# Delivering Extended Cellular Coverage and Capacity Using High-Altitude Platforms
## 1 Introduction  
With the need for ubiquitous wireless coverage and seamless connectivity, interest in high-altitude platforms (HAPs) is significantly increasing. HAPs are aeronautic platforms located conventionally between 17-22 km altitude and can be used for wireless communications. They offer some advantages over terrestrial systems due to their elevated look-angle and better propagation performance. The increasing optimism in HAPs is partly due to the possibility of the use of one platform for multiple applications and their potential for low cost, high availability wireless communications service provision over an extended area compared to terrestrial and satellite systems [1; 2; 3; 4]. Despite the potential of HAPs for wide geographic coverage, most HAP studies and projects are based on a limited coverage area of under 30 km radius, which is underwhelming. Extending the achievable coverage using a HAP will further maximise its cost-effectiveness and utility, which are desirable especially in rural areas with minimal or no coverage. Therefore, understanding the extent of HAP coverage achievable while still guaranteeing a minimum quality of service (QoS) is important, given the significant population of the world without connectivity [5].  
A HAP communication system forms elliptical beams on the ground, at a given elevation angle, to deliver both coverage and capacity to users [6]. These beams are used to form cells that are isolated by the HAP antenna radiation pattern [7], and they are limited by the antenna array beam-forming capability. Ideally, each antenna beam delivers uniformillumination to its corresponding cell, ensuring, through a steep roll-off, that no power is detected outside the cell boundaries. The ability to analytically model this HAP cellular system to predict the bounds of network coverage and capacity performance is relevant for modelling HAP networks. However, no existing study in the literature has specifically developed models to predict HAP system performance within the context of determining the limit of coverage extension by a HAP, which is what this paper aims to provide. In addition, the paper also looks at how proper beam pointing can be used to extend and improve HAP contiguous coverage and capacity while minimising inter-cell interference (ICI).  
Proper beam pointing with an adequate antenna system and characteristics is necessary due to the imperfect roll-off of practical antenna beams, which introduces ICI that is worsened by beam-forming limitations [8], especially with inadequate beam pointing. This paper provides a framework for analysing HAP coverage extension and highlights the feasibility of delivering contiguous cellular coverage over an extended area using a HAP. It develops models for HAP network performance prediction and proposes an algorithm to evaluate the practical behaviour of the extended HAP system given the developed models. The algorithm herein is enhanced from its original form, which was proposed in our conference paper [9], by presenting the detailed theoretical framework formulation and further discussion. Furthermore, the performance of the algorithm is further validated using simulated annealing (SA) heuristic optimisation technique [10], which is essential in the field of radio network planning and optimisation.