# A Non-WSSUS Channel Simulator for V2X Communication Systems
## 6 Simulation Examples
### Results of Changes of the Frame Length  
For these simulation experiments, the BER performance was evaluated in low mobility conditions transmitting different numbers of OFDM data symbols by considering initial speeds of \(v_{T}=v_{R}=40\) km/h, acceleration magnitudes of \(a_{T}=a_{R}=20\) m/s\({}^{2}\), and a scenario with isotropic scattering (\(\kappa=0\)). Figure 9 shows that the BER performance of the LS estimation in Scenario I decreased as the size of the frame increased. This drop in performance is due to the channel variations between the transmitted OFDM data symbols, which causes the initial LS estimation to gradually lose its validity until it becomes practically obsolete for very large frames. In this case, the worst performance for the LS estimator occurred after the frame length exceeded 128 OFDM data symbols. Regarding the STA technique, the results showed that as the updating factor increased (e.g., from \(\alpha=2\) to \(\alpha=20\)), the performance of the STA technique improved, as shown in Figure 9. In such a case, as the parameter \(\alpha\) in (20) increased, the estimated channel tends to be similar to the LS estimation. Furthermore, the performance of the STA technique was benefited in low mobility scenarios with small frame lengths, as observed for \(F=32\). Finally, by increasing the frame length and/or decreasing the updating factor \(\alpha\), the performance of the STA technique approached the case where there was no channel estimation because the weighted average in (20) became imprecise in non-WSSUS channels, whose statistics changed before the transmission of a data frame ended [58]. Table 6 presents the required Eb/No levels to achieve 10% and 1% BER by employing the LS and STA techniques in low mobility conditions, assuming frame lengths ranging from 16 to 128 OFDM symbols in the three propagation scenarios described previously. This table shows that as the frame length increased, the performance of both the LS estimator and STA technique with \(\alpha=20\) decreased. As observed in Table 5 for changes in the initial speed, the BER performance of the STA technique with \(\alpha=2\) always remained greater than 10%. For frames of 64 OFDM symbols or less, the performance of \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Scenario I**} & \multicolumn{6}{c}{**Scenario II**} & \multicolumn{6}{c}{**Scenario III**} \\ \hline Initial MS speed & 20 & 40 & 80 & 100 & 20 & 40 & 80 & 100 & 20 & 40 & 80 & 100 \\ \(v_{T}=v_{R}\) (km/h) & & & & & & & & & & & & & \\ \hline Estimator & BER & & & & & & & & & & & & \\ \hline LS & \(10^{-1}\) & 4.73 & 5.12 & 8.69 & 16.51 & 4.67 & 5.37 & 13.54 & NA & 4.81 & 5.29 & 12.88 & NA \\ \hline STA (\(\alpha=2\)) & \(10^{-1}\) & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA \\ \hline STA (\(\alpha=20\)) & \(10^{-1}\) & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA \\ \hline LS & \(10^{-2}\) & 16.99 & NA & NA & NA & 16.94 & NA & NA & NA & 16.91 & NA & NA & NA \\ \hline STA (\(\alpha=2\)) & \(10^{-2}\) & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA \\ \hline STA (\(\alpha=20\)) & \(10^{-2}\) & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA & NA \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Required energy per bit-to-noise spectral density ratio (Eb/No) levels to attain 10% and 1% BER over Scenarios I, II, and III at different initial speeds by considering acceleration components of \(a_{T}=a_{R}=20\) m/s\({}^{2}\) and a constant frame length of \(F=64\) (NA—not achieved). the LS and STA (with \(\alpha=20\)) techniques was similar in the three considered scenarios approaching the 10% BER with comparable Eb/No levels. In particular, in the case of short frames with 32 symbols or less, an Eb/No level greater than 4.61 dB and 7.15 dB for the LS estimator and STA technique (with \(\alpha=20\)), respectively, guaranteed a BER lower than 10% for all the propagation scenarios.