# Research on Vehicle-to-Vehicle MIMO Wireless Channels in Various Tunnels
## 5 Numerical Results and Discussions
### Channels of RT and RT with Arched Ceiling  
Figures 11 and 12 show the absolute values of the space CCFs of the LoS and NLoS propagation links. It can be found that when we set the antenna element spacing as \(\delta_{T}=\delta_{R}=0\), the spatial correlation between the two elements of conventional RT is larger than that of RT with arched ceiling. Moreover, when the element spacing increases, the SCCF gradually attenuates and fluctuates in stable states. Compared with Figure 11, SCCF fluctuates above 0.4, indicating that the correlation can be reduced by increasing the element spacing or adjusting the tunnel communication scenarios.  
Figure 11: SCCF of SRT and without ceiling for NLoS scenario \((c_{R}=0)\). (**a**) SCCF of SRT. (**b**) SCCF of SRT without ceiling.  
Figure 12: SCCF of SRT and without ceiling for NLoS scenario \((c_{R}=1)\). (**a**) SCCF of SRT. (**b**) SCCF of SRT without ceiling.  
Figure 10: DPSD of SET and without ceiling. (**a**) DPSD of SET. (**b**) DPSD of SET without ceiling.  
In Figure 13, the impacts of the Rice distribution factor on the temporal ACFs of the propagation links in the proposed V2V channel model for tunnel scenarios are studied. It can be found that when the values of \(c_{R}\) decrease, the correlation properties of the propagation links in the time domain increase gradually. Finally, the simulation results of the reference model match with the theoretic results very well.  
Figure 14 shows the frequency CCFs of the proposed V2V channel model for tunnel scenarios with respect to the different Rician factor. It can be found that the correlation properties of the normal SRT are larger than those of RT with arch ceiling. Furthermore, when we decrease the value of the \(c_{R}\), the frequency CCFs of the propagation links decay much faster. The simulation results fit very well with the analytical results, which demonstrate the accuracy of the aforementioned discussions.  
Figure 13: ACF of SRT and without ceiling for NLoS scenario \((c_{R}=1)\). (**a**) SCCF of SRT. (**b**) SCCF of SRT without ceiling.  
Figure 15a shows the frequency CCFs of the proposed V2V channel model for tunnel scenarios with respect to the model parameters of the LoS and NLoS propagation links. It can be found that when we increase the value of the cross-sectional width of the tunnel from 8 to 16, i.e., the scattering range increases, the coherence bandwidth decreases from 60 to 40 MHz. In Figure 15b, we notice that the coherence bandwidth decreases gradually as we increase the width.  
Figure 16 shows the Doppler PSDs of the proposed V2V channel model for tunnel scenarios with respect to the motion directions of the transmitter and receiver. It can be found that when we increase the height of the tunnel in the proposed V2V channel model, the curves of the Doppler PSDs behave more obviously. Furthermore, when the transmitter and receiver move in the inverse directions, the values of Doppler PSDs increase gradually. Therefore, we can conclude that all the aforementioned results have a great influence on the V2V propagation characteristics for tunnel wireless scenarios.  
Figure 14: FCF of SRT and without arched ceiling for Rice factors (\(c_{R}\)). (**a**) FCF of SRT. (**b**) FCF of SRT without ceiling.  
Figure 16: _Cont._  
Figure 15: FCF of SRT and without arched ceiling for geometric parameters. (**a**) FCF of SRT (**b**). FCF of SRT without ceiling.