## 1 Introduction  
High altitude platforms (HAPs) are considered to be a novel solution for providing telecommunications services for a wide range of smart wireless sensor network (WSN) devices [1]. In recent years, they have attracted the attention of the telecommunications community [2]. The most important advantages of these networks include their easy and incremental deployment, flexibility, low-cost operation, low propagation delay, high elevation angles, broad coverage, broadcast capability, broadband capability and their ability to be moved around in emergency situations, which are all very suitable for WSNs [3]. Additionally, the advantages of an unconstrained orbital mechanism and low fuel consumption make them the preferred option for a wide range of services, including monitoring, observation, and sensing applications [4]. As an emerging communication platform, the HAP has received growing attention and some progress has been made on this technology. Researchers have proposed consideration of the HAP as a mobile base station in 4G/LTE and 5G networks. It was envisaged that the HAP could improve the coverage while reducing the cost of network construction [5], and the HAP is one of the most promising alternative infrastructures for realizing a wide range of high-data-rate collection applications for WSNs and next-generation wireless networks [6]. The fading of the wireless channel can have a strong negative impact on the link quality of HAP to WSNs devices (named users), so how to effectively deal with the negative impact will be crucial in the HAP network design. Diversity techniques are widely used in wireless communication networks to overcome the negative impact of wireless channel fading. The most common diversity techniques include time diversity, frequency diversity, and space diversity. Compared with time diversity and frequency diversity, space diversity can enhance network performance by configuring multiple antennas at the transmitting and receiving ends to overcome channel fading effects without additional bandwidth [7]. For a specified coverage area, multiple HAPs tend to be used, or a named constellation of interconnected HAPs, to increase the transmission rate, enhance capacity, and improve the quality of service (QoS) in WSNs [8]. A multiple HAP network can achieve a higher data rate by combining the capabilities of several HAPs that individually operate at modest data rate. The responsibilities of each HAP reduce linearly with the number of HAPs in the network [9]. Each HAP can allocate more of its resources to each user, satisfying higher data rate requirements. Therefore, increasing the number of HAPs in the coverage area yields linear increases in the achievable rate of information flow from each user. The impact of component failures, blockage, or rain/cloud cover can be reduced by space diversity if there are redundant communication links [10]. The link redundancy can be provided by overlapping coverage of the HAPs. From the users' perspective, this is also known as multiple assets in view. For example, a mobile sensor device can select, from all of those in view, the HAP with the clearest line of sight, which can reduce service outages and improve availability [11]. Equivalently, at a specified rate, the level of integrity increases with the number of HAPs. The energy per symbol \(\gamma_{s}\) increases when there are more HAPs in view, as a result of the increased dwell time allowed by the receiving terminal [12]. Then, linear increases in the dwell time result in linear increases in the energy per symbol to noise density ratio (\(\gamma_{s}/N_{0}\)) [13]. The integrity will then improve almost exponentially, since the error probability can be approximated as an exponential function of \(\gamma_{s}/N_{0}\). Furthermore, increasing the HAPs in view decreases the probability that users are unable to communicate with a HAP in the network via a direct link due to line-of-sight obstruction by buildings and other tall objects.