# Time-Varying Communication Channel High Altitude Platform Station Link Budget and Channel Modeling
## 4 Discussion  
The noise spectral density is normalized by \(P(1\mathrm{W}/\mathrm{Hz})=3.5\times 10^{6}\mathrm{s}^{-1}\). Transmit power is 0.5 Mw. The level of receiver thermal noise is 200 dBm/Hz. Free space path loss is 10 m. The receiver noise coefficient is 15 dB, \(\beta\) is set by 1.  
The relationship between the transmit power of the HAPS and the antenna gain at different carrier-to-noise ratios is shown in Figure 5.  
As can be seen from Figure 5, as the carrier-to-noise ratio C/N increases, the transmit power of the HAPS also increases proportionally. At the same time, the antenna gain is also increased with C/N. The duration simulation of the HAPS wireless communication link at different altitudes is shown in Figure 6.  
Figure 5: The transmitted power and antenna gain under different carrier noise ratio.  
As can be seen from Figure 6, the higher the HAPS space base station, the longer its average link duration. Here the HAPS height is increased from 20 km to 30 km. But the average link duration does not increase linearly, as \(\Delta\) increases, the average link duration also increases with a non-linear growth trend.  
It can be seen from Figure 7 that the higher the HAPS space base station, the higher its elevation angle, and as \(\Delta\) increases, the elevation angle also increases accordingly. Under the same \(\Delta\), the higher the HAPS, the higher the elevation angle.  
Whether the channel is encoded or not has a large influence on the bit error rate (BER), and its bit error rate \(P_{e}\) at different \(E_{b}/N_{0}\) can be shown in Figure 8.  
Figure 6: Average link duration time.  
Figure 7: Relationship between elevation angles at different HAPS altitudes.  
It can be seen from Figure 8 that when the value of \(E_{b}/N_{0}\) is small, the un-coded performance is better than the coded (8 PSK) channel case; when \(E_{b}/N_{0}\) is greater than 3.5, the coded channel has a bit error rate BER smaller than that of the un-coded channel. Overall, the bit error rate \(P_{e}\) in the coding case is lower than the un-coded.  
The influence of the elevation angle between the HAPS platform and the user in the near space on the transmission performance of the HAPS cannot be ignored. This is because if the elevation angle is small, the inclination path from the platform to the user will be large. This will increase free space loss and rain attenuation. Therefore, it will affect the HAPS link communication performance. Figure 9 simulates the error rate at different elevation angles \(\phi\).  
As can be seen from Figure 9, in the case of the same \(E_{b}/N_{0}\) value, the larger the elevation angle \(\phi\), the smaller the bit error rate. When the elevation angle C is \(20^{\circ}\), PSK (8 phase shift keying) is used  
Figure 8: The BER (Bit Error Rate) under different encoding.  
Figure 9: The BER (Bit Error Rate) under different elevation angle.  
respectively, coding with the Golay code (23, 12) and the Hamming code (15, 11), the simulation results are shown in Figure 10.  
It can be seen from Figure 10 that when \(E_{b}/N_{0}\in(0,4)\), the bit error rate \(P_{e}\) of the PSK is lower than the Golay code and the Hamming code; when \(E_{b}/N_{0}\in(4,10)\), the bit error rate of the Golay code is lower than the PSK and Hamming codes.