# A Robust Timing Synchronization Algorithm Based on PSSS for LTE-V2X
## 1 Introduction
The instability of the local oscillator between the transmitter and receiver introduces a considerable frequency deviation. A 1 ppm error, for instance, leads to a frequency offset of 5.91 kHz at a frequency of 5.91 GHz. These factors contribute to the emergence of'secondary peaks' near the correct correlation peak, thereby affecting the Correct Detection Rate (CDR) process in synchronization. 3. The cycle of LTE-V2X synchronization signals (160 ms) is 32 times that of LTE 4G synchronization signals (5 ms) and 4 times that of LTE Device-to-Device (D2D) synchro  
Figure 1: LTE-V2X synchronization scenario. nization signals (40 ms). When utilizing correlation calculation results, especially those involving multi-symbol accumulation, for symbol synchronization, the computational complexity significantly increases, leading to a reduction in synchronization efficiency. In scenarios such as connected vehicle networks, where sensitivity to latency is critical, improving the efficiency of time synchronization is of paramount importance. Numerous timing synchronization methods have been proposed in the literature, encompassing both data-aided and blind detection schemes [10]. Blind detection methods leverage the specific frame structure in the orthogonal frequency division multiplexing (OFDM) system for symbol timing synchronization. Examples include the Cyclic Prefix (CP)-based maximum likelihood detection method [11], CP-based auto-correlation method [12] and minimum difference and difference square methods [13]. However, these methods may be less suitable for the LTE-V2X system due to their reliance on multiple OFDM symbol accumulations for improved performance and susceptibility to noise. Data-assisted methods comprise pilot-based auto-correlation [14] and pilot-based cross-correlation [15]. The auto-correlation method involves repeated pilot correlation in the received signal, and the cross-correlation method correlates the received signal's pilot with the locally duplicated one. LTE-V2X employs the frequency domain Zadoff-Chu (ZC) sequence as the pilot, and the selection of the root sequence enhances the pilot's resistance to frequency offset. Consequently, this article primarily investigates the symbol timing synchronization algorithm based on the pilot, specifically the PSSS. Given the complexity of the communication environment and the unique frame structure in LTE-V2X, numerous scholars have proposed corresponding synchronization algorithms based on the PSSS. In [16], [PERSON] et al. employed a selective summing function for correlated peaks detected, leveraging the continuous transmission feature of the PSSS in LTE-V2X. Spefifically, peaks detected in a subframe are added with peaks detected in the same subframe at a known relative distance between the two PSSS symbols. Subsequently, another judgment was applied, significantly enhancing the algorithm's performance in adverse channel conditions. However, in cases of an excessively large frequency offset, the \"secondary peaks\" within the primary peaks are prone to misjudgment, resulting in a failure of symbol timing synchronization. The study in [17] utilized the phase difference between the PSSS and the Sidelink Secondary Synchronization Signal (SSSS) to achieve a joint estimation of symbol timing synchronization and carrier frequency offset. This approach effectively mitigates the impact of multipath and Doppler frequency offset. In [18], the algorithm employed the accumulation of correlated results from multiple half-frames to enhance the robustness and accuracy of synchronization results. However, due to the Sidelink Synchronization Signal (SLSS) period being 160 ms, significantly larger than the 5 ms period of synchronization signals in the LTE downlink, improving the symbol timing algorithm through the enhanced algorithm of accumulating correlations across multiple subframes substantially increases its complexity. In [19], [PERSON] et al. aimed to improve algorithm performance by accumulating results from the detection of multiple symbols.