## 2 Proposed Framework
### NN Design via Hankelization-Based Preprocessing
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**SNR [dB]**} & \multirow{2}{*}{
\begin{tabular}{c} **Proposed** \\ **Method (with** \\ **FGT-Processed Signal)** \\ \end{tabular} } & \multirow{2}{*}{**Deep Learning**} & \multirow{2}{*}{**SCNN2**} & \multirow{2}{*}{**CLDNN**} & \multirow{2}{*}{**LSTMDAE**} \\  & & & & & & \\ \hline \(-20\) & \(0.2500\pm 0.0000\) & \(0.2500\pm 0.0000\) & \(0.2460\pm 0.0102\) & \(0.2500\pm 0.0196\) & \(0.2545\pm 0.0113\) & \(0.2490\pm 0.0123\) \\ \hline \(-18\) & \(0.2500\pm 0.0000\) & \(0.2500\pm 0.0000\) & \(0.2428\pm 0.0149\) & \(0.2636\pm 0.0167\) & \(0.2529\pm 0.0099\) & \(0.2454\pm 0.0066\) \\ \hline \(-16\) & \(0.3046\pm 0.0164\) & \(0.2504\pm 0.0011\) & \(0.2826\pm 0.0199\) & \(0.3299\pm 0.0198\) & \(0.3394\pm 0.0138\) & \(0.2476\pm 0.0054\) \\ \hline \(-14\) & \(0.3881\pm 0.0146\) & \(0.3433\pm 0.0934\) & \(0.4354\pm 0.0181\) & \(0.4505\pm 0.0152\) & \(0.4627\pm 0.0282\) & \(0.2984\pm 0.0692\) \\ \hline \(-12\) & \(0.5205\pm 0.0217\) & \(0.5630\pm 0.0279\) & \(0.5496\pm 0.0215\) & \(0.5693\pm 0.0103\) & \(0.5888\pm 0.0176\) & \(0.6123\pm 0.0145\) \\ \hline \(-10\) & \(0.6560\pm 0.0097\) & \(0.6671\pm 0.0164\) & \(0.6389\pm 0.0112\) & \(0.6491\pm 0.0175\) & \(0.6834\pm 0.0176\) & \(0.6912\pm 0.0131\) \\ \hline \(-8\) & \(0.7206\pm 0.0056\) & \(0.7036\pm 0.0211\) & \(0.6894\pm 0.0128\) & \(0.6915\pm 0.0208\) & \(0.7140\pm 0.0077\) & \(0.7251\pm 0.0078\) \\ \hline \(-6\) & \(\mathbf{0.7394\pm 0.0083}\) & \(\mathbf{0.7334\pm 0.0060}\) & \(0.7184\pm 0.0138\) & \(0.7129\pm 0.0160\) & \(0.7292\pm 0.0146\) & \(0.7329\pm 0.0148\) \\ \hline \(-4\) & \(0.7395\pm 0.0052\) & \(0.7380\pm 0.0038\) & \(0.7205\pm 0.0142\) & \(0.7336\pm 0.0092\) & \(0.7274\pm 0.0082\) & \(0.7409\pm 0.0138\) \\ \hline \(-2\) & \(0.7346\pm 0.0040\) & \(0.7285\pm 0.0121\) & \(0.7125\pm 0.0264\) & \(0.7674\pm 0.0321\) & \(0.7264\pm 0.0098\) & \(0.7428\pm 0.0609\) \\ \hline \(0\) & \(0.7406\pm 0.0137\) & \(\mathbf{0.8194\pm 0.0445}\) & \(0.6911\pm 0.0217\) & \(0.8005\pm 0.0418\) & \(0.7297\pm 0.0655\) & \(0.7316\pm 0.0119\) \\ \hline \(2\) & \(0.8102\pm 0.0317\) & \(\mathbf{0.9084\pm 0.0171}\) & \(0.6986\pm 0.0277\) & \(0.8603\pm 0.0564\) & \(0.8229\pm 0.0843\) & \(0.8408\pm 0.0097\) \\ \hline \(4\) & \(0.8085\pm 0.0379\) & \(\mathbf{0.9439\pm 0.0147}\) & \(0.7368\pm 0.0180\) & \(0.9133\pm 0.0500\) & \(0.8396\pm 0.0614\) & \(0.8456\pm 0.0196\) \\ \hline \(6\) & \(0.8569\pm 0.0346\) & \(\mathbf{0.9614\pm 0.0046}\) & \(0.7458\pm 0.0261\) & \(0.9151\pm 0.0493\) & \(0.8306\pm 0.0560\) & \(0.8508\pm 0.0120\) \\ \hline \(8\) & \(0.8641\pm 0.0217\) & \(\mathbf{0.9574\pm 0.0132}\) & \(0.6789\pm 0.0256\) & \(0.8835\pm 0.0558\) & \(0.8316\pm 0.0607\) & \(0.8545\pm 0.0112\) \\ \hline \(10\) & \(0.8870\pm 0.0395\) & \(\mathbf{0.9699\pm 0.0073}\) & \(0.7286\pm 0.0240\) & \(0.9261\pm 0.0118\) & \(0.8482\pm 0.0125\) & \(0.8448\pm 0.0182\) \\ \hline \(12\) & \(0.8899\pm 0.0165\) & \(\mathbf{0.9484\pm 0.0561}\) & \(0.6784\pm 0.0234\) & \(0.9089\pm 0.0558\) & \(0.8341\pm 0.0159\) & \(0.8512\pm 0.0281\) \\ \hline \(14\) & \(0.8698\pm 0.0214\) & \(\mathbf{0.9647\pm 0.0106}\) & \(0.6959\pm 0.0157\) & \(0.8958\pm 0.0434\) & \(0.8336\pm 0.0535\) & \(0.8619\pm 0.0221\) \\ \hline \(16\) & \(0.8656\pm 0.0282\) & \(\mathbf{0.9669\pm 0.0064}\) & \(0.6790\pm 0.0252\) & \(0.9014\pm 0.0544\) & \(0.8326\pm 0.0676\) & \(0.8945\pm 0.0196\) \\ \hline \(18\) & \(0.8473\pm 0.0536\) & \(\mathbf{0.9623\pm 0.0093}\) & \(0.6876\pm 0.0226\) & \(0.9111\pm 0.0329\) & \(0.8403\pm 0.0687\) & \(0.8898\pm 0.0159\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean of detection rate \(\pm\) standard deviation according to SNR. detection rate improves as more singular values are retained, highlighting the benefit of preserving sufficient spectral information. Furthermore, the FFT-processed variant consistently outperforms the original signal variant, particularly when a sufficient number of singular values is used.