# On the Impact of Multiple Access Interference in LTE-V2X and NR-V2X Sidelink Communications +
## 4 Analytical Characterization of the Sidelink Operations  
In this section, we provide an analytical characterization of the multiple access interference affecting C-V2X sidelink operations, referring to the system scenario provided in Section 2. The link between the tagged transmitter and the platooning head in Figure 1 is considered, and all the other communicating vehicles are treated as interfering vehicles. We denote the tagged vehicle as \(i\) and assume that its transmit power is \(P_{tx,i}\). Thus, it is expected that both multi-path propagation and shadowing caused by impediments will negatively impact communication between the vehicle \(i\) and the platoon head vehicle \(j\).  
The received power at the platoon head can be expressed as follows by adopting an inverse power model for the link gain:  
\[P_{rx,i,j}=\frac{c_{0}P_{rx,i}}{d_{i,j}^{\alpha}}f_{i}\exp(y_{i}), \tag{1}\]  
where \(d_{ij}\) is the distance between the sending and receiving vehicles. The constant \(c_{0}=C_{0}G_{t}G_{r}\) includes the power gain at the reference distance of 1 m \(C_{0}\), the transmit antenna gain \(G_{t}\) and the receiving antenna gain \(G_{r}\). In the operating conditions for V2X networks, the inverse of \(c_{0}\) (i.e., the path loss at the reference distance) is in the range of 40-60 dB [35]. The path loss exponent \(\alpha\), ranges from 2 for open space propagation to 6  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Features** & **LTE-V2X** & **NR-V2X** \\ \hline Communication types & Broadcast & Broadcast, Groupcast \& \\ MCS & QPSK \& 16-QAM \& QPSK, 16-QAM \& 64-QAM \\ Waveform & SC-FDMA & OFDM \\ Re-transmissions & Blind & HARQ \\ PHY channels & PSCCH \& PSSCH & PSCCH, PSSCH \& PSSCH \\ Control and data multiplexing & FDM & TDM \\ DMRS & Four/sub-frame & Flexible \\ Sub-carrier spacing & 15 kHz & sub-6 GHz: 15, 30, 60 kHz \& \\  & mmWave: 60, 120 kHz \\ Scheduling interval & one sub-frame & slot, mini-slot or multi-slot \\ Sidelink modes & Mode 3 \& Mode 4 & Mode 1 \& Mode 2 \\ Sidelink sub-modes & N/A & Modes 2(a) \& 2(d) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of LTE-V2X and NR-V2X.  
for severe propagation conditions [36]. Under the hypothesis of Nakagami distributed fading, the factor \(f_{i}\) simulates the channel power gain due to multi-path propagation, which exhibits the Gamma distribution. We assume a Nakagami distribution with a parameter \(\kappa\geq 0.5\) and p.d.f.  
\[p_{f_{i}}(z)=\kappa^{\kappa}\frac{(z)^{\kappa-1}}{\Gamma(\kappa)}\exp(-\kappa z), \tag{2}\]  
where \(\Gamma(\kappa)\) is the fundamental Gamma function \(\Gamma(\kappa)=\int_{0}^{\infty}\exp(-x)x^{\kappa-1}dx\). We point out that the Nakagami distribution can simulate fading environments with varying degrees of severity and is extremely general. Shadow fading is here modeled by the normal random variable \(y_{i}\sim\mathcal{N}(0,\sigma_{i}^{2})\), and thus the shadowing term \(\exp(y_{i})\) in Equation (1) follows the log-normal distribution. The model we adopted is reliable for urban environments, in which devices may not be always in visibility. In a real-world system, the transmission power, path loss parameters, and standard deviation of the shadow fading of each interfering transmitting vehicle can vary and this needs to be considered in the model.