# Second-Order Statistical Properties of Vehicle-to-Vehicle Rician Fading Channel
## 4 Discussion
It provides empirical support for the general trend of the Rician factor (\(K\)) modeled as a function of propagation distance. The results show that as the distance decreases, the \(K\)-factor tends to increase, indicating stronger LoS dominance. This is accompanied by lower crossing rates at LCR and AFD plots and a more pronounced peak in the LCR curve for MSS. Conversely, more considerable separation distances result in a lower \(K\)-factor, suggesting reduced LoS contribution, which leads to an increased LCR and AFD crossing rates and a more flattened LCR slope profile for LSS. The analysis in Figure 5a,b examines the LCR characteristics of different signal propagation paths with different vehicle traffic densities, i.e., high-VTD and low-VTD environments. The following assumptions are made to mimic the VTD environment: the SBT and SBR rays primarily capture the reflection from stationary scatterers and have the predominant power concentration under a low-VDT scenario. However, in a high-VDT environment, DB rays are predominant in modeling the high-moving scatterers due to their ability to capture complex interactions involving multiple reflections, and hence they have more power concentration. These assumptions align well with the observed LCR and AFD data. Figure 3: Sensitivity of channel parameters on LCR and AFD: (**a**) plot of LCR resulting from sensitivity of channel parameters; (**b**) plot of AFD resulting from sensitivity of channel parameters. Figure 2: Scatterer behavior and Tx-Rx directionality impact on LCR and AFD: (**a**) plot of LCR resulting from scatterer behavior and Tx-Rx directionality; (**b**) plot of AFD resulting from scatterer behavior and Tx-Rx directionality. The high-VTD scenario exhibits wider and flatter peaks in the LCR envelope, indicating increased signal fluctuation due to increased multipath and rapid environmental changes. It also has a higher crossing than the low-VTD cases at a given threshold. Additionally, the influence of transmitter-receiver movement directions is observed for SB rays but disappears for DB rays due to the independent relationship between arrival and departure angles. The low-VTD scenario has fewer signal fluctuations, resulting in more pronounced narrow peaks in the LCR profile and lower threshold crossing rates than the high-VTD case. The effect of Tx-Rx movement is more pronounced for DB rays while less significant for SB rays, owing to the stronger signal power of SB rays and the interdependence between their angles of arrival and departure during low VTD, and the relationship reverses for high VTD. This observation is consistent with research findings in [26]. In summary, the results shown in Figure 5a,b demonstrate the significant effects of VTD on LCR and AFD, with higher VTD resulting in frequent signal fluctuation and having insignificant effects on the Tx-Rx movement with DB rays. They are obtained using the parameters \(v_{T}=8.33\) ms\({}^{-1}\) (high VDT) and \(v_{T}=16.67\) ms\({}^{-1}\) (low VTD). Figure 6a,b compares the theoretical LCR and AFD of vehicle-to-vehicle Rician fading channels with the measured results from a highway environment. Based on the measured data in [23], the theoretical LCR and AFD were obtained using manually chosen parameters \(K=2.43\), \(\mu_{T}=12.5\), \(\mu_{R}=154.5\), \(k_{T}=20.2\), \(k_{R}=18.5\), \(\Delta_{T}=\Delta_{R}=0.033\), \(\eta_{T}=0.043\)  
Figure 4: The effects of Tx-Rx distance separation (d) on LCR and AFD: **(a)** LCR plot resulting from Tx-Rx separation; **(b)** AFD plot resulting from Tx-Rx separation. Figure 5: Impact of high and low VTD on LCR propagation paths: **(a)** plot of LCR characteristics at high-VTD; **(b)** plot of LCR characteristics at low-VTD. \(\eta_{R}=0.037\), and \(\eta_{TR}=0.92\). The excellent compatibility between the theoretical results and the measured data confirms the model utility.