# Timing and Frequency Synchronization Using CAZAC Sequences for OFDM Systems
###### Abstract  
Since orthogonal frequency division multiplexing (OFDM) systems are very susceptible to symbol timing offset (STO) and carrier frequency offset (CFO), which cause inter-symbol interference (ISI) and inter-carrier interference (ICI), accurate STO and CFO estimations are very important. In this study, first, a new preamble structure based on the Zadoff-Chu (ZC) sequences was designed. On this basis, we proposed a new timing synchronization algorithm, called the continuous correlation peak detection (CCPD) algorithm, and its improved algorithm: the accumulated correlation peak detection (ACPD) algorithm. Next, the correlation peaks that were obtained during the timing synchronization were used for the frequency offset estimation. For this, the quadratic interpolation algorithm was adopted as the frequency offset estimation algorithm, which was better than the fast Fourier transform (FFT) algorithm. The simulation results showed that when the correct timing probability reached 100%, under the parameters of \(m=8\) and \(N=512\), the performance of the CCPD algorithm was 4 dB higher than that of [PERSON]'s algorithm, and that of the ACPD algorithm was 7 dB. Under the same parameters, the quadratic interpolation algorithm also had a great performance improvement in both small and large frequency offsets, when compared with the FFT algorithm. orthogonal frequency division multiplexing (OFDM); timing synchronization; correlation operation; Zadoff-Chu (ZC) sequence; frequency offset estimation; fast Fourier transform (FFT)  
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the autocorrelation of the received signals. The training sequences are repeated sequences, and the receiver performs a delayed autocorrelation on the received signal sequences and then determines the timing synchronization position using the autocorrelation peak. The other one is based on the cross-correlation of the received signals. The receiver performs a sliding cross-correlation between the received signal sequences and the known training sequences, so that the sharp correlation peak can be obtained at the timing synchronization point and so that it is easy to determine the accurate synchronization position [7]. Based on the literature search of the related works, we found that using CAZAC sequences as a preamble for synchronization in an OFDM system is more effective than using PN sequences. Furthermore, the correlation value is proportional to the length of the preamble; therefore, a longer preamble can achieve higher synchronization estimation accuracy. On the other hand, the frequency offset has a greater impact on a longer preamble. In order to reduce this effect, segmenting the preamble is a common and effective method. This is the source of the research idea of this paper. The innovation points and main contributions of this paper are summarized as follows:  
1. A new preamble structure based on ZC sequences was designed;
2. On this basis, a new timing synchronization algorithm, called the continuous correlation peak detection (CCPD) algorithm, was proposed;
3. In addition, an improved algorithm of the CCPD algorithm, called the accumulated correlation peak detection (ACPD) algorithm, was proposed;
4. Next, the correlation peaks that were obtained during the timing synchronization were used for the frequency offset estimation;
5. The frequency offset estimation algorithm adopted the quadratic interpolation algorithm, which was improved from the FFT algorithm. The remainder of this paper is organized as follows: In Section 2, the related works in recent years are introduced. In Section 3, some necessary background is provided, including the OFDM signal model, the CAZAC sequences, and the FFT frequency estimation algorithm. In Section 4, first, a new preamble structure is presented. Based on this foundation, a new timing synchronization algorithm and its improved algorithm are proposed. Next, the frequency offset is estimated by using the correlation peaks extracted by the synchronization algorithm.