## 4 Simulation and Analysis  
The system is implemented in Python 3.8, utilizing Keras framework with TensorFlow serving as the backend for tensor operations. Both the training and test datasets are generated randomly using MATLAB R2022a, while the simulation parameters are presented in Table 2.  
The MHSA-1D CNN-Bi-LSTM hybrid model consists of a Conv1D layer with 64 filters, kernel size of six, stride of one, and the \"same\" padding. ReLU activation is applied post-convolution to enhance learning performance. L2 regularization with a weight decay factor 0.01 is utilized to mitigate overfitting and enhance generalization during the training process. A subsequent max pooling layer follows the convolutional layer with a window size of two and stride of one. Power normalization is utilized to compress symbols to simulate hardware constraints accurately. Two Bi-LSTM layers ensue, where the first consists of 100 neurons and the second has only 20 neurons. In the MHSA-CNN-Bi-LSTM hybrid model, we set the dropout rate to 0.3 based on our experimental observations, striking a favorable balance between enhancing model performance and mitigating overfitting. Our cross-validation results indicate that lower dropout rates fail to adequately suppress overfitting, while higher rates may result in information loss. Therefore, by retaining adequate information and reducing the risk of overfitting, a dropout rate of 0.3 ensures the model's ability to generalize effectively to unknown data. Subsequently, an attention layer employing a two-headed self-attention mechanism employs a total of 64 neurons for enhanced representation capability. Finally, the output layer encompasses two fully connected layers, with one comprising 10 neurons and another consisting solely of 1 neuron responsible for generating the final result. During the training process, we load the labeled dataset from a CSV file, which includes both the pre-FTN shaping data and the disturbed post-FTN shaping data. To enhance the effectiveness of model training, we normalize the disturbed data to ensure a mean of 0 and a standard deviation of 1. Subsequently, we divide the dataset into training and test sets in an 80/20 ratio. Mean square error is employed as the loss function during training, optimized using the Adam optimizer. The model undergoes 100 training epochs while monitoring both training loss and validation loss to assess convergence and generalization capability. Upon completion of training, we evaluate predictive performance using metrics such as R\({}^{2}\), root mean square error (RMSE), and mean absolute error (MAE) to demonstrate its efficacy in handling disturbed signals  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline size of data & \(2\times 10^{6}\) \\ training dataset & \(1.6\times 10^{6}\) \\ test dataset & \(4\times 10^{5}\) \\ batch size & 256 \\ cycle index & 100 \\ dropout & 0.3 \\ learning rate & 0.0001 \\ loss function & MSE \\ optimizer & Adam \\ \multicolumn{2}{c}{strong:\(1.13\times 10^{-13}\) m\({}^{-2/3}\)} \\ \multicolumn{2}{c}{medium:\(1.13\times 10^{-14}\) m\({}^{-2/3}\)} \\ \multicolumn{2}{c}{weak:\(1.13\times 10^{-17}\) m\({}^{-2/3}\)} \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation parameters.  
and further validate its potential. Finally, for future analysis and application purposes, we save both the trained model and its normalizer.