# Second-Order Statistical Properties of Vehicle-to-Vehicle Rician Fading Channel
## 4 Discussion  
This section provides a detailed numerical analysis of the LCR and AFD, the two key second-order statistical properties of the non-isotropic V2V flat fading channel, as derived in Section 3. Notably, the scatterers are cascaded into SB and DB components, or SBT, SBR, and DB components, and analyzed separately to provide a better intuition into the characteristics of the channel. The analysis examines the effects of the following parameters: high VTD, scattering assumption, mean angle (\(\mu_{\rm T(R)}\)), angle spread (\(\gamma_{\rm T(R)}\)), Tx-Rx separation distance (\(\rm d\)), and the relative direction Tx-Rx motion [same direction (SD), opposite direction (OD)]. In summary, the abovementioned parameters can influence LCR and AFD channel properties while providing insight into the channel performance. For instance, the scatterers' behavior in either SB or DB path can indicate the stability of the channel and its dependency on the AoA and AoD. The Tx-Rx movement describes the sensitivity of varying propagation paths in SB and DB rays with respect to the LCR and AFD. The Tx-Rx distance separation and \(K\)-factor explore the dominance of LoS, SB, and DB rays in the channel, and how it affects the LCR and AFD. The scattering mean angle and angle spread influence the LCR and AFD crossings and threshold. The last is the VTD parameter, which shows the effect of different traffic densities on the SB and DB rays. Furthermore, our analysis compares the theoretical LCR and AFD results with the empirical data reported in prior studies [23]. The numerical analysis uses the following parameters: \(\rm f_{c}=5.2\) GHz, \(\rm f_{Tmax}=\rm f_{Rmax}=500\) Hz, \(\rm D=300\) m, and \(\rm R_{T}=\rm R_{R}=40\) m. The Rician K-factor is estimated using the approach outlined in earlier work [24], while the other model parameters are determined using the methodology presented therein [25]. Figure 2a,b reveals the distinct behaviors of SB and DB scatterers and the impact of Tx-Rx directionality on the second-order channel characteristics. The visualized LCR and AFD data show that SB rays are more sensitive to the Tx-Rx movement and disappear for DB rays, and this sensitivity is reflected in the LCR and AFD diagrams. The SB introduces a stronger directional dependence in the channel due to the inter-dependent relationship of the SB AoD and AoA, making LCR and AFD more sensitive to Tx-Rx movement. The DB scatterers contribute to a more stable channel by creating more diverse paths with less directional dependence and the independent relationship of AoA and AoD. The model can be achieved using the following parameters: \(\rm k_{T}=\rm k_{R}=2.6\), \(\rm\mu_{T}=45^{\circ}\), \(\rm\mu_{R}=145^{\circ}\) for the different scenarios (SD): \(\rm\gamma_{T}=\rm\gamma_{T}=0\), \(\rm\eta_{T}=0.46\); and \(\rm\eta_{T}=0.31\), (OD): \(\rm\gamma_{T}=0,\rm\gamma_{R}=180\). Figure 3a,b illustrates the sensitivity of LCR and AFD to variations in the angle spread and mean angle channel parameters for the non-isotropic Rician channel. The SB and DB scatterers systematically change for different non-isotropic scenarios, and hence angle spread (\(k_{T},k_{R}\)), and mean angles (\(\mu_{T}\), \(\mu_{R}\)) parameters significantly impact the LCR and AFD crossings and thresholds. Therefore, comprehending these parameters' behavior is crucial for accurately modeling the LCR and AFD characteristics in this channel environment. The LCR and AFD are obtained using the parameters \(\rm\gamma_{T}=\gamma_{R}=0\) for different isotropic scenarios. \(a\) (\(S_{a}\)): \(k_{T}=k_{R}=2.5\), \(\rm\mu_{T}=45^{\circ}\), and \(\rm\mu_{R}=145^{\circ}\). \(b\) (\(S_{b}\)): \(k_{T}=k_{R}=6\), \(\mu_{T}=60^{\circ}\)  
and \(\mu_{R}=160^{\circ}\). \(c\) (\(S_{c}\)): \(k_{T}=k_{R}=2.5\), \(\mu_{T}=120^{\circ}\), and \(\mu_{R}=45^{\circ}\). \(d\) (\(S_{d}\)): \(k_{T}=k_{R}=4\), \(\mu_{T}=130^{\circ}\), and \(\mu_{R}=60^{\circ}\). Figure 4a,b depicts the effects of Tx-Rx separation on the LCR and AFD metrics under a low-VTD scenario.