## 7 Simulation Results and Analysis
### Simulation Results of V2X  
In the simulation, according to [29; 30], we set the mmWave massive MIMO communication system to operate in the 73 GHz band, the number of transmit antennas at the BS is set to \(N_{t}=16\), the number of RF chains is \(M_{t}=16\), the number of receive antennas at the vehicle is \(N_{r}=4\), and the number of receive RF chains is \(M_{r}=4\). The antenna spacing is a half-wavelength length, the number of RIS elements is \(N_{RIS}=64\), the number of complex gain propagation paths is \(L_{BR}=L_{RU}=4\), and the number of data streams is \(N_{s}=4\). The downlink uses the following transmission frame structure: \(T_{1}=120\), \(T_{2}=5\), \(T_{3}=45\). The azimuths of AOA and AOD are uniformly distributed in the interval \([-\pi,\pi)\) and the elevation angles of AOA and AOD are uniformly distributed in the interval \(\left[-\frac{\pi}{2},\frac{\pi}{2}\right)\). The maximum Doppler shift is \(f_{\max}\) and the noise power is \(\sigma^{2}=-80\) dBm. The speed of the vehicle is set to 0-150 km/h and the range of exponential factors \(\omega\) is \([1/1024,7/512,9/256,\)\(15/128,\)\(30/64,\)\(50/32]\). In this section, we use the spectral efficiency described in [42] and the defined signal-to-noise ratio (SNR) in [32] as evaluation metrics; the SNR is expressed as  
\[SNR=\frac{P_{t}\big{\|}\mathbf{W}_{all}^{H}\mathbf{H}_{all}\mathbf{F}_{all} \big{\|}_{F}^{2}}{\sigma^{2}N_{\mathrm{s}}} \tag{84}\]  
Considering the ideal phase shift, the proposed method is compared with the No RIS, random phase shift, orthogonal matched tracking (OMT) and sum path gain maximization-semipositive definite relaxation (SPGM-SDR) to obtain the following simulation results. At the same time, the DOA tracking algorithm proposed in this paper is compared with conventional likelihood PF (CL-PF), projection approximation subspace tracking (PAST),  
Figure 7: Outage probability of FSO link with different turbulence strengths and pointing errors. modified PAST (MPAST), and PAST with deflation (PASTD). The root mean square error (RMSE) is used to evaluate the tracking accuracy of the DOA tracking algorithm. \[RMSE=\frac{1}{N_{R}}\sum_{m=1}^{N_{R}}\sqrt{\left[\psi_{m}(n)-\overline{\psi}_{ m}(n)\right]^{2}} \tag{85}\]  
where \(N_{R}\) is the total number of ultrasonic array elements, \(\psi_{m}(n)\) is the estimated value of DOA tracking in the \(n\)-th time slot, and \(\overline{\psi}_{m}(n)\) is the actual value of DOA tracking in the \(n\)-th time slot. DOA tracking is important in communication systems, as it is used to adjust beamforming and improve system performance. We compared the proposed ultrasonic-assisted DOA tracking algorithm with others. In Figure 8, it can be seen that PAST, MPAST and PASTD have larger errors at some estimation points because these algorithms are based on updated subspace. It is more difficult to guarantee the orthogonality of the signal and noise subspace during the update process. The performance of PF-MUSIC is close to that of our proposed algorithm, but PF-MUSIC requires a large number of eigenvalue decompositions and suffers from high complexity and high computational power. Our algorithm maintains good RMSE performance at the same SNR. In summary, the ultrasonic-assisted DOA tracking algorithm proposed in this paper has better results than other algorithms, which can provide more accurate phases for the phase shift matrix of RIS. Figure 9 depicts the relationship between spectral efficiency and transmit power of BS. The overall spectral efficiency of No RIS is much lower than the others, indicating that the signal transmission of the No RIS system is more affected by the transmission route. The other algorithms improve the capacity of the system more obviously. The random phase shift is less effective because the accuracy of the phase shift angle cannot be guaranteed. The performance of SPGM-SDR and OMP is similar. The proposed algorithm has the best spectral efficiency, and the results are slightly higher those of than SPGM-SDR and OMP.