# Delivering Extended Cellular Coverage and Capacity Using High-Altitude Platforms
## 1 Introduction
### Literature Review  
While there are no existing analytical models for estimating the HAP coverage area and spectral efficiency (SE) for understanding operational bounds, the studies in [1; 6; 11; 12; 13] have investigated the deployment of HAP beams for multi-cellular communications. The use of scanning beams that scan across an arrangement of cells randomly was proposed in [1], but the scheme requires buffering for traffic, which complicates the system and significantly increases the scanning time, especially for wide area networks. The studies in [11] propose the use of a uniform hexagonal cell grid architecture over a 30 km radius using antenna beams illuminating the hexagonal cells, but it cannot be used for extended coverage with elevation angle lower than 30\({}^{\circ}\). In [6; 13], HAP cell footprints are described mathematically as functions of antenna beamwidth, elevation and azimuth angles, but again, these functions are only valid within an area of 30 km radius due to increased inaccuracies and approximation errors at extended distances. [PERSON] et al. [14; 15] studied the use of intelligent beam-forming strategies for HAP coverage and capacity while providing protection to terrestrial system users and proposed a beam-pointing scheme based on \(k\)-means clustering but limited to an area of 30 km radius like most of the other studies.  
Similarly, an insufficient number of studies [16; 17; 18; 19; 20] have been carried out on the capacity of HAP systems. [PERSON] et al. [16] investigated the capacity of HAP wideband code division multiple access systems with respect to the number of users that can be supported on the forward and reverse links of the HAP. They derive capacity based on the number of users supportable by the HAP links and show that a HAP cell can support more users than a terrestrial base station. The effect of platform displacement on HAPs, which shows that horizontal displacement affects capacity significantly more than vertical displacement, was presented in [18]. [PERSON] et al. [17] studied the uplink capacity of an integrated HAP-Terrestrial system where low-mobility users connect to the terrestrial base station while high-mobility users connect to the HAP. The capacity of worldwide interoperability for microwave access, deployed from a HAP over a very limited coverage area of 20 km radius to compare the delivery of broadband services from terrestrial and HAP systems, was investigated in [19]. In [20], a capacity analysis based on a constellation of interconnected HAPs using a proposed virtual multiple input multiple output model was presented.  
Since some terrestrial macro cells can provide coverage within an area of up to 30 km radius [21], and the higher elevation angles to HAPs result in better propagation character istics, it is reasonable to study HAP beam performance beyond the common 30 km radius state-of-the-art. This is potentially important for cost-effective communications in low user density areas. Given that there is no existing study yet on the spectral efficiency (SE) and area spectral efficiency (ASE) achievable in a HAP cell and how these vary at the edge of the extended coverage area considering the beam-forming and propagation limitations of the HAP antenna system, this work becomes crucial. Estimating the shape, size, and capacity of a cell pointed at any given distance from the sub-platform point of a HAP is quite relevant in extended HAP coverage network design. This helps in determining the bounds of coverage extension given other variables such as antenna characteristics.