function as optimized. The \(\alpha\) is set to be 0.1, \(V_{\pi}\) of the MZI phase shift is 5 V, the \(V_{b}\) is set to be \(-5\) V, \(G\) is set to be 20, and the responsivity \(R\) is set to be 1. Therefore, \(\varphi_{b}\) is set to be -\(\pi\), and \(g_{\varphi}\) is set to be 0.4\(\pi\). Figure 11 shows the transmission coefficient (i.e., \(\frac{|f(z)|^{2}}{|z|^{2}}\)) of the electro-optic nonlinear activation function with normalized input field \(Z\). We can observe that the electro-optic nonlinear activation function defined exhibits similarities to the sigmoid function but shifted towards the positive \(x\)-axis. In the simulation work here, the \(\alpha=0.1\) is used for reducing the loss for electro-optic nonlinear activation function. The electro-optic nonlinear activation function will have different characteristics under different \(\varphi_{b}\) and \(g_{\varphi}\). Here, we found that the nonlinear activation function as illustrated in Figure 11 has a better performance in our model. Therefore, \(\varphi_{b}\) is set to be \(-\pi\), and \(g_{\varphi}\) is set to be 0.4\(\pi\). Figure 12 illustrates the accuracy and loss performance of different normalized input signal amplitudes with the electro-optic nonlinear activation function. Comparing the results to the ONN model without an electro-optic nonlinear activation function shown in Figure 10, the accuracy and loss performance in Figure 12 have been significantly improved, particularly at low input signal powers. We can observe that even when the normalized  
Figure 11: Modified ONN model with electro-optic nonlinear activation functions. Figure 10: Modified ONN model with electro-optic nonlinear activation functions. MZI: Mach–Zehnder Interferometer; EO: electro-optic nonlinear activation function; PD: photodetector. input signal amplitude is as low as 0.1, the accuracy remains at an impressive value of 99.7%. Analyzing the BER performance of PAM4 signals involves using the modified ONN with an electro-optic nonlinear activation function. It can be observed that the BER performance of the modified ONN model with the electro-optic nonlinear activation function is nearly the same as that without the activation function illustrated in Figure 8. The data rate achieving the SD-FEC threshold (i.e., BER = 2.4 \(\times\) 10\({}^{-2}\)) can be up to 200 Gbit/s.