# A Non-WSSUS Channel Simulator for V2X Communication Systems
## 6 Simulation Examples
### Results of the STA Modification Proposal  
Since the reference model in (2) was developed for non-WSUS channels, its second order statistics depend on both time and frequency, as demonstrated in [42]. Consequently, the averages made with the STA technique in the frequency domain are not entirely accurate in this type of channel, as can be \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Scenario I**} & \multicolumn{6}{c}{**Scenario II**} & \multicolumn{6}{c}{**Scenario III**} \\ \hline Mean AOA & \multicolumn{3}{c}{\(0\)} & \(0\) & \(\frac{\pi}{2}\) & \(\frac{3\pi}{4}\) & \(0\) & \(0\) & \(\frac{\pi}{2}\) & \(\frac{3\pi}{4}\) & \(0\) & \(0\) & \(\frac{\pi}{2}\) & \(\frac{3\pi}{4}\) \\ \(\mu_{R}\) & \multicolumn{3}{c}{(\(\kappa=0\))} & & & & & & & & & & & \\ \hline Estimator & BER & \multicolumn{6}{c}{Required Eb/No (dB)} \\ \hline LS & \(10^{-1}\) & 5.67 & 4.32 & 5.87 & 5.88 & 6.11 & 8.14 & 5.12 & 4.43 & 6.06 & 4.27 & 5.44 & 7.16 \\ \hline STA (\(\kappa=2\)) & \(10^{-1}\) & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA \\ \hline STA (\(\kappa=20\)) & \(10^{-1}\) & 9.18 & 6.98 & 11.86 & 12.02 & 10.78 & NA & 9.00 & 6.94 & 10.85 & 7.03 & 9.67 & 19.03 \\ \hline LS & \(10^{-2}\) & NA & 16.03 & 17.53 & 17.33 & NA & 20.14 & 17.35 & 15.88 & NA & 15.11 & 17.76 & 19.89 \\ \hline STA (\(\kappa=2\)) & \(10^{-2}\) & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA \\ \hline STA (\(\kappa=20\)) & \(10^{-2}\) & NA & 22.09 & NA & NA & NA & NA & NA & NA & 21.18 & NA & 18.98 & NA & NA \\ \hline LS & \(10^{-3}\) & NA & NA & 38.90 & 29.67 & NA & 31.93 & NA & 39.75 & NA & 24.94 & NA & NA \\ \hline STA (\(\kappa=2\)) & \(10^{-3}\) & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA \\ \hline STA (\(\kappa=20\)) & \(10^{-3}\) & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Required Eb/No levels to attain 10%, 1%, and 0.1% BER over Scenarios I, II, and III for isotropic and non-isotropic scattering conditions by considering initial speeds of \(\upsilon_{T}=\upsilon_{R}=100\) km/h and acceleration components of \(a_{T}=a_{R}=20\) m/s\({}^{2}\), with a constant frame length of \(F=32\) (NA—not achieved). Figure 10: System performance over isotropic and non-isotropic scattering conditions with initial speeds of \(\upsilon_{T}=\upsilon_{R}=100\) km/h and acceleration components of \(a_{T}=a_{R}=20\) m/s\({}^{2}\) for Scenario I, by assuming a constant frame length of \(F=32\). seen in the simulation experiments presented earlier in this work. Therefore, we propose a modification to the STA technique that consists of eliminating the frequency averaging process for each subcarrier shown in (19), so that the new channel estimation is given by:  
\[\langle\widehat{\mathbf{H}}_{ssc}^{\mathrm{d}}\rangle_{m,k}=\left(1-\frac{1}{ \alpha}\right)\langle\widehat{\mathbf{H}}_{ssc}^{\mathrm{d}}\rangle_{m,k-1}+ \frac{1}{\alpha}\langle\widehat{\mathbf{H}}_{ssc}^{\mathrm{d}}\rangle_{m,k} \tag{21}\]  
where \(\langle\widehat{\mathbf{H}}_{ssc}^{\mathrm{d}}\rangle_{m,k}\) is the dynamic channel estimation shown in (18). The BER performance curves corresponding to Scenario I by using the proposed estimation in (21) are shown in Figure 11. We assumed isotropic scattering (\(\kappa=0\)) in a low mobility scenario at initial speeds of \(\
u_{T}=\
u_{R}=40\) km/h, acceleration magnitudes of \(a_{T}=a_{R}=20\) m/s\({}^{2}\), and frame lengths of \(F=32\) and \(64\), and \(128\) OFDM symbols. We can observe that the performance of the STA technique obtained with (21) improved significantly in comparison to the case where the frequency averaging process was included. Even if the MSs were accelerating, the frame length was increased or a small value of \(\alpha\) was used for the estimation process, and the BER performance was better than when the frequency averaging was considered.