## 2 Materials and Methods
### Dataset Descriptions  
In our simulations, we utilize quadrature phase-shift keying (QPSK) modulated baseband signals with a length of 512 samples. Each symbol within the signal consists of 8 samples. For pulse shaping, we utilize a square-root raised cosine filter with a roll-off factor of 0.25 and a span of 10. To simplify the analysis and implementation, we set the sampling frequency to 1 in our simulations.  
During the training of the CFO network, we utilize CFO values that are uniformly distributed within the range of \([-0.01,0.01]\) relative to the data rate. To simplify the training process, we keep the phase offset and SNR constant. The constant phase offset was chosen because it should not have an affect on the CFO estimation. Moreover, we use a relatively high SNR of 20 dB to enable the network to effectively learn the patterns caused by the CFO. Our training dataset comprises 20,000 signals, each of which consists of 512 samples with in-phase and quadrature components. We partition this dataset into 70% for training and 30% for validation. For ease of training, we normalize the CFO values to fall within the range of \([-1,1]\), simplifying their use as target variables in the network. Additionally, we generate a separate test dataset consisting of 20,000 signals. This test dataset introduces phase offset values that are uniformly distributed from \(-45\) to \(45\) degrees in 10-degree increments and SNR values that are uniformly distributed from 0 to 20 dB in 5 dB steps.  
Table 2 provides a concise summary of the datasets utilized for both training and testing the CFO estimation network.  
The training and testing datasets for the U-Net-based autoencoder are presented in Table 3, following a similar fashion as the CFO estimation dataset.  
During the training of the U-Net-based autoencoder network, the trained CFO estimation network is used for CFO correction. This involves mitigating CFO in the data with  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Set** & **CFO (Data Rate)** & **Phase Offset (Degrees)** & **SNR (dB)** & **Size** \\ \hline Training & \([-0.01,0.01]\) & 30 & 20 & 20,000 \\ Test & \([-0.01,0.01]\) & \([-45\text{:}10\text{:}45]\) & [0:5:20] & 20,000 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of datasets used for CFO estimation network training and testing.  
Figure 3: U-Net based autoencoder architecture.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Set** & **CFO (Data Rate)** & **Phase Offset (Degrees)** & **SNR (dB)** & **Size** \\ \hline Training & \([-0.01,0.01]\) & \([-45\text{:}10\text{:}45]\) & [0:5:20] & 20,000 \\ Test & \([-0.01,0.01]\) & \([-45\text{:}10\text{:}45]\) & [0:5:20] & 20,000 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Summary of datasets used for U-Net-based autoencoder network training and testing.  
estimated values before U-Net training. It is important to note that some residual CFO remains due to estimation limitations. This approach mimics real-world scenarios with residual CFO, enhancing the U-Net's ability to handle remaining CFO components and improve practical performance.  
Before discussing training and testing setups, we must describe the energy detection dataset. It consists of 10,000 signals with RF impairments, generated as previously explained. Additionally, 10,000 noise vectors following the complex normal distribution represent scenarios where the null hypothesis cannot be rejected. These sub-datasets are merged to form the final dataset for energy detection.