# Delivering Extended Cellular Coverage and Capacity Using High-Altitude Platforms
## 5 Performance Evaluation
### Beam-Pointing performance  
Having estimated the possible limit of the HAP extended coverage in the previous subsection, we therefore evaluate if it is achievable practically. Heuristically using the antenna profile in (1), it is determined that the edge-of-cell subtended angle \(\rho=3.5^{\circ}\), resulting in an SPPC of approximately 2.5 km diameter. This is used in Algorithm 1 with the resulting cell centre coordinates used as boresights in the antenna module. The CNR and CINR of all users in the service area are evaluated using (4) and (8), respectively. The results are compared with those of regular, equidistant, and equiangular cell placement schemes as well as the state-of-the-art [14]. In the equidistant scheme, cells are pointed such that neighbouring cells are approximately 2.5 km apart. Figure 12 shows the user CNR contour of the equidistant scheme, with antenna boresights at the centres of the cells. The contour highlights the significant overlap between neighbouring cells resulting from beam broadening. The severe overlap gives rise to high ICI, which worsens at the edges of cells and service area. Therefore,  
Figure 11: Average area spectral efficiency against distance of cell centre. considering beam broadening and overlap is important. Figure 13 shows the user CNR contour with cells pointed such that neighbouring antenna boresights are \(7^{\circ}\) apart, which is the equiangular scheme. Similarly, this scheme results in severe overlap between cells because it does not explicitly consider beam broadening. The severe overlap and poor CNR, especially towards the edges of cells and coverage area, make these schemes challenging in practical systems due to significant ICI. Unlike the equidistant and equiangular schemes, Algorithm 1 produces properly structured cells with better overlap control and CNR performance as shown in Figure 14, due to the direct consideration of beam broadening. The algorithm's CINR performance is also compared with the equidistant and equiangular schemes in addition to schemes proposed in [14]. The empirical CDFs of user CINR distribution obtained with the different cell-pointing schemes are given in Figures 15 and 16. Over 90% of the users using the proposed scheme achieve a CINR greater than 0 dB compared with the the equiangular  
Figure 12: CNR contour within cells of the equidistant scheme. Figure 13: CNR contour within cells of the equiangular scheme. and equidistant schemes with less than 50% of the users achieving above 0 dB CINR, as shown in Figure 15. The scheme proposed in this section results in a CINR improvement of 7-15 dB. Furthermore, random and regular pointing of cells are presented in [14], as well as the proposed state-of-the-art clustering of users using \(K\)-means clustering with cells pointed at the centroid of the clusters. The CDFs of user CINR distributions of these schemes are compared with that of the enhanced and validated scheme proposed. Using the schemes in [14], Figure 16 shows that less than 60% of the users achieve over 0 dB CINR compared with the over 90% obtainable using the proposed scheme with the additional CINR improvement ranging from 5 to 10 dB. Furthermore, Figure 17 highlights the effect of altitude on achievable CINR per user from the proposed scheme. With increasing altitudes, the beam footprint on the ground broadens and CINR per user decreases as more losses occur in the link due to the increasing path distance. Consequently, the spectral efficiency of the system reduces with increasing HAP altitude. The effect of overlap ratio \(\varepsilon\) on both user allocation probability and 95 th percentile user throughput is shown in Figure 18. On the one hand, user allocation probability is evaluated as the ratio of the number of users allocated to a cell to the total number of users. On the other hand, the 95 th percentile is obtained by calculating the throughput of all users in the HAP system using (11).