# Adaptive Damping Log-Domain Message-Passing Algorithm for FTN-OTFS in V2X Communications
## 4 Simulation Results  
In this section, the BER performance of the proposed ADL-MP detection algorithm is evaluated under the EVA channel model and the HST scenario. These scenarios were selected to represent realistic and challenging V2X wireless communication environments. The BER performance of the ADL-MP detection algorithm is compared to that of the conventional linear minimum mean square error (LMMSE) and maximal ratio combining (MRC) [25] detection algorithms. Then, we compare the bit error rate performance of FTN-OTFS and OFDM under the EVA model. The simulation parameters used in the simulations are summarized in Table 1, offering a comprehensive overview of the system configuration. In this section, the BER performance of the proposed ADL-MP detection algorithm is evaluated under both the EVA channel model and the HST scenario, which were chosen to represent realistic and challenging V2X wireless communication environments. The BER performance of the ADL-MP algorithm is compared with that of conventional detection algorithms, specifically linear minimum mean square error (LMMSE) and maximal ratio combining (MRC) [25]. In addition, we compare the BER performance of FTN-OTFS and OFDM under the EVA model. The simulation parameters are summarized in Table 1, providing a comprehensive overview of the system configuration. Figure 3 illustrates the BER performance of the proposed ADL-MP detection algorithm under the EVA channel model (In the EVA model, the delay taps are [0, 30, 150, 310, 370, 710, 1090, 1730, 2510] ns, with the Doppler shift for the \(i\)th path generated from a uniform distribution \(U(0,\
u_{\max})\)[25], where \(\
u_{\max}\) denotes the maximum Doppler shift) with a speed of 120 kmph. The results compare the BER performance of the ADL-MP algorithm and the conventional LMMSE detection algorithm across different compression factor pairs \((\alpha,\beta)\) over a range of SNR values. As depicted in Figure 3, the LMMSE and ADL-MP algorithms achieve comparable performance in the low-to-medium SNR range (0 to 15 dB). However, beyond 15 dB, the ADL-MP algorithm consistently outperforms LMMSE, delivering significantly lower values of BER. This improvement highlights the \begin{table}
\begin{tabular}{c c} \hline Number of Subcarriers \(M\) & 64 \\ \hline Number of Time Slots \(N\) & 64 \\ \hline Mapping & 4-QAM \\ \hline Subcarrier Bandwidth & 15 kHz \\ \hline Channel & EVA and HST \\ \hline Vehicular Speed & 120 kmph and 500 kmph \\ \hline Carrier Frequency & 4 GHz \\ \hline ADL-MP Iteration Count & 15 \\ \hline \end{tabular}
\end{table} 
Table 1: Simulation Parameters. superior capability of ADL-MP to suppress noise and interference in highly dynamic multi-path environments, such as those encountered in V2X communication systems. When the compression factors are set to \((\alpha,\beta)=(1,1)\), the system behaves equivalently to a conventional OTFS system. Under these conditions, the ADL-MP and LMMSE algorithms perform comparably at low and moderate SNR levels. However, as \((\alpha,\beta)\) decrease, the ADL-MP algorithm manages to maintain a BER below \(10^{-3}\) across the high-SNR range, satisfying the requirement for reliability in V2X communication. In contrast, the BER performance of the LMMSE algorithm degrades significantly at higher compression rates, particularly in the high-SNR range, compromising system reliability. Figure 4 illustrates the BER performance of the proposed ADL-MP detection algorithm under the HST scenario (The HST scenario is modeled as a single-path line-of-sight channel with zero delay, where the Doppler shift is set to the maximum value \(\
u_{\max}\) determined by the train speed and carrier frequency [26]). The system is evaluated at a high speed of 500 km/h to represent the challenging conditions created by high mobility in vehicular communication systems.