## 3 Simulation and Results  
In this section, we will provide the detailed parameters of the proposed AEGSM system and a comparison of the performances of the AE-8 QAM, Norm-8 QAM, and PO-8 QAM in a simulation environment. The parameters of the autoencoder are summarized in Table 1. The neural-network-based channel model is optimized via stochastic gradient descent (SGD), and the training batch size is 256. The parameter N is selected upon the principle that \((2\text{N}+1)\cdot 2\) should converge towards the optimal length of the channel memory. Through continuous experimentation and exploration, we determine N to be 12 to simulate the memory of the channel to the greatest extent. After completing the training of the channel model, we embed the channel model into the autoencoder and freeze its weights, and then use [PERSON] to train the encoder and decoder weights in the autoencoder with a batch size of 128. When the training is completed, we use the RPO algorithm to optimize the shaping scheme generated by the autoencoder at the bit-wise level, and then we can obtain the AE-8 QAM. Two types of channels are used in our simulation experiments. The first type of channel is the additive white Gaussian noise (AWGN) channel, which can be expressed as  
\[y=x+n_{WGN} \tag{5}\]  
where \(x\) and \(y\) represent the input and output of the channel, and \(n_{WGN}\) represents the white Gaussian noise. The second type of channel is the simulated VLC (simu-VLC) channel, which contains frequency fading, additive noise, and nonlinear distortions. It can be expressed as  
\[y=IFFT\Big{[}e^{-f}FFT\big{[}f(x)\big{]}\Big{]}+n_{WGN} \tag{6}\]  
where \(f(\cdot)\) represents the nonlinear effect of the LED light source, \(f\) is the frequency, and \(e^{-f}\) is the negative exponential frequency fading of the UVLC channel. The function expression of \(f(\cdot)\) can be described as  
\[f(x)=\frac{3.036}{1+e^{-3 epp*x/(\max(x)-\min(x))}}-2.206 \tag{7}\] \begin{table}
\begin{tabular}{l c c} \hline \hline
**Type of Layer** & **Number of Neurons** & **Activation** \\ \hline Transmitters–Encoder & & \\ Input & 8 & None \\ Hidden Layer1 & 256 & ReLU \\ Hidden Layer2 & 256 & ReLU \\ Hidden Layer3 & 256 & ReLU \\ Output & 2 & None \\ Flatten & & \\ Neural-Network-Based Channel Model & & \\ Input & \((2\text{N}+1)\times 2\) & None \\ Hidden Layer1 & \(66\times 2\) & ReLU \\ Hidden Layer2 & \(18\times 2\) & ReLU \\ Output & 2 & None \\ Receiver–Decoder & & \\ Input & 2 & None \\ Hidden Layer1 & 256 & ReLU \\ Hidden Layer2 & 256 & ReLU \\ Hidden Layer3 & 256 & ReLU \\ Hidden Layer4 & 256 & ReLU \\ Output & 8 & Softmax \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Structure and parameters of the autoencoder. where \(vpp\) represents the simulated driving voltages [33]. The performance of the Norm-8 QAM and PO-8 QAM severs as the baseline in the simulation. The transmitted signals are mapped by our AE-8 QAM, and then after being CAP-modulated, they are sent to the simulation channel, and finally the received signals are demodulated and de-mapped to calculate the BER, and their performance is compared with baseline. Figure 3 illustrates a comparison of BER performance versus different SNRs with different shaping schemes in the AWGN channel. We can see that in the case of an extremely low signal-to-noise ratio, none of the three shaping schemes can resist strong noise, so they all show extremely poor performance, and there is no obvious performance gap. Thus, the constellations of the three schemes in region (i) are all severely distorted. But with the improvement in the signal-to-noise ratio, the performance of the PO-8 QAM and AE-8 QAM gradually improves compared to that of the Norm-8 QAM due to their self-adaptive ability. According to the constellations in region (ii) and region (iii), the AE-8 QAM and PO-8 QAM can be adaptively adjusted according to the channel signal-to-noise ratio to achieve a better performance.