# Neural-Network-Based Synchronization Acquisition with Hankelization Preprocessing
## 1 Introduction  
In wireless communication systems, the preamble is a fundamental component for achieving synchronization between the transmitter and the receiver. It is a specially designed signal sequence transmitted at the start of communication to ensure precise alignment between the two ends. This process involves synchronizing the time, frequency, and phase of the transmitted and received signals, which is crucial for enabling efficient and reliable data transmission. A representative sequence used in preamble design is the Zadoff-Chu (ZC) sequence [1]. The ZC sequence is a complex-valued sequence with constant amplitude and excellent correlation properties. It exhibits zero autocorrelation for cyclic shifts and maintains low cross-correlation between different root sequences, making it effective for synchronization, channel estimation, and interference mitigation. Due to its ideal correlation characteristics, the ZC sequence has been adopted for use in random access in LTE and 5G NR [2, 3]. The transmitter generates a ZC sequence based on a specific length and root index, modulates it, and transmits it. As the signal travels through the wireless channel, it encounters multipath fading, Doppler shifts, thermal noise, and interference. The receiver correlates the received signal with the ZC sequence to determine the transmission time and compensate for frequency offsets. Because the ZC sequence exhibitsideal autocorrelation properties, a distinct correlation peak appears at the correct timing. This feature enables the base station to detect new terminals and coordinate access. Accurate synchronization minimizes timing and frequency errors, thereby reducing data transmission errors. Conversely, failure in synchronization acquisition can compromise the integrity of the transmitted data, leading to communication failures. As such, preamble-based synchronization acquisition is a critical technique for ensuring stable and robust communication performance in wireless systems. Preamble detection method-based synchronization acquisition techniques have been extensively studied in various environments. Previous research on preamble detection algorithms includes the peak-to-average ratio after deleting quasi-users (PAR-DQ) preamble detection technique for LTE-satellite communication systems [4] and 5G physical random access channel (PRACH)-based preamble detection methods [5], both of which aim to enhance detection performance in multipath environments. Additionally, energy efficient random access techniques for low-Earth-orbit (LEO) systems have gained attention [6]. Traditional random access methods tend to consume excessive power to ensure high reliability. Moreover, a study on preamble detection performance in long-range (LoRa) systems [7] evaluated cross-correlation-based preamble detection techniques and proposed performance optimization strategies for low-power wide-area networks. In general, synchronization acquisition typically involves calculating the cross-correlation function between the received signal and the known preamble. However, this method typically relies on a predefined threshold, which may fail to provide optimal performance in dynamic environments. An improperly low threshold increases the risk of false detections due to noise, while an excessively high threshold may result in missed detections. To overcome this issue, the constant false alarm rate (CFAR) technique has been adopted to dynamically adjust the threshold in response to changing noise conditions [8; 9]. CFAR optimizes detection performance by analyzing the noise distribution, setting the threshold based on the average noise level, and maintaining a consistent false alarm rate [10; 11; 12]. Recent advancements in wireless communication have highlighted the potential of machine learning (ML)-based signal processing methods to improve detection performance, particularly in noisy environments. While traditional methods are predominantly based on linear signal models, practical wireless channels often exhibit nonlinear characteristics.