# Second-Order Statistical Properties of Vehicle-to-Vehicle Rician Fading Channel
## 3 LCR and AFD for the V2V Flat Fading Channel
By setting \(m=0\), we can determine the value of the parameter \(b_{0}\) as  
\[b_{o}=b_{0}^{SBT}+b_{0}^{SRR}+b_{0}^{DB}=\frac{1}{2(K+1)}\, \tag{8}\]  
where \(b_{0}^{SBT}\), \(b_{0}^{SRR}\), and \(b_{0}^{DB}\) are given as  
\[b_{0}^{SBT}=\frac{\eta_{T}}{2(K+1)}\int\limits_{-\pi}^{\pi}\frac{e^{k_{T}cos( \alpha_{T}-\mu_{T})}}{2\pi I_{0}(k_{T})}\ da_{T}=\frac{\eta_{T}}{2(K+1)}, \tag{9}\]  
\[b_{0}^{SRR}=\frac{\eta_{R}}{2(K+1)}\int\limits_{-\pi}^{\pi}\frac{e^{k_{R}cos( \alpha_{R}-\mu_{R})}}{2\pi I_{0}(k_{R})}\ da_{R}=\frac{\eta_{R}}{2(K+1)}\, \tag{10}\]  
\[b_{0}^{DB}=\frac{\eta_{TR}}{2(K+1)}\int\limits_{-\pi}^{\pi}[\frac{e^{k_{T}cos( \alpha_{T}-\mu_{T})}}{2\pi I_{0}(k_{T})}\times\frac{e^{k_{R}cos(\alpha_{R}- \mu_{R})}}{2\pi I_{0}(k_{R})}]da_{T}da_{R}=\frac{\eta_{TR}}{2(K+1)}. \tag{11}\]  
Similarly, by substituting the relevant expressions for \(b_{m}\) and considering the von Mises PDFs for the SB and DB TR models, the expression for \(b_{1}\) and \(b_{2}\) can be obtained, where \(m\in[1,\ 2)\), respectively,  
\[b_{m}=b_{m}^{SBT}+b_{m}^{SRR}+b_{m}^{DB}\, \tag{12}\]  
\[b_{m}^{SBT}=(2\pi)^{m}b_{0}^{SBT}\int\limits_{-\pi}^{\pi}\frac{e^{k_{T}cos( \alpha_{T}-\mu_{T})}}{2\pi I_{0}(k_{T})}\times\left[f_{Tmax}cos(\alpha_{T}-\mu _{T})\ +\ f_{Rmax}cos(\alpha_{R}-\mu_{R})\right]^{m}da_{T}\, \tag{13}\]  
\[b_{m}^{SRR}=(2\pi)^{m}b_{0}^{SRR}\int\limits_{-\pi}^{\pi}\frac{e^{k_{R}cos( \alpha_{R}-\mu_{R})}}{2\pi I_{0}(k_{R})}\times\left[f_{Tmax}cos(\alpha_{T}-\mu _{T})\ +\ f_{Rmax}cos(\alpha_{R}-\mu_{R})\right]^{m}da_{R}\, \tag{14}\]\[b_{m}^{DB}=(2\pi)^{m}b_{0}^{DB}\int\limits_{-\pi}^{\pi}\int\limits_{-\pi}^{\pi} \left[\frac{e^{k_{T}cos(\alpha_{T}-\mu_{T})}}{2\pi I_{0}(k_{T})}\times\frac{e^{k _{R}cos(\alpha_{R}-\mu_{R})}}{2\pi I_{0}(k_{R})}\right]\times\left[f_{Tmax}cos( \alpha_{T}-\mu_{T})+f_{Rmax}cos(\alpha_{R}-\mu_{R})\right]^{m}d\alpha_{T}d \alpha_{R}. \tag{15}\]  
Through the substitution of the relevant expressions for \(\alpha_{R}\) and \(\alpha_{T}\) from Section 2, and using approximate relations of \(sin\chi\approx\chi\) and \(cos\chi\approx 1\) where \(\chi\) is very small, and also using the following trigonometric transformations and inequalities \(\int\limits_{-\pi}^{\pi}e^{\alpha cos(c)+bsin(c)}dc=2\pi I_{0}(\sqrt{a^{2}+b^{ 2}})\) and \(\int\limits_{-\pi}^{\pi}e^{\alpha cos(\theta)}cos(m\theta)d\theta=2\pi I_{m}(x)\) ([21], Equations (3.3339) and (8.4111)), where \(I_{0}\) denotes zeroth-order Bessel function of the first kind and \(I_{m}\) is the \(m\)th-order Bessel function of the first kind. The closed-form expressions for the parameters \(b_{1}\) are  
\[b_{1}^{SBT}=b_{0}^{SBT}\bigg{[}2\pi f_{Tmax}cos(\mu_{T}-\gamma_{T})\frac{I_{1} (k_{T})}{I_{0}(k_{T})}+2\pi f_{Rmax}\left(\frac{I_{1}(k_{T})}{I_{0}(k_{T})}. \Delta_{T}sin\gamma_{R}sin\mu_{T}-cos\gamma_{R}\right)\bigg{]} \tag{16}\]  
\[b_{o}=b_{0}^{SBT}+b_{0}^{SRR}+b_{0}^{DB}=\frac{1}{2(K+1)}\, \tag{8}\]0  
\[b_{o}=b_{0}^{SBT}+b_{0}^{SRR}+b_{0}^{DB}=\frac{1}{2(K+1)}\, \tag{8}\]1  
\(b_{2}\) can also be expressed as:  
\[b_{o}=b_{0}^{SBT}+b_{0}^{SRR}+b_{0}^{DB}=\frac{1}{2(K+1)}\, \tag{8}\]2 \[b_{o}=b_{0}^{SBT}+b_{0}^{SRR}+b_{0}^{DB}=\frac{1}{2(K+1)}\, \tag{8}\]3 \[b_{o}=b_{0}^{SBT}+b_{0}^{SRR}+b_{0}^{DB}=\frac{1}{2(K+1)}\, \tag{8}\]4  
\[b_{o}=b_{0}^{SBT}+b_{0}^{SRR}+b_{0}^{DB}=\frac{1}{2(K+1)}\, \tag{8}\]5 \[b_{o}=b_{0}^{SBT}+b_{0}^{SRR}+b_{0}^{DB}=\frac{1}{2(K+1)}\, \tag{8}\]6 \[b_{o}=b_{0}^{SBT}+b_{0}^{SRR}+b_{0}^{DB}=\frac{1}{2(K+1)}\, \tag{8}\]7  
\[b_{o}=b_{0}^{SBT}+b_{0}^{SRR}+b_{0}^{DB}=\frac{1}{2(K+1)}\, \tag{8}\]8 \[b_{o}=b_{0}^{SBT}+b_{0}^{SRR}+b_{0}^{DB}=\frac{1}{2(K+1)}\, \tag{8}\]9  
The close-form expressions for the constants \(b_{0}\), \(b_{1}\), and \(b_{2}\) are derived from the scatter components' power spectrum and are thus an integral part of the LCR derivation. These constants have a significant impact on second-order statistics (LCR). It is important to note that a detailed derivation of (16)-(21) is provided in Appendix A.