## 4 Simulation Results
### Power Delay Profile (PDP)  
The PDP is one of the most important parameters to characterize multipath propagation in complex environments. From its information, relevant parameters are derived to describe the frequency selectivity of the channel such as the RMS DS or the MED. Figure 14 shows the PDP for the selected frequency (28 GHz); the values are obtained for the receiver yellow car located on the opposite road lane of the transmitter, at a distance of approximately 26 m (see Figure 5 for reference). Figure 14a,b correspond to the directional antenna radiation pattern, and Figure 14c,d correspond to the omnidirectional antenna radiation pattern under the two scenarios conditions.  
Although the 3D-RL simulations does not theoretically impose a limit in the dynamic range (DR), in this paper a 60 dB DR is used, an in between value within some DR of 240 dB [72], 178 dB [69], and 30 dB [71] found in the literature from experimental studies. This limitation in the DR value also provides a realistic approach, so achieving results more consistent with the restrictions and performance limits of hardware elements, as demonstrated in [65]. It is worth noting from the figure, the marked disappearance of cluster paths in the directional pattern cases compared to those in the omnidirectional pattern cases. This is caused because the directional beam only uses a spatial sector for transmission, and as a result, fewer reflected/diffracted paths find their way to the receiver.  
As stated, the omnidirectional antenna transmission is simulated with lower gain power than the directional pattern. Figure 14c shows the PDP when a large vehicle (bus) is found in the LOS path between the transceivers. It is noteworthy that some of the first resolvable paths are heavily affected compared to their counterpart (Figure 14d), a small vehicle (car). This is closely related to the poor penetration of signals at mmWave frequencies bands. The decrease in received power of some of the first-order resolvable paths is especially notable. This corresponds to rays of shorter paths travel distances, consequently strongly affected by the obstruction. The rest of the multipath components are less affected as they are related to high delays and, consequently, greater distances traveled, thus possibly being related to paths away from the obstruction.  
For the directional pattern, Figure 14a,b depict the PDPs of the bus obstruction and a car obstruction, respectively. Similarly, there is a strong influence of the large obstacle over the first-order paths. Other feature defined in the directional pattern PDP in both situations is the grouping of the different multipath components into regional clusters, in accordance with the spatial consistency of deterministic approaches.  
An important multipath parameter that can be extracted from the PDP is the MED, this parameter is determined by Equation (4) and is defined as the first moment of the PDP [73].  
\[MED=\frac{\sum_{k}P(\tau_{k})\tau_{k}}{\sum_{k}P(\tau_{k})} \tag{4}\]where \(P(\tau_{k})\) is the power (dB) of the \(k\)th path, and \(\tau_{k}\) is the delay of the \(k\)th path. Table 3 shows the mean excess delay values at the receiver point for both radiation patterns and both obstructed simulations. In the simulation with an omnidirectional pattern, the MED registers values of 245.7 ns for the scenario with a regular car and 227.8 ns for the bus obstruction. Similarly, in the scenarios with a directional pattern, values of 294.6 ns and 221.5 ns are found for the obstruction by small and large vehicles, respectively. Although the values cannot be compared between radiation patterns (due to the difference in transmission power gain), the increase in MED in the cases of obstruction by a small vehicle to the bus simulations are noticeable. This is related to the substantial attenuation received by first-order paths when impacting a large object.