# Timing and Frequency Synchronization Using CAZAC Sequences for OFDM Systems
## 2 Related Works
[20] introduced a control problem with unique finite/fixed-time stability considerations, namely time-synchronized stability, and accordingly, presented sufficient conditions for it. In the same year, [PERSON] et al. [21] studied the CFO synchronization technology in OFDM, analyzed CFO in the time and frequency domains, and simulated the performance of CFO synchronization technology based on OFDM. Compared with PN sequences, constant amplitude zero autocorrelation (CAZAC) sequences had better autocorrelation and cross-correlation properties [22]. Therefore, many synchronization algorithms that are based on CAZAC sequences were proposed in succession. In 2005, [PERSON] et al. [23] proposed a new timing and frequency offset estimation method. This was based on a new constant envelope preamble that was generated by the discrete Fourier transform (DFT) of a CAZAC sequence. This method almost eliminated the sidelobes and significantly improved the accuracy of the timing offset estimation. [PERSON]'s method performed well under additive white Gaussian noise (AWGN) channels; however, its performance degraded significantly under multipath fading channels. New synchronization algorithms, which were based on CAZAC sequences, were proposed by [PERSON] and [PERSON] in [24; 25]. In both, they used different weighting factors from those of [PERSON], which improved the synchronization performance under multipath fading channels, effectively utilized the properties of CAZAC sequences, and achieved stable and accurate combined timing and frequency synchronization for OFDM systems. In 2015, [PERSON] et al. [26] proposed a timing and frequency synchronization algorithm using the Zadoff-Chu (ZC) sequence (one type of CAZAC sequence). This had joint signal detection, timing synchronization, and CFO estimation, which simplified the complete synchronization structure and improved the synchronization performance. In 2017, [PERSON] et al. [27] designed a preamble, which was based on Golay sequences and CAZAC sequences, and they proposed a low-complexity timing and frequency synchronization algorithm for OFDM systems. When compared with the existing alternative methods, this novel scheme achieved competitive performance and significantly reduced computational complexity. In 2018, [PERSON] et al. [28] developed new CAZAC and near CAZAC sequences to enable robust fine timing and frequency synchronization, which endowed OFDM preamble waveforms with a compact spectrum and a low peak-to-mean envelope power ratio (PMEPR). In the same year, [PERSON] et al. [29] proposed a new near-CAZAC sequence to construct spectrally compact OFDM preamble waveforms. The new waveforms had robust timing and frequency synchronization and very low PMEPR, compared to waveforms that had been built using traditional CAZAC sequences. In 2019, [PERSON] et al. [30] proposed a new synchronization algorithm, which was based on scrambling sequences, to improve the synchronization performance of OFDM systems in the presence of interference. This redesigned the training sequence with CAZAC sequences and additional scrambling operations. Compared with the traditional algorithm based on scrambling sequences, the simulations showed that the proposed synchronization algorithm could maintain a sharper correlation peak in an interference environment and could achieve accurate STO and CFO estimations. In 2020, [PERSON] et al. [31] proposed a time-frequency synchronization scheme that was based on a new synchronization preamble, using CAZAC sequences. This effectively improved the stability and accuracy of OFDM system synchronization. In 2021, [PERSON] et al. [32] built a compact band-pass filter with improved band-stop and band-pass characteristics for wireless applications with four internal conductive poles in a single resonating cavity, which added novel quad-resonating modes to the realization of the band-pass filter. In 2022, [PERSON] et al.