## 4 Simulation Results
On the contrary, for the baseline scheme 1, the base station is unable to fully utilize the available degrees of freedom in beamforming design because the both the energy beam \(V\) and artificial noise \(V_{0}\) are fixed. Finally, with the increase of \(P\), the proposed scheme achieves higher harvested energy power than other schemes for every channel realization. The reason for this is that the proposed scheme takes into account the nonlinearity of practical EH circuits leading to mismatches in beamforming design. In Figure 3, we study the average minimum harvested energy power per energy vehicular receiver versus the maximum power of the base station, \(P\), for \(K_{E}=3\) energy vehicular receivers, and different than the maximum channel estimation errors, \(\delta_{E}^{2}\). As can be seen, with the increase of \(P\), the average minimum harvested energy power per energy vehicular receiver increases for increasing maximum channel estimation error, \(\delta_{E}^{2}\). Indeed, with increasing the imperfectness of channel estimation, the base station has to allocate less power to the artificial noise and energy signals to ensure vehicular secure communication. In Figure 4, we move on to investigating how the average harvested energy power per energy vehicular scales with the minimum required SINR of the information vehicular receiver, \(r\), for \(K_{E}=3\) energy vehicular receivers, \(\delta_{E}^{2}=0.02\), and different beamforming design schemes. It can seen that the average minimum harvested energy power per energy vehicular receiver of the proposed scheme is a monotonically increasing function of \(r\). This is owing to the fact that there is a trade-off of the proposed beamforming design scheme between power collecting of the energy vehicular receivers and the guarantee of physical layer secure of information vehicular receiver. In particular, the achieved SINR of the information vehicular receiver and the minimum harvested energy power per energy vehicular receiver can not be maximized simultaneously with fixed \(r_{k}\) and vice versa. Among all the considered beamforming design schemes, the proposed nonlinear EH scheme still achieves a better performance than the other beamforming design schemes. Figure 2: Average minimum harvested power per energy vehicular receiver versus total transmit power, \(P\). Figure 5 shows the average minimum harvested energy power per energy vehicular receiver versus the number of the transmit antenna, \(N_{T}\), for \(K_{E}=3\) energy vehicular receivers, \(\delta_{E}^{2}=0.02\), and different beamforming design schemes. It can observed that the average minimum harvested energy power per energy vehicular receiver in the considered system increases with the increasing number of antennae. These results advise that a higher amount of energy is available in the RF for energy collecting when the number of the transmit antennae increases. This is owing to the fact that with more transmit antennae the direction of energy beamforming matrix \(\mathbf{V}\) can be more accurately steered towards the energy vehicular receivers, which further increase the amount of energy available in the RF for energy collecting. Among all the considered beamforming design schemes, the proposed beamforming design scheme also achieves a better performance than the other beamforming design schemes. Figure 4: Average minimum harvested power per energy vehicular receiver versus the minimum required SINR of the information vehicular receiver, \(r\). Figure 3: Average minimum harvested power per energy vehicular receiver versus total transmit power \(P\) with different \(\delta_{E}^{2}\). Figure 6 illustrates the average minimum harvested energy power per energy vehicular receiver versus the maximum channel estimation error, i.e., \(\delta_{E}^{2}\), for different beamforming design schemes.