# A Robust Timing Synchronization Algorithm Based on PSSS for LTE-V2X
## 5 Results and Discussion  
### Software Simulation  
This section presents the corresponding simulation works to verify the performance of the improved timing synchronization algorithm. An LTE-V2X timing synchronization simulation system is built, and the performances of the cross-correlation algorithm, the block cross-correlation algorithm, the selective summing algorithm and the improved algorithm are compared and analyzed under different frequency offsets. The simulation parameters are shown in Table 1. \(\varepsilon\) denotes the normalized frequency offset. When the positions of the two precise synchronization points calculated by each algorithm and the synchronization signal are within five sampling points, the synchronization is determined to be successful, and the CDR of successful synchronization in 1000 frames is finally counted. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Carrier Frequency & 5.915 GHz \\ Sub-carrier Spacing & 15 kHz \\ Transmission Bandwidth & 20 M (100 RBs) \\ FFT Size & 2048 \\ Sample Rate & 30.72 M \\ LTE-V2X Subframe & SC-FDMA \\ Cyclic Prefix Type & Normal \\ Threshold & T1 = 0.2/T2 = 0.7 \\ Modulation Order & QPSK (Quadrature Phase Shift Keying) \\ Channel Parameters & AWGN \(\varepsilon=0/\varepsilon=0.5/\varepsilon=1\) \\ Simulation Window & 1000 LTE-V2X subframe \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 9 compares the performance of the improved algorithm and the traditional algorithms under the Additive White Gaussian Noise (AWGN) channel when the normalized frequency offset is 0. In the figure, CCA, BCCA and SSA refer to the cross-correlation algorithm, block cross-correlation algorithm and selective summing algorithm in Section 3, respectively. M represents the number of blocks for the BCCA. Through the comparison of these algorithms, we can make conclusions as follows:  
1. The proposed improved algorithm in this paper exhibits significant improvement in PSSS detection compared to other algorithms. The enhancement is approximately 6-8 dB compared to the CCA, M = 4 and M = 2 BCCAs and around 2 dB compared to the SSA. The improved algorithm maintains a CDR close to 0.9 even at \(-\)20 dB. 2. In comparison to the BCCA and CCA, the SSA demonstrates superior PSSS detection performance with an improvement of approximately 4-6 dB. The SSA achieves a CDR close to 0.9 at an SNR of \(-\)18 dB. 3. The M = 2 and M = 4 BCCAs perform similarly to the CCA when the SNR is greater than \(-\)15 dB. However, when the SNR is below \(-\)15 dB, the performance of the M = 4 BCCA is 2-3 dB worse than that of the M = 2 BCCA and the CCA. This discrepancy is attributed to the increased number of blocks leading to noise superposition, resulting in poor synchronization performance at a low SNR. In Figure 10, we compare the performance of the improved algorithm and the other traditional algorithms under the AWGN channel when the normalized frequency offset is set to 0.5. From the simulation results, we can make conclusions as follows:  
1. The improved algorithm demonstrates superior PSSS detection performance compared to other algorithms, with an approximate 3 dB improvement over the SSA and about a 4 dB improvement over the M = 4 and M = 2 BCCAs. Additionally, the improved algorithm maintains a CDR close to 0.9 at \(-\)16 dB. 2. For the M = 4 and M = 2 BCCAs, their performance surpasses that of the CCA. Under various SNRs, the CDR of the BCCA consistently exceeds that of the CCA. This is attributed to the block, which reduces the cumulative effect of frequency offset. Figure 9: Performance of different symbol timing synchronization algorithms in AWGN channels when \(\varepsilon\) = 0. Figure 11 illustrates the performance of each algorithm under the AWGN channel with a normalized frequency offset of 1. The conclusions are as follows:  
1. The improved algorithm demonstrates superior resistance to a high frequency offset compared to other algorithms.