## 1 Introduction
### Related Works and Motivation  
Many researches have been investigated on the HAPs communications between stratospheric HAPs and terrestrial terminals. These topics mainly include the HAP channel modeling, constellation of multiple HAPs, and V-MIMO HAPs network, which are as follows:  
[PERSON] _et al._[16] proposed a 3-D geometry-based single-bounce reference model for the Rician fading channels in the HAP-MIMO network. The proposed model provides guidelines for the network design and performance analysis of HAP-MIMO networks with line-of-sight (LOS) and non-line-of-sight (NLOS) connections at the L and S frequency bands. [PERSON] _et al._[17] provided the channel models associated with an integrated HAP, satellite, and terrestrial network and then applied multiple antenna networks to evaluate and investigate the gains that could be achieved by utilizing MIMO techniques in such networks. [PERSON] _et al._[18] considered that the channel experienced by HAPs played a key role for the provision of reliable communications services. He proposed a novel channel model and a related channel simulator especially tailored for HAP-based communication systems. All of these three references [16; 17; 18] focus on channel modeling which is critical for our follow-up study. [PERSON] _et al._[19] investigated a multiple HAP scenario where all HAP's operate on the same channel. Interfere with each other was assessed in terms of the carrier to interference plus noise ratio (CINR) and spectral efficiency. It is shown that with the number of HAPs increasing from 4, 8 to 16, the system capacity increases almost pro-rata. [PERSON] [20] proposed that the uplink capacity of a CDMA system was improved by using multiple HAPs. By dynamically choosing a serving HAPS among multiple ones in the HAPs network, the required transmit power could significantly be lowered in the proposed scheme,and the overall interference in the uplink can thus be reduced, resulting in an increase of the uplink capacity of the system. [PERSON] _et al._[21, 22] and [PERSON] _et al._[23] addressed the potential gain of using various compact MIMO antenna array configurations in conjunction with HAP diversity techniques for the first time. It is shown that a compact MIMO-cube antenna array is superior to the vector element antenna since it has twice the number of independent channels, which will give a higher capacity. They also investigated the effects of spatial correlation and mutual coupling between the separate antenna elements on the system performance. However, the papers mainly showed the effects of spatial correlation and mutual coupling between the separate antenna elements of the MIMO-Cube array, and the effects of separation angle between HAPs on system capacity. [PERSON] _et al._[24] analyzed the performance of transmit diversity based on space-time block coding (STBC), in particular Alamouti and extended Alamouti schemes, using fixed wide-lobe receive antennas. The performance was compared with the reference receive diversity scheme based on best HAP selection that requires highly directional and steerable antennas in a V-MIMO scenario, with a constellation of multiple HAPs. However, only some experimental data is given, theoretical performance analysis is absent. [PERSON] _et al._[5] considered that there was a very low probability that all radio paths would exhibit deep fade. If all received signals are properly combined, the HAP network performance can be significantly improved. Obviously, these ideal assumptions will not work in practice. Although the problems of V-MIMO in constellations of interconnected HAPs network have been extensively studied, there are still some vital issues that need to be addressed, especially for the situation with diversity receiving from multiple HAPs in WSNs. There are quite a few works in the literature that have addressed the issue of diversity receiving in WSNs.