## 5 Simulation Results and Discussion  
This section evaluates the performance of the proposed beamforming scheme via MATLAB simulations. It was assumed that there are 100 sensors randomly located in the coverage area of AP. The sensors were grouped based on the MUI-aware scheduling scheme in Section 3.2. For the sake of illustration, the numbers of blocks along the \(x\)-direction and \(y\)-direction were fixed at \(B_{x}=B_{y}=5\). One sensor was picked randomly from each group, and the number of total selected sensors was \(L=20\) (five sensor groups were empty). The large-scale fading was modeled using the statistical propagation model for air-terrestrial transmission with low-altitude AP, which was proposed in [14]. In particular, the path loss was modeled as the summation of the free space path loss (in dB) and an extra path loss term (in dB). According to Figure 3[14], it was assumed that the extra path loss term for each sensor varied randomly from 0 dB to 10 dB. The PAS of the channel was modeled as \(S\left(\varphi,\theta\right)=S_{h}\left(\varphi\right)S_{v}\left(\theta\right)\), where \(S_{h}\left(\varphi\right)\) and \(S_{v}\left(\theta\right)\) denote the PASs in horizontal and vertical directions, respectively. As in [15; 31], \(S_{h}\left(\varphi\right)\) and \(S_{v}\left(\theta\right)\) were modeled using the von Mises distribution and truncated Laplacian distribution, respectively. The simulation parameters are summarized in Table 1.  
We first compare the SE performance of proposed beamforming schemes with MF beamforming [10] and DFT beamforming [13] in Figures 3 and 4. Note that the MF beamforming required the instantaneous CSI and full number of RF chains (equal to \(N_{x}N_{y}\)) at AP. The requirement on CSI and the number RF chains for DFT beamforming was the same as the strongest-path beamforming. Figure 4 simulates the SE performance as a function of the duration of WET phase \(\tau\). With the full number of RF chains, it was seen that the proposed statistical max-SINR beamforming achieved a similar performance with MF beamforming at the optimal \(\tau\). This makes the statistical max-SINR beamforming attractive, since it did not need the estimation of instantaneous CSI. With the limited number of RF chains, the strongest-path beamforming outperformed the DFT beamforming considerably, since it focused the signal power on the sensor's direction in a more effective way. When comparing with the MF beamforming, the strongest-path beamforming suffered from an SE loss of 11% due to the lack of instantaneous CSI. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline System bandwidth & 1 MHz \\ Thermal noise floor & \(-100\) dBm \\ Central frequency & 1.2 GHz \\ Rician factor & 0 dB \\ The number of AP antennas & \(N_{x}=N_{y}=25\) \\ Angular spread & \(\Delta\varphi_{l}=5^{\circ}\), \(\Delta\theta_{l}=2.5^{\circ}\) \\ Energy conversion efficiency & \(\eta=0.6\)[42] \\ Duration of each frame & \(T=500\) symbol times \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 3: The SE performance as a function of AP’s altitude. 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 processing energy of sensor is set to \(E_{l}^{p}=10^{-10}\) J. Figure 5 simulates the SE performance for different AP transmit powers, where \(\sum_{l=1}^{L}p_{l}\) increases from 28 dBm to 48 dBm. The duration of the WET phase was optimized with respect to SE. It is seen that the SE loss of strongest-path beamforming to the widely-used MF beamforming was quite small (about 6%) for large transmit SNR. However, the SE loss to the statistical max-SINR scheme became larger with the increase of transmit power. This was because the effect of residual MUI was dominant in the large SNR region.