# Neural-Network-Based Synchronization Acquisition with Hankelization Preprocessing
## 5 Conclusions  
In this paper, we propose an NN model combined with a Hankelization-based preprocessing technique to enhance synchronization signal detection in wireless communication systems. Unlike traditional methods that directly utilize the correlation function as the input for the NN, the proposed approach applies the inverse Fourier transform and Hankelization to the correlation function, followed by SVD to extract primary signal features. These features are then used as inputs to the NN, effectively addressing the noise sensitivity and processing inefficiencies of conventional synchronization detection methods. By incorporating this preprocessing step, the proposed method achieves optimized detection performance, particularly in low-SNR environments. Simulation results demonstrate that the Hankelization-based preprocessing technique significantly improves synchronization signal detection accuracy compared to conventional methods. This approach exhibits robustness against noise and outperforms existing methods by enhancing detection reliability, particularly in conditions with low signal quality. These observations validate the effectiveness of the proposed NN-based synchronization detection model, showcasing its potential to overcome the limitations of existing approaches. While the proposed method exhibits strong performance in synchronization acquisition, further refinements can enhance its applicability for practical deployment. In particular, the computational complexity of the SVD may introduce challenges for real-time implementation, and the singular value spectrum can exhibit numerical sensitivity under extreme noise conditions. To mitigate these issues, in future work, we will extend our research by applying approximate SVD algorithms, such as the randomized SVD method, which utilizes random sampling, and the truncated SVD method, which selectively retains only the dominant singular values, to reduce computational complexity. Additionally, we will conduct a broad investigation into various algorithms to improve numerical stabil  
Figure 8: Detection error rate for the synchronization signal in practical channel according to SNR. (**a**) \(P=37\). (**b**) \(P=41\). ity, ultimately working towards enhancing our approach with more advanced algorithms. From the perspective of integration with system performance evaluation, especially in ultra-reliable communications, a comprehensive bit error rate (BER) analysis remains critical to fully assessing the broader impact of the proposed method on overall system performance. Expanding the evaluation framework to include BER analysis would offer deeper insights into the effectiveness of the proposed approach in enhancing the reliability of random access communication systems. Finally, we aim to further explore the adaptability of our method to realistic conditions, where SNR variations may occur, thereby enhancing its practical applicability and robustness. Conceptualization, W.-H.L. and J.-H.L. ; software, J.-H.K. ; writing--original draft preparation, G.-E.K. and J.-H.K. ; writing--review and editing, W.-H.L and J.-H.L. ; visualization, G.-E.K. and 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 an Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. RS-2023-00217885, Development of integrated interference analysis technology for improving frequency utilization efficiency) and in part by a National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. RS-2023-00239349). Not applicable. The data supporting the reported results in this study can be shared upon reasonable request. Interested researchers should contact the corresponding author to discuss access. Please note that data sharing may be subject to restrictions due to privacy, ethical considerations, or intellectual property agreements with funders. The authors declare no conflict of interest.