## 2 Proposed Framework
### NN Design via Hankelization-Based Preprocessing
Figure 9 presents the detection performance of the proposed method under varying row sizes of the Hankelized matrix across different SNR conditions. The number of singular values retained is fixed to the row dimension, while the row size is varied to assess the effect of the matrix shape. The results indicate that a well-chosen row size, even without strictly enforcing a near-square matrix structure, can still lead to a high detection rate. Notably, the FFT-processed variant achieves relatively higher accuracy in most SNR settings when the row size is sufficiently large. These observations suggest that high detection performance can be attained by appropriately selecting the number of singular values and the row size of the Hankelized matrix. Table 4 presents the computational complexity of each model in terms of the number of floating-point operations (FLOPs) and network parameters required for a single inference. Recalling the width of each hidden layer, denoted by \(P_{W}\), and the depth of the NN \(d\), the FLOP complexity of an FC model is given by \(\mathcal{O}(dP_{T}P_{W})\). Although the proposed methods introduce an additional computational cost of \(\mathcal{O}(P_{T}^{2}P_{T}^{\prime})\) due to singular value extraction via Hankelization, this step is performed as part of offline preprocessing. As shown in Table 4, both variants of the proposed method--one using the original signal and the other using the FFT-processed signal--require only \(5.72\times 10^{3}\) FLOPs and \(2.86\times 10^{3}\) parameters, demonstrating significantly lower complexity compared to other baseline

Figure 8: Detection rate according to the number of singular values. (**a**) SNR = 4 dB. (**b**) SNR = 10 dB. (**c**) SNR = 16 dB. Figure 9: Detection rate according to row size for the Hankelized matrix. (**a**) SNR = 4 dB. (**b**) SNR = 10 dB. (**c**) SNR = 16 dB. methods. In particular, CNN-based architectures such as SCNN2 and CLDNN require up to \(1.42\times 10^{8}\) and \(7.89\times 10^{6}\) FLOPs, respectively, with network sizes ranging from \(1.73\times 10^{5}\) to \(3.50\times 10^{4}\) parameters. The baseline methods follow the same NN configuration described in Section 3.1, ensuring a fair comparison in terms of network depth and width. The findings highlight that, although a mathematically complex preprocessing step is employed, the proposed method maintains high computational efficiency. ## 4 Conclusions

In this paper, we proposed a NN-based framework for AMC, incorporating Hankelization preprocessing. The proposed approach transforms the received signals into Hankelized matrices, from which singular values are extracted to form low-dimensional yet informative feature vectors. Two variants of the method were investigated--one based on time-domain signals and the other incorporating frequency-domain features via FFT. These features are then fed into an NN composed of a simple FC structure to perform classification across various SNR environments. The key strength of the proposed framework lies in its ability to effectively extract modulation-relevant features without relying on deep or complex NN architectures. Unlike conventional methods that depend on either handcrafted features or high-capacity models, our approach employs a concise design with minimal layers and moderate width, demonstrating that high performance can still be achieved when combined with appropriate signal representations. Experimental results confirm that the FFT-enhanced variant consistently achieves the highest detection accuracy across a wide range of SNR levels. Notably, it performs reliably even under low-SNR conditions and with limited training data, maintaining stable detection rates. In addition, the model converges rapidly within a small number of training epochs. Latent space analysis further supports the ability of the model to form well-separated representations across modulation types.