# Neural-Network-Based Synchronization Acquisition with Hankelization Preprocessing
## 1 Introduction
However, ML-based approaches are relatively robust against this dependency due to using the correlation function outputs as training data to learn the patterns associated with signal presence and absence [13; 14]. One such approach is the threshold-free random access preamble detection method based on a statistical analysis of the timing metric and \(K\)-means clustering [15]. Leveraging this approach provides more adaptive synchronization performance than conventional methods and demonstrates the potential to overcome the limitations of fixed-threshold-based approaches. ML techniques, such as neural networks (NNs), excel in learning such nonlinear patterns, enabling more robust signal detection. Through this learning process, the NN detects synchronization signals in an effective way, overcoming the limitations of static threshold settings. Additionally, [16] explored deep learning methods as an alternative to correlation-based packet detection in satellite-based massive machine-type communication (mMTC) and Internet of Things (IoT) scenarios. This study demonstrates that supervised learning techniques, including random forests, can significantly enhance detection performance even in the presence of interference. Similarly, another deep learning-based approach proposed in [17] addresses preamble detection in asynchronous grant-free random access. This work demonstrates that ML-based methods can outperform traditional correlator-based methods by adapting to complex channel conditions and extracting more representative signal features. The results suggest that deep learning models can effectively overcome the limitations of static threshold settings in synchronization acquisition and provide more adaptive and reliable detection performance. To further enhance the effectiveness of NN-based synchronization acquisition, this paper proposes a novel framework leveraging a Hankelization-based preprocessing technique [18,19]. Conventional correlation function-based methods often struggle to distinguish signals from noise, particularly in low signal-to-noise-ratio (SNR) environments where the false detection rate can increase significantly due to threshold sensitivity. To address this issue, the proposed Hankelization-based method can emphasize the structural characteristics of the signal, providing higher detection performance compared to conventional methods. Additionally, by utilizing SVD to extract meaningful information from the signal, this approach maintains accuracy. Furthermore, by using a low-dimensional feature vector as the input for the NN, effective learning can be achieved even with a limited amount of data. The proposed Hankelization-based method addresses these issues through a three-step process. First, the inverse Fourier transform is applied to the correlation result between the desired and received signals. Second, the transformed signal is converted into a Hankel matrix, followed by singular value decomposition (SVD). Finally, the resulting singular value vector is used as the input for the NN for synchronization signal acquisition [20]. This preprocessing approach emphasizes the structural characteristics of the signal, facilitating more effective NN training. More specifically, the proposed method is based on the hypothesis that treating the cross-correlation results between signals as an approximate sparse vector, followed by inverse Fourier transform and Hankelization, enables the extraction of data that are more conducive to optimizing the NN model. Similar Hankelization-based techniques have demonstrated their utility in prior studies. For instance, such preprocessing was employed to enhance signal classification performance in Rician and Rayleigh fading channels [21]. Another study utilized Hankelization to classify near-field and far-field signals in extremely large-scale massive multiple-input multiple-output (XL-MIMO) systems [22].