## 4 Simulation Results and Analysis
### System Performance Comparison  
In this section, we run a number of simulations to confirm the suggested algorithm's efficacy in terms of performance and accuracy. We adopt the EVA channel [27], which is specified by 3 GPP for V2X scenarios. In addition, the path amplitude follows the Rayleigh distribution, and the average energy is exponentially decreasing over time. Each tap has a Doppler shift, which is randomly generated by [PERSON]'s model \(f_{i}=f_{\text{max}}\cos(\theta_{i})\), where \(\theta_{i}\) indicates a uniform distribution between \(-\pi\) and \(\pi\). In this paper, we simulate some scenarios with normalized maximum Doppler shift ranging from 3% to 15%, matching the speeds range of from 137 km/h to 685 km/h. In addition, existing channel estimation schemes are used for simulation comparison, including traditional pulse channel estimation based the threshold method [6] and the basis coefficient estimation algorithm based on LS, MMSE and SBL algorithms. The normalized mean square error (NMSE) and BER are utilized as evaluation criteria to assess the performance of the suggested algorithm and confirm its superiority and efficacy in the V2X channel. NMSE is defined as follows:  
\[\text{NMSE}=10\log_{10}\frac{\mathbb{E}\left[\left\|\mathbf{h}-\mathbf{\hat {h}}\right\|^{2}\right]}{\mathbb{E}\left[\left\|\mathbf{h}\right\|^{2}\right]} \tag{42}\]  
Figure 2: Runtime comparisons when SNR = 20 dB. where \(\hat{\mathbf{h}}\) denotes the estimated DD domain channel vector. The system simulation parameter for this paper is displayed in Table 1.  
Figure 3a presents the NMSE curve of channel estimation when \(f_{d}=3\%\). It is found that the NMSE of the traditional pulse channel estimation-based threshold method curve will produce a platform effect with the increase of SNR and cannot continue to decline. For the basis coefficient estimation model derived in this paper, the NMSE will continue to decline as SNR increases, which proves the superiority of the channel model. At the same time, the NMSE performance of the GAMP-SBL algorithm is basically equal to that of the SBL algorithm and close to the lower bound LMMSE algorithm. It proves that the GAMP-SBL algorithm can not only greatly reduce the complexity, but also guarantee good estimation performance. In Figure 3b, we illustrate the performance comparison of NMSE at \(f_{d}=15\%\). In high-speed scenarios, the traditional pulse channel estimation-based threshold method can only estimate the channel response in the DD domain of a single point, but cannot capture the channel change in each Doppler sampling point. Therefore, the platform effect is more serious, and it is not suitable for channel estimation in V2X scenarios. The NMSE performance of GAMP-SBL improves significantly with the increase in the SNR ratio. Therefore, the proposed scheme can achieve accurate channel estimation in complex scenarios, such as V2X. Figure 4a,b show the performance comparison of BER in different scenarios, where the perfect channel BER serves as the benchmark, and the traditional MMSE algorithm is used as the symbol detector in the OTFS system. It is found that the proposed GAMP-SBL \begin{table}
\begin{tabular}{c c} \hline \hline
**Simulation Parameters** & **Settings** \\ \hline Carrier frequency & 5.9 GHz \\ Subcarrier spacing & 15 KHz \\ Modulation method & QPSK \\ Number of subcarriers (\(M\)) & 32 \\ Number of symbols (\(N\)) & 16 \\ CP length & 7 \\ Basis extended dimension \(Q\) & 8 \\ Channel model & EVA \\ Maximum user’s velocity & 121.5–607.5 km/h \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System simulation parameter. Figure 3: The NMSE performance comparison with velocities of 121.5–685 km/h, i.e., \(f_{d}=3\)–15%. algorithm achieves satisfactory BER performance, which is close to the performance of the MMSE algorithm in the OTFS system. The channel response obtained using the traditional method is not accurate, which leads to poor BER performance, especially in high-speed scenarios.