# Delivering Extended Cellular Coverage and Capacity Using High-Altitude Platforms
## 5 Performance Evaluation
### Determining Operational Bounds  
In order to determine the theoretical bounds of operation of the HAP extended coverage system based on the desired minimum QoS at the edge of coverage, the capacity performance of the derived models in Section 3 is evaluated. The results of the capacity evaluation facilitate the determination of the theoretical bounds of operation of the extended coverage system based on the desired minimum QoS at the coverage edge. To evaluate the average SE of the system, a cell is pointed at increasing distances from the sub-platform point up to the edge of the extended coverage area. After pointing the cell, the area, average SE, and average ASE are evaluated. The upper and lower limits of the average ASE are obtained. The lower limit is obtained by assuming that all users in the cell have a CNR equal to that of a user at the boundary of the cell (i.e., 9 dB corresponding to the edge-of-cell CNR). This is then used in the Shannon equation (i.e., \(Log_{2}(1+CNR_{min})\)) to compute the lower limit average ASE by dividing with the cell area. For the upper limit, it is assumed that all users have a CNR equal to the peak CNR in the CNR distribution, which is the CNR at boresight. This is used in the Shannon equation (i.e., \(Log_{2}(1+CNR_{max})\)) to obtain the maximum achievable average SE, which is divided by the cell area to obtain the average ASE. The lower and upper limit average ASE give the bounds of each pointed cell. A different set of average ASE is also obtained by evaluating (36) using numerical integration. The parameters in Table 2 and a 30 dB transmit antenna gain [8] at the boresight are used to simplify the integration and validate the derived expression (36). These average ASE values (i.e., lower limit, upper limit, and integral) are plotted against the distance of the cells from the SPP, as shown in Figure 11. Note that the values represent the best case scenario because they are obtained without considering interference by assuming that the system is only noise limited. In practical systems, the achieved average ASE is expected to be lower when interference is taken into \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Simulation Values** \\ \hline HAP height \(h_{p}\) & 20 km \\ HAP transmit power \(P_{i}^{t}\) & 33 dBm \\ Channel bandwidth \(B\) & 20 MHz \\ Noise figure \(N_{f}\) & 5 dB \\ Receiver noise floor \(N\)* & \(-95\) dBm \\ Frequency \(f\) & 2.1 GHz \\ Service area radius \(R\) & 60 km \\ Angle subtended \(\rho\) & \(3.5^{\circ}\) \\ Overlap ratio \(\varepsilon\) & 0.1 \\ User density \(\lambda\) & 2 users/km\({}^{2}\) \\ Receive antenna gain \(G_{i}^{r}\) & 1.5 dB \\ Number of Antenna elements \(MN\) & 1600 \\ \hline \hline \end{tabular}  
* The receiver noise floor is evaluated in dBm using \(10 Log_{10}(kTB)+N_{f}+30\), where \(k=1.38\times 10^{-23}\) J/K is Boltzmann constant, \(T=290\) K is the assumed receiver temperature, \(\tilde{B}=20\) MHz is the assumed channel bandwidth, \(N_{f}=5\) dB is the noise floor based on 3 GPP TR 36.942 [40].  
\end{table} 
Table 2: Details of the simulation parameters. account. The level of interference depends on the number of cells formed and the distance between the cells in addition to the antenna beam profile. Figure 11 shows the average ASE of cells pointing at increasing distances from the SPP. Notably, the integral average ASE values are close to the maximum because peak transmit gain is used to simplify the (36), as mentioned above. The average ASE reduces with increasing distance from the SPP due to two main factors: increasing path loss and cell area. The number of interfering cells, their proximity to the cell under consideration and the HAP antenna beam profile are some other factors. The average ASE starts tailing-off as the cell centre distance from the SPP approaches 60 km. The value at 60 km is approximately 0.05 bit/s/Hz/km\({}^{2}\).