## 4 Results and Discussion  
The numerical results are provided in this section, which illustrate our previously stated analytical expressions for the diversity performance of the HAP constellations over V-MIMO shadowed Rician fading channels. The simulations were carried out using the MATLAB R2014a simulator. In order to implement the multiple HAP networks model, a subfunction of channel fading matrix was used with LOS and NLOS components. The LOS component follows the the lognormal distribution, and the NLOS component follows the i.i.d. complex Gaussian distribution \(\sqrt{1/(\kappa+1)}\times\aleph_{C}(0,1)\). The HAPs and the sensor device are described in the main function. The PDF and CDF of the received SNR is simulated in the first step. The outage probability, ASER for BPSK and QPSK, and capacity are carried for various configurations in order to make effective comparisons. Table 2 lists the parameters used in simulations and their values. in Figure 8, for both perfect CSI and unknown CSI. Finally, the ergodic capacity with various Rician factors \(\kappa\) is depicted in Figure 9 under different SNR conditions. A comprehensive analysis of the diversity reception performance in multiple HAP networks is described. In all the figures below, the label \((N_{H},N_{r})\) denotes the number of HAPs and the number of receiver antennas. Since it is assumed that each HAP installs one downlink antenna, the number of transmitter antennas is equal to the number of HAPs \(N_{H}\). Figures 2-5 depict the results of analysis and Monte Carlo, respectively. We run the simulated program \(10^{4}\) times and take the average of results to observe whether the Monte Carlo results are consistent with the performance analysis. In each time, the channel matrix is generated randomly with the same parameters. Firstly, the influence of the HAP and user antenna configurations on the PDF and CDF of the received SNR is investigated. Assuming \(N_{H}\) is 1,2,4, \(N_{r}\) is 1,2,4, and five representative network configurations are considered, which are (1,1), (2,2), (4,2), (2,4), and (4,4). When \(\kappa=1\), Figures 2 and 3 depict the PDF and CDF of the received SNR. We can observe that the results of Monte Carlo are completely consistent with that of the previous performance analysis, thus further proving the accuracy and effectiveness of the proposed method. Figure 4: Outage probability versus the average SNR with various HAP and user antenna configurations (\(\gamma_{th}=10\ \mathrm{dB}\)). Figure 5: Outage probability versus the SNR threshold \(\gamma_{th}\) with various HAP and user antenna configurations (\(\gamma=10\ \mathrm{dB}\)). the approach proposed in this paper. Figures 2 and 3 indicate that increasing the number of HAPs and antenna elements improves the opportunity for the user to achieve larger SNR values, implying a better performance. Secondly, Figures 4 and 5 show the outage probability versus the average SNR and SNR threshold \(\gamma_{th}\). We can observe that the performance of (2,4) is better than that of (2,2). This is because even  
Figure 6: ASER versus the average SNR with various HAP and user antenna configurations (BPSK, _i.e._, \(a=1,b=1;\kappa=1\)). Figure 7: ASER versus the average SNR with various HAP and user antenna configurations (QPSK, _i.e._, \(a=2,b=\sin^{2}(\pi/4);\kappa=1\)). though the number of HAPs is equal, the number of user antennas has been increased to provide more sub-channels (or diversity paths) of communication links between the transmitter and the receiver. The configuration (2,2) has 4 sub-channels, and (2,4) has 8 sub-channels. Therefore, (2,4) can provide a higher diversity reception gain. In addition, it can be observed from Figure 4 that the performance of (4,4) is better than that of (4,2), and the performance of (4,2) is better than that of (2,2), while the performance of (1,1) is the worst. Therefore, this further illustrates that multiple HAPs can indeed provide better system performance than a single HAP.