# Interference Analysis for Vehicle-to-Vehicle Communications at 28 GHz
## 2 System Model  
A typical V2V communication scenario, for a two-lane highway, is considered like [32]. As shown in Figure 1, each lane constitutes a cluster of vehicles \(\mathcal{V}=\{V_{j}|j=1,2,3...N\}\), wherein each vehicle is equipped with a single antenna. In each cluster, there are \(N-1\) member vehicles besides the cluster head (CH) which assists the member vehicles to forward their messages across the network. It is worth highlighting that this paper focuses on the performance analysis of V2V communications at 28 GHz. Therefore, we assume that the roadside unit (RSU) selects a CH based on some preset criteria. The selection criteria of the CH is beyond the scope of this work. Besides, a block fading model has been considered where the wireless link changes randomly from a one-time slot to another but remains unchanged within a particular time slot [33]. Due to usage of the same frequencies, the transmission in one of the clusters causes interference in the adjacent cluster. In this case, the received signal at the CH can be written as  
\[\sqrt{P_{c}}|h_{c}|^{2}s_{c}+\sqrt{P_{i}}|h_{i}|s_{i}+n, \tag{1}\]  
where \(P_{c}\) is the power of the main signal, \(h_{c}\) is the channel gain of the channel between a member vehicle and the CH, \(s_{c}\) is the symbol transmitted by the member vehicle of the main cluster, \(P_{i}\) is the power of the interfering signal, \(h_{i}\) is the channel gain of the channel between a member vehicle of the interfering cluster and the CH, \(s_{i}\) is the symbol transmitted by the member vehicle of the interfering cluster, and \(n\) is the additive white Gaussian noise (AWGN) with zero mean and \(N_{0}\) variance. The signal-to-noise ratio at the received signal is written as \(\frac{\lambda_{c}}{\lambda_{i}+1}\), where  
\[\lambda_{c}=\frac{P_{c}|h_{c}|^{2}}{N_{0}} \tag{2}\]  
and  
\[\lambda_{i}=\frac{P_{i}|h_{i}|^{2}}{N_{0}}. \tag{3}\]  
All the links are considered to follow \(\alpha-\eta-\kappa-\mu\) distribution [34]. In order to model LOS and non-LOS conditions at 28 GHz, this composite fading distribution has shown significant promise [34]. This distribution is defined by six main parameters including \(\alpha,\eta,\kappa,\mu,p,q\). The details of these parameters along with their individual significance can be easily found in [34]. Primarily, these parameters characterize the effect of nonliterary and multipath components of the wireless channel. In this work, generalized expressions are investigated, however, it is worth pointing out that different values of fading parameters may refer to different channel conditions in mmWave band. In particular, when \(\alpha=2.2,\eta=73,\kappa=5.7,\mu=1.01,p=1.05,q=1\) the distribution resembles to LOS outdoor channel, whereas, when \(\alpha=2.545,\eta=0.006,\kappa=2.5,\mu=1.98,p=1.5,q=1.05\) the distribution follows non-LOS outdoor channel conditions at 28 GHz [34]. The probability density function (PDF) of envelop of \(\alpha-\eta-\kappa-\mu\) distribution is given as [35]  
\[f_{R}\left(\rho\right)=\frac{\alpha\rho^{(\alpha\mu-1)}\exp\left(-\frac{\rho^ {\alpha}}{2}\right)}{2^{\mu}\Gamma\left(\mu\right)}\sum_{k=0}^{\infty}\frac{k!c _{k}}{\left(\mu\right)_{k}}L_{k}^{\left(\mu-1\right)}\left(2\rho^{\alpha}\right), \tag{4}\]  
where \(\Gamma(. )\) is the well-known gamma-function, \((. )_{k}\) is the Pochhammer symbol, and \(L_{s}^{t}(. )\) is the Laguerre polynomial [36]. Moreover, the value of \(c_{k}\) is calculated using ([35] (15), (30), (31)). Consequently, the CDF of the of the envelop is given as [35]  
\[F_{R}\left(\rho\right)=\sum_{k=0}^{\infty}\frac{k!m_{k}}{\left(\mu+1\right)_{ k}}L_{k}^{\mu}\left(\frac{2\left(\mu+1\right)\rho^{\alpha}}{\mu}\right)\times \frac{\rho^{(\alpha\mu)}\exp\left(-\frac{\rho^{\alpha}}{2}\right)}{2^{(\mu+1)} \Gamma\left(\mu+1\right)}, \tag{5}\]where \(m_{k}\) can be obtained with the help of \(\alpha,\eta,\kappa,\mu,p,q\) ([35] (16), (33), (34)).