# A Robust Timing Synchronization Algorithm Based on PSSS for LTE-V2X
## 2 PSSS in LTE-V2X  
The LTE system's physical layer is traditionally divided into the uplink and downlink. In contrast, the physical layer of LTE-V2X, known as the sidelink, has evolved based on LTE-D2D technology, inheriting most of the air interface characteristics [21]. To address the limitations of mobile terminal transmission performance, LTE-V2X employs SC-FDMA to convert frequency domain signals into time domain signals, mitigating the Peak-to-Average Power Ratio (PAPR) effect. Physical channels in LTE-V2X are categorized based on their functions, including broadcast, discovery, shared and control channels. Figure 2 illustrates the placement of the Sidelink Synchronization Signal (SLSS) in the physical sidelink broadcast channel (PSBCH).  
To reduce the overhead of time-frequency resources, the period of the SLSS is 160 ms, which is much larger than the period of synchronization signals in LTE (5 ms). Meanwhile, the PSSS is transmitted in two adjacent SC-FDMA symbols in the same subframe.  
Figure 2: SLSS in PSBCH.  
The generation and nature of the synchronization signal is as follows. The SLSS carries 336 physical layer sidelink synchronization identifications \(N_{\text{ID}}^{\text{SL}}\in\{0,1,\ldots,335\}\), according to  
\[N_{\text{ID}}^{\text{SL}}=N_{\text{ID}}^{(1)}+168N_{\text{ID}}^{(2)} \tag{1}\]  
where \(N_{\text{ID}}^{(2)}\in\{0,1\}\) is the cell identification (ID) that indicates whether the terminal is covered, and the PSSS carries it. \(N_{\text{ID}}^{(1)}\in\{0,1,\ldots,167\}\) is the group identification that indicates the ID of the terminal, and it is taken by the SSSS.  
The sequence \(d(n)\) used for the PSSS is generated from a frequency domain ZC sequence according to  
\[d_{u}(n)=\left\{\begin{array}{ll}e^{-j\frac{\pi m(n+1)}{63}}&n=0,1,\ldots,30 \\ e^{-j\frac{\pi m(n+1)(n+2)}{63}}&n=31,32,\ldots,61\end{array}\right. \tag{2}\]  
where \(u\in\{26,37\}\) is the root index. If \(N_{\text{ID}}^{(2)}=0\), \(u=26\), and if \(N_{\text{ID}}^{(2)}=1\), \(u=37\).  
Due to the inherent properties of the ZC sequence, the PSSS exhibits excellent autocorrelation and cross-correlation characteristics, as illustrated in Figure 3 below. During auto-correlation operations on an identical PSSS, a prominent 'peak' is observed at the zero point, indicating a large correlation value. Conversely, when performing cross-correlation calculations for distinct main synchronization signals, the correlation value is nearly zero. These properties of the PSSS establish a robust foundation for its detection in the terminal. Furthermore, the PSSS possesses time domain symmetry, implying that its time domain representation is centrosymmetric. This particular property can be leveraged to reduce the complexity of the synchronization algorithm [22].  
The mapping of the sequence to resource elements depends on the frame structure. In the frequency domain, a PSSS with a length of 62 is mapped to the middle six Resource Blocks (RB) in the time-frequency resource grid, that is, 72 sub-carriers and the 5 sub-carriers at the two ends are vacant as the guard interval. In the time domain, the PSSS is continuously transmitted on the second and third OFDM symbols.  
Figure 3: Auto-correlation and cross-correlation value of PSSS.