# Neural-Network-Based Synchronization Acquisition with Hankelization Preprocessing
## 4 Simulation Results
### Performance for Detecting Synchronization Signal  
Figure 2 shows the classification accuracy of the proposed method. Specifically, the row-normalized results depict the percentages of correctly and incorrectly classified observations for each true class, while the column-normalized results represent the percentages for each predicted class. For instance, as shown in Figure 1(a), the classification accuracy for signals with the presence of synchronization signals is 98.3%. Furthermore, among the predicted signals, the percentages of correct and incorrect classifications are 99.8% and 0.2%, respectively. Figure 3 presents the detection error performance of the proposed method compared to conventional approaches for synchronization signal detection. The simulations used \(10^{4}\) training data points within an SNR range of \(-20\) dB to 5 dB. Figure 2(a) shows the results for \(P=37\), and Figure 2(b) shows the results for \(P=41\). The proposed method employs a Hankelization-based preprocessing technique, while conventional methods use the absolute values of the correlation function or the IFFT results as the input for the NN, the random forest method, and the adaptive threshold method. In Figure 2(a), the proposed method achieves significantly lower detection error rates across all SNR levels. For SNR values above 0 dB, the error rate is below \(10^{-3}\), while conventional methods remain above \(10^{-2}\), showing minimal improvement even at higher SNR levels. Similarly, in Figure 2(b), the proposed method maintains superior performance, achieving error rates below \(10^{-3}\) for SNR values exceeding 0 dB. Conventional methods, particularly the IFFT-based approach, show persistently high error rates and negligible improvement. These results highlight the  
Figure 2: Confusion matrices of the proposed method (SNR = 0 dB). (**a**) \(P=37\). (**b**) \(P=41\). effectiveness of the proposed Hankelization-based preprocessing technique in achieving robust detection performance under various SNR conditions. Figure 4 shows the detection error rate of the proposed method compared to other baseline methods under different training dataset sizes. The proposed method consistently achieves the lowest detection error rate, demonstrating stable performance across different training dataset sizes. These results confirm the robustness of the proposed method in synchronization signal detection, ensuring reliable performance regardless of the dataset size. Figure 5 shows the detection rate of the proposed method compared to four baseline methods across different sequence lengths \(P\) and NN widths. Based on (11), the detection rate is derived from the detection error rate, reflecting its complementary relationship. In Figure 5a, the proposed method consistently achieves superior accuracy, even with a constrained NN width of 24, maintaining over 90% detection accuracy for longer sequence lengths. In contrast, the baseline methods exhibit noticeable performance degradation for longer lengths of sequence. This indicates the ability of the proposed method to handle increased data complexity and dimensionality efficiently. Also, Figure 5b shows the detection  
Figure 4: Detection error rate for the synchronization signal according to size of the training dataset. (SNR = 0 dB) (**a**) \(P=37\). (**b**) \(P=41\). Figure 3: Detection error rate for the synchronization signal according to SNR. (**a**) \(P=37\). (**b**) \(P=41\). rate with an increased NN width of 48. The baseline methods exhibit improved performance for longer sequence lengths compared to the results in Figure 5a, particularly Baseline 1 (Deep learning method based on cross-correlation). However, the proposed method remains largely unaffected by the increase in NN complexity, consistently achieving high detection accuracy regardless of the NN width. This robustness highlights the efficiency of the proposed method in extracting and utilizing critical features without relying on a highly complex NN architecture.