## 7 Simulation Results and Analysis
### Simulation Results of V2X
This proves the effectiveness of the proposed tensor-based ultrasonic and RIS-assisted beamforming, and the RIS also can improve the spectral efficiency of the system. Figure 8: The performance of DOA tracking with different algorithms. Figure 10 shows the spectral efficiency versus SNR. From Figure 10, it can be seen that no RIS has the worst performance because the direct path between the BS and vehicle is obscured, resulting in a large loss of signal reaching the vehicle. The random phase shift can establish communication with the vehicle through RIS more effectively, which improves the spectral efficiency compared to that of No RIS. But the phase shift angle cannot be updated effectively and performs less well than other three algorithms. The proposed algorithm has higher spectral efficiency than the SPGM-SDR and OMP because the proposed algorithm considers the effect of vehicle's mobility, and the ultrasonic-assisted RIS phase shift angle self-organized is updated, which is more helpful for the update of the RIS phase shift matrix and has better spectral efficiency. The performance of the RIS-assisted communication system greatly depends on the number of reflecting elements. To investigate the dependency between them, we simulate the spectral efficiency performance of the proposed algorithm for different numbers of RIS reflecting elements. Figure 11 shows the trend of spectrum efficiency with the number of RISs' reflecting elements for five algorithms. As the number of RISs' reflective elements increases, the spectral efficiency of all the algorithms except No RIS is significantly improved. The proposed algorithm always achieves the highest spectral efficiency compared with the chosen baseline algorithms. SPGM-SDR can only approximate the spectral efficiency without reaching the optimal result. While the proposed algorithm can obtain a better solution via a joint iterative update, the proposed algorithm can obtain significant improvement in spectral efficiency. In Figure 12, we investigate the number of RISs' reflecting elements on the BER. As the number of RISs' reflecting elements increases, the BER can be improved at the same speed. RIS can improve signal strength and quality by focusing the signal on the target receiver through beamforming and can also reduce signal impairment. This indicates that RIS- assisted V2X communication can improve the system's performance. Figure 9: The relationship between spectral efficiency and transmission power. In V2X communication, Doppler shift will affect the communication performance of the system. Figure 13 shows the BER versus the maximum Doppler shift caused by the change of vehicle speed. It can be seen that the BER of the communication system is related to the Doppler shift and deteriorates with the increase in Doppler shift. A larger Doppler shift at higher vehicle speeds leads to frequency deviation of the received echo signal, which affects the effectiveness of beamforming. Compared with other algorithms, the proposed algorithm still maintains good stability and robustness because the proposed algorithm considers the time-varying channel with Doppler shift and uses ultrasonic-assisted DOA  
Figure 11: The effect of the number of RISs’ reflecting elements on the spectral efficiency. Figure 10: The relationship between spectral efficiency and SNR. tracking and beam angle update. This shows that the proposed beamforming algorithm has better performance.