## 5 Conclusions  
This paper has investigated the diversity performance on multiple HAPs via V-MIMO transmission in the WSNs. Firstly, a virtual MIMO system model has been established by modeling a constellation utilizing interconnected HAPs, and the concept of MAV has been proposed. Secondly, assuming the channel is shadowed Rician fading, the PDF and CDF of received SNR have been derived. The ASER with BPSK and QPSK have then been given. When BPSK modulation is used, \(\gamma=10\:\mathrm{dB}\), and the  
Figure 9: Ergodic capacity changes along with Rician factor under different SNR (\(N_{H}\:=\:N_{r}\:=\:4\)).  
network configurations are (4,4) and (2,2), the ASER performances are 16.8 dB and 3.5 dB better than that of (1,1). When QPSK modulation is used, \(\gamma=15\,\mathrm{dB}\), and the network configurations are (4,4) and (2,2), the ASER performances are 10.1 dB and 3.1 dB better than that of (1,1), respectively. Additionally, the system capacity has been investigated for a perfect CSI and an unknown CSI respectively. Most significantly, we discovered that the more visible HAPs can enhance the signal energy, and provide rate and integrity improvements. To best of our knowledge, this study has been the first time that the ergodic capacity with various SNR and Rician factors for different network configurations has been analyzed. We have found that the LOS signal damages the HAPs system capacity as the Rician factor is increased. Finally, the simulation has verified the effectiveness of our design and performance analysis. We conclude that the V-MIMO with multiple HAPs is a promising solution for future high-data-rate and frequency-efficient smart wireless sensor networks. In the paper, the MAV is 100% by default. In fact, the degree of overlapping coverage is always different, especially for multiple sensor devices in the overall networks. Therefore, further studies should extend the MAV to the possible percentage of overlapping coverage. In addition, we have mainly investigated the diversity performance provided by multiple HAPs. The multi-hop transmission (relay) can also increase the transmission performance of wireless systems. Therefore, one of the next steps to this work will be the research on multi-hop relay transmission in the HAPs networks.  
This work is supported by National Natural Science Foundation of China under Grant No. (61231011, 91338201, 91438109, and 91338106). The authors thank [PERSON], from College of Communications Engineering, PLA University of Science and Technology, for his beneficial suggestions and promising instruction on HAP network performance analysis, and V-MIMO techniques in wireless sensor networks. The author is deeply indebted to all helpers of the papers quoted. Finally, the authors would like to thank the anonymous reviewers for their constructive comments.  
[PERSON] and [PERSON] directed the study, conceived the idea and was responsible for proof-reading the manuscript. Together with [PERSON], both worked on designing and analyzing the system model, did the diversity performance analysis and carried out the evaluation. [PERSON] and [PERSON] were the reviewer and responsible for proof-reading the manuscript as well. [PERSON] was responsible for the writing of the paper.  
The authors declare no conflict of interest.