# A Non-WSSUS Channel Simulator for V2X Communication Systems
## 6 Simulation Examples
### Results over Non-Isotropic Scattering  
The following experiment was carried out with the objective of analyzing scenarios where the IOs that surrounded the \(R_{X}\) were distributed in a particular region. This condition emulates a scenario where there is a large amount of free space and the IOs are concentrated in one given direction, e.g., rural environments. In this simulation, high mobility conditions with initial speeds of \(\
u_{T}=\
u_{R}=100\) km/h, acceleration magnitudes of \(a_{T}=a_{R}=20\) m/s\({}^{2}\), and a fixed frame length of \(F=32\) were considered to transmit data over highly non-isotropic scattering scenarios with \(\kappa=20\) and three different means \(\mu_{R}=0\), \(\pi/2\), and \(3\pi/4\). We compared the results with the isotropic scenario using \(\kappa=0\). Figure 10 shows the BER performance curves for this experiment according to Scenario I (see Figure 5). The plot shows that the performance of the LS estimator improved remarkably in non-isotropic conditions, i.e., when the IOs were concentrated in a region. In this scenario, the maximum propagation delay decreases as the IOs concentrate in a region that is closer to the transmitting vehicle, so the frequency selectivity of the channel is reduced [42]. Furthermore, the performance of the LS estimator depends on the mean \(\mu_{R}\) of the AOAs and also on the directions of motion (\(\gamma_{T}\) and \(\gamma_{R}\)) of the MSs. For example, taking as a reference the propagation scenario shown in Figure 5, assuming \(\kappa=20\), \(\mu_{R}=3\pi/4\), \(\gamma_{T}=\rho_{T}=60^{\circ}\), and \(\gamma_{R}=\rho_{R}=120^{\circ}\), the IOs were concentrated in a region that was closer to \(T_{X}\), so that the maximum propagation delay was smaller, which benefited the performance of the LS estimator. Similarly, by considering \(\mu_{R}=\pi/2\) or \(\mu_{R}=0\), which meant that the IOs were further away from \(T_{X}\), the maximum propagation delay was larger resulting a more frequency-selective channel, and as a consequence, a poorer performance of the LS estimator. Finally, the LS estimator performance was almost insignificantly affected by the magnitude and direction of the MSs acceleration (i.e., \(a_{T}\), \(a_{R}\), \(\rho_{T}\), and \(\rho_{R}\)) since the estimation was carried out by the two initial OFDM training symbols on the frame. These results are consistent with [57] for non-WSSUS channels, where there are no acceleration components. In the case of the STA technique, the main drop in its performance was caused by the channel non-stationarities, regardless of the initial speed or acceleration components of the MSs. This was due to the dynamic channel estimation in (18), which becomes obsolete rapidly even between two consecutive OFDM symbols. Therefore, although considering the data transmission over highly non-isotropic scattering scenarios, the performance of the STA technique with small values of \(\alpha\) always approaches the case where there is no channel estimation, as observed in Figure 10.  
Table 7 shows the required Eb/No levels to attain 10%, 1%, and 0.1% BER over the described propagation scenarios for isotropic and non-isotropic scattering conditions. We considered initial speeds of \(\
u_{T}=\
u_{R}=100\) km/h and acceleration components of \(a_{T}=a_{R}=20\) m/s\({}^{2}\), with a constant frame length of F = 32 OFDM symbols. The results showed that the BER performance of both LS and STA (with \(\alpha=20\)) techniques depended on the placement of the IOs. This behavior occurred since the propagation delays depends on the AOAs, which are determined by the location of the IOs that surround the receiving vehicle. The BER performance decreases when the maximum propagation delay increases, which occurrs when the IOs were located further from the transmitting vehicle. Therefore, the initial positions and motion profiles of the MSs also impacted the BER performance in non-isotropic conditions.