## 2 Proposed Framework
### NN Design via Hankelization-Based Preprocessing
In summary, the proposed Hankelization-based AMC framework provides a practical and effective solution by integrating signal structure-aware preprocessing with a simple NN architecture. Future work may extend this framework to broader modulation families or more complex channel environments. Conceptualization, W.-H.L., J.-H.L. and O.-S.S.; software, J.-H.K. ; writing--original draft preparation, J.-H.K. ; writing--review and editing, W.-H.L., J.-H.L. and O.-S.S.; visualization, J.-H.K. ; funding acquisition, J.-H.L. All authors have read and agreed to the published version of the manuscript. This work was supported in part by the Dongguk University Research Fund of 2024 (S-2024-G0001-00025) and in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. RS-2023-00239349). Not applicable. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Method** & **FLOPs** & **\# Params** \\ \hline Proposed method (with original signal) & \(5.72\times 10^{3}\) & \(2.86\times 10^{3}\) \\ \hline Proposed method (with FFT-processed signal) & \(5.72\times 10^{3}\) & \(2.86\times 10^{3}\) \\ \hline Deep learning (CNN with real and imaginary values of signal) & \(2.04\times 10^{6}\) & \(1.58\times 10^{5}\) \\ \hline SCNN2 & \(1.42\times 10^{8}\) & \(1.73\times 10^{5}\) \\ \hline CLDNN & \(7.89\times 10^{6}\) & \(3.50\times 10^{4}\) \\ \hline LSTMDAE & \(3.53\times 10^{6}\) & \(1.48\times 10^{4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of computational complexity in terms of FLOPs and the number of parameters. Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy. The authors declare no conflicts of interest. ## Abbreviations

The following abbreviations are used in this manuscript: \begin{tabular}{l l} AMC & Automatic modulation classification \\ ML & Machine learning \\ SVM & Support vector machine \\ k-NN & k-nearest neighbors \\ NN & Neural network \\ CNN & Convolutional neural network \\ RNN & Recurrent neural network \\ DL & Deep learning \\ SNR & Signal-to-noise ratio \\ SVD & Singular value decomposition \\ SISO & Single-input single-output \\ CIR & Channel impulse response \\ AWGN & Additive white Gaussian noise \\ FFT & Fast Fourier transform \\ t-SNE & t-distributed stochastic neighbor embedding \\ FC & Fully connected \\ Adam & Adaptive moment estimation \\ RMSProp & Root mean square propagation \\ MLP & Multilayer perceptron \\ STFT & Short-time Fourier transform \\ LSTM & Long short-term memory \\ DAE & Denoising autoencoder \\ FLOP & Floating-point operation \\ \end{tabular} 

## References

* _[PERSON] et al. (2020)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] 6G: Opening new horizons for integration of comfort, security, and intelligence. _IEEE Wirel. Commun._**2020**, _27_, 126-132. [CrossRef]
* _[PERSON] et al. (2007)_ [PERSON]; [PERSON]; [PERSON]; [PERSON] Survey of automatic modulation classification techniques: Classical approaches and new trends. _IET Commun._**2007**, \(1\), 137-156. [CrossRef]
* _[PERSON] et al. (2021)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Automatic modulation classification: A deep architecture survey. _IEEE Access_**2021**, \(9\), 142950-142971. [CrossRef]
* _[PERSON] et al. (2018)_ [PERSON]; [PERSON]; [PERSON] Over-the-air deep learning based radio signal classification. _IEEE J. Sel. Top. Signal Process._**2018**, _12_, 168-179. [CrossRef]
* _[PERSON] et al. (2010)_ [PERSON]; [PERSON]; [PERSON] Efficient modulation classification for adaptive wireless OFDM systems in TDD mode. In Proceedings of the 2010 IEEE Wireless Communications and Networking Conference, Sydney, Australia, 18-21 April 2010; pp. 1-6. * _[PERSON] et al. (2023)_ [PERSON]; [PERSON]; [PERSON] Automatic modulation classification with deep neural networks. _Electronics_**2023**, _12_, 3962. [CrossRef]
* _[PERSON] et al.