## 3 System Model
### V2V Channel Model for Straight Road Scenario
#### 3.2.3 Scenario Assumptions  
Assume that \(T_{X}\) and \(R_{X}\) are moving towards each other in two lanes at a speed of 14 m/s. Considering only one type of scatterer, the most common trees are selected as scatterers. The remaining relevant parameters are set as follows: \(D_{0}=100\) m, D = 71.4 m; hr1 = 20.8 m, hr2 = 37 m; \(\alpha_{T_{0}}=-21.9^{\circ}\), \(\alpha_{R_{0}}=158.73^{\circ}\), \(\alpha_{T_{1}}=15^{\circ}\), \(\alpha_{R_{1}}=105.63^{\circ}\); \(f_{c}=6\) GHz. We substitute these values into the formulas provided in the previous two sections to calculate  
\[h_{TR}^{LOS}(t)=\sqrt{R/(R+1)}e^{-j4000\pi}e^{j1041.6\pi t}, \tag{8}\]  
\[h_{TR}^{NLOS}(t)=\sqrt{1/(R+1)}\mu e^{j(\theta-5600\pi)}e^{i692.16\pi t}. \tag{9}\]  
By substituting (8) and (9) into (1), the final expression for the complex channel fading envelope is obtained as  
\[h_{TR}(t)=\sqrt{\frac{R}{R+1}}e^{-j4000\pi}e^{j1041.6\pi t}\quad+\sqrt{\frac{1 }{R+1}}\mu e^{j(\theta-5600\pi)}e^{j692.16\pi t}. \tag{10}\]  
At this point, the only unknowns in expression \(h_{TR}(t)\) are the scatterer reflection coefficient \(\mu\) and the Rician factor R. In different vehicular network scenarios, \(\mu\) and R are key parameters affecting signal propagation, and their variations directly determine the characteristics of channel fading in each scenario. By substituting the values of \(\mu\) and R in different scenarios into (10), we can construct a more accurate system model.  
The time-domain channel gain \(h_{TR}(t)\) described by (1)-(10) represents a simplified scenario in vehicular communication, where the channel gain is considered to vary only with time \(t\), without explicitly capturing the multipath delay characteristics. This model is suitable for scenarios where the bandwidth is relatively narrow. However, in practical wideband multipath environments, frequency selectivity plays a crucial role in determining the performance of OFDM systems. To bridge the gap to the OFDM-IM system model presented later, we need to extend \(h_{TR}(t)\) to a channel model that includes a time-varying impulse response with multipath delays:  
\[h_{TR}(\tau,t)=\sum_{p=1}^{P}\alpha_{p}(t)e^{i\phi_{p}(t)}\delta(\tau-\tau_{ p}), \tag{11}\]  
where \(\alpha_{p}(t)\) and \(\phi_{p}(t)\) represent the time-varying amplitude and phase of the \(p\)-th path, \(\tau_{p}\) is the path delay, and \(P\) is the number of paths. This formulation models the channel as the superposition of multiple delayed components, leading to frequency-selective fading.  
If multipath effects are negligible or simplified to a single path, and the delay of this path can be considered zero (or negligibly small), \(h_{TR}(\tau,t)\) reduces to a function without explicit dependence on \(\tau\). Thus, the original \(h_{TR}(t)\) is a special case of \(h_{TR}(\tau,t)\) under certain conditions. If \(P=1\) and \(\tau_{1}\approx 0\), then  
\[h_{TR}(t)\approx\int h_{TR}(\tau,t)d\tau=\alpha_{1}(t)e^{i\phi_{1}(t)}. \tag{12}\]When considering the multipath structure shown in (11), the channel is no longer a narrowband gain function solely in time; instead, it becomes a two-dimensional function of the delay and time. When an OFDM system is introduced, along with a cyclic prefix and DFT operations, the multipath convolution in the time domain can be transformed into independent subcarrier gains in the frequency domain.