## 5 Simulation Results and Discussion
Figure 6 shows the effect of sensor's processing energy \(E_{l}^{p}\) on SE performance, where we assumed that the processing energies for all sensors are the same and vary from \(10^{-11}\) J to \(10^{-8}\) J, as suggested in [42]. The duration of the WET phase was optimized with respect to SE. As expected, the SEs of all schemes approached zero with the increase of \(E_{l}^{p}\) since the energy and time resources left for the WIT phase became less. In this case, AP must increase the transmit power or equip more antennas in order to maintain the system performance. Figure 3 shows the effect of AP's altitude on the SE performance  
Figure 4: The SE performance versus \(\tau\). The number of AP antennas is \(N_{x}=N_{y}=25\). The total transmit power of AP is set to \(\sum_{l=1}^{L}p_{l}=40\) dBm. The altitude of AP is 100 m. The processing energy of the sensor is set to \(E_{l}^{p}=10^{-10}\) J.  
Figure 5: The SE performance versus AP transmit power. The number of AP antennas is \(N_{x}=N_{y}=25\). The altitude of AP is 100 m. The processing energy of sensor is set to \(E_{l}^{p}=10^{-10}\) J.  
of proposed beamforming schemes. The duration of the WET phase was optimized to maximize the SE. It is seen that the SE performances of all schemes degraded with the altitude of AP since more path loss was introduced. At last, it is noted from Figures 3 and 4 that the analytical SE based on (33) gave a good approximation to the Monte Carlo result. Figure 7 shows the EE performance of the strongest-path beamforming as a function of per antenna circuit power consumption \(p_{\text{ant}}\). The proposed EE optimization scheme was compared with that in [21] where the maximum number of antennas was used at AP (i.e., \(\bar{N}_{x}=\bar{N}_{y}=25\)). The figure shows that the EE performance was greatly improved by optimizing the number of the AP's active antennas, especially when the per antenna circuit power consumption \(p_{\text{ant}}\) was large. In particular, it is seen that the performance gain increased from 1.9 times to 5.2 times when \(p_{\text{ant}}\) varied between 10 dBm and 30 dBm. Figure 6: The SE performance versus processing energy of sensor \(E_{l}^{p}\). The number of AP antennas is \(N_{x}=N_{y}=25\). The total transmit power of AP is set to \(\sum_{l=1}^{l}p_{l}=40\) dBm. The altitude of AP is 100 m.  
Figure 7: The EE performance versus per antenna circuit power consumption of AP. The maximum number of AP’s antennas is \(N_{x}=N_{y}=25\). The altitude of AP is 100 m. The processing energy of sensor is set to \(E_{l}^{p}=10^{-10}\) J. The maximum transmit power of AP is set to \(p_{\text{max}}=46\) dBm. The data rate requirement of each sensor is \(r_{T}=1\) nat\(/\text{s}/\text{Hz}\). Figure 8 simulates the effect of processing energy of sensor \(E_{l}^{p}\) on the proposed EE optimization scheme. It is seen that, for small \(E_{l}^{p}\), the proposed optimization scheme can provide considerable gain. When \(E_{l}^{p}\) was greater than \(10^{-9}\) J, the EE performance under the proposed optimization scheme converged to that of [21]. This is because in this case, AP must utilize the maximum number of antennas in order to meet the achievable rate constraint and processing energy consumption of the sensor. As a result, the same solution was obtained by the two optimization schemes. Figure 9 shows the effect of AP's altitude on the proposed EE optimization scheme. Similarly, we can see that the two optimization schemes gave rise to the same EE performance for a large altitude of AP. Figure 8: The EE performance versus processing energy of sensor \(E_{l}^{p}\). The altitude of AP is 100 m. The per antenna circuit power consumption \(p_{\text{ant}}\) is set to 15 dBm. The maximum transmit power of AP is set to \(p_{\text{max}}=46\) dBm. The data rate requirement of each sensor is \(r_{T}=1\) nat/s/Hz. Figure 9: The EE performance versus the altitude of AP. The per antenna circuit power consumption \(p_{\text{ant}}\) is set to 20 dBm. The maximum transmit power of AP is set to \(p_{\text{max}}=46\) dBm.