# 5G V2X Performance Comparison for Different Channel Coding Schemes and Propagation Models
## 2 Proposed V2X Communication System Model
### Simulation System Model  
Figure 1 shows the simulation system model that is used throughout this article.  
In our simulation model we implement and use six coding/decoding schemes: BCJR, logBCJR, maxlogBCJR and SOVA turbo coding, polar and LDPC coding. The process of turbo coding is implemented according to [20]. Although the implementation of the coding scheme is identical for every algorithm, the decoding procedure varies among BCJR [15], maxlogBCJR [17; 18], logBCJR [19] and SOVA [16]. Turbo coding is implemented using four iterations, based on the recommendation given in [33] for V2X communications, which was confirmed by the simulations. Polar coding and decoding were implemented according to [60], where the authors briefly describe the implementation based on [32]. LDPC coding and decoding were implemented according to the offset min-sum algorithm, where the base matrices are provided in the NR standard specification TS 38.212 [32]. From our simulations, we concluded that after 12 iterations, the results reach an equilibrium, so we chose to use 12 iterations for each implementation of the LDPC decoder. Although polar and LDPC in 5G NR have flexible coding rates set, turbo coding has a fixed coding rate in 4G-LTE equal to 1/3. This is the reason that we chose a coding rate value of 1/3. Subsequently, the frame data are modulated at the transmitter and demodulated at the receiver by a Binary Phase-Shift Keying (BPSK) modulator and demodulator, respectively, as depicted in Figure 1.  
The V2V mobile channel is implemented according to Section 2. Our goal is to implement a V2V model, where accuracy meets generality [61] in a simple and fast simulation framework, since our communication model is less complex compared to geometry-based models, without significant losses in accuracy. That is why we decided to implement a stochastic model and avoided using a geometry-based model, similarly to [53] and [62]. Therefore, for a realistic simulation setup, we use a stochastic V2V channel using the model described in [8]. A carrier frequency equal to 5.9 GHz is also considered, similarly to [34].  
Figure 1: Simulation model using V2X stochastic channel model and BPSK modulation.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Channel State**} & \multirow{2}{*}{**Traffic Model**} & \multicolumn{3}{c}{**K Factor (dB)**} \\ \cline{3-4}  & & **Mean \(\mu_{K}\)** & **Std. Deviation \(\sigma_{K}\)** \\ \hline \multirow{2}{*}{LOS} & urban & 3.48 & 2 \\ \cline{2-4}  & highway & 9 & 3.5 \\ \hline NLOSv & urban, highway & 0 & 4.5 \\ \hline NLOS & urban & Rayleigh \\ \hline \hline \end{tabular}
\end{table}
Table 5: K-factor distribution parameters for LOS, NLOSv and NLOS states [7; 8].  
We also assume that the vehicles are moving at a constant speed of 50 Km/h in an urban environment and at a constant speed of 100 Km/h in the highway traffic model.  
Large-scale fading is computed according to Table 4, where we assume that the distance between the antennas of the two vehicles is 5 m. Further, for the NLOSv state, we assume that each case (Table 3) is equiprobable. Small-scale fading is computed as flat Rayleigh for the NLOS case and flat Rician for the LOS and the NLOSv case, where the parameters of the channels are derived from Table 5 and calculated separately for each frame. Path modelling is implemented using a Jakes Doppler spectrum, with a Doppler shift that can be specified by [8] (p. 31). Jakes model is created according to the sum of the sinusoids technique, where eight sinusoids are used, similar to [33]. Moreover, in [63], a similar V2X channel model was used with 16 sinusoids. Thus, our channel model is verified to be used in V2X systems.