## 6 Atmospheric Gaseous Losses Profile for Aircraft-Stratospheric Basestation (SB) Link  
The communication channel between SB and aircraft is affected by three main regions according to the aircraft altitude and the elevation angle to SB. Figure 6 demonstrates these three flight regions or stages where the atmospheric absorption in the troposphere has a considerable impact at the coverage boundary between neighbored SBs and during the climbing and descending periods, while the most efficient communication channel performance is expected when the aircraft is at full height in the cruise stage and not near the SB coverage boundary. The atmospheric absorption increases when the signal passes in longer paths in the troposphere where atmospheric gases, clouds, rain, fog, and other factors impact the signal propagation by absorbing its energy [25; 26; 27; 28; 29]. Fortunately, the aircraft is temporarily flying at low altitudes such as during takeoff or landing and also during overlapping regions of neighbouring SBs, therefore, it is expected that most of the time it receives high performance communication with the SB as it will be above clouds during cruise stage. The clear sky between aircraft and SB and the much lower communication range compared to the lowest-altitude of 340 km satellite systems [9] make a SB cellular network as an ideal solution for the provision of broadband services during flight and improves the efficiency of aircraft monitoring. Therefore, the signal loss due to atmospheric attenuation is analyzed during the complete flight duration in this section. A simple model for the flight stages is shown in Figure 7 where the slant distance between SB and aircraft passes mainly in the troposphere and stratosphere layers. Most of the atmospheric gases and water vapor exist in the troposphere and their densities are decreased largely in the stratosphere. As a proof of concept and for investigation purposes, we may apply the simple formulas of the International Telecommunication Union (ITU) recommendations, so according to the ITU radio recommendation No.676-10 [27], the atmospheric attenuation is due to the absorption of signal energy by atmospheric gases, mainly Oxygen and water vapor. Most of the designated frequencies for 5G services and networks are ranging from 3.5 GHz up to 66 GHz [30]. The carrier frequencies are organized in two sets namely FR1 and FR2 where FR1 frequencies are sub 6 GHz while FR2 are above 6 GHz [17]. In this paper, we will modify these two sets to include 3.5, 6, and 10 GHz in FR1 while FR2 includes 26, 28, 40, 50 and 66 GHz. At these mm-wave frequencies, the atmospheric attenuation changes drastically especially at the higher frequencies [4]. For the aircraft-SB cellular network, the flight profile will be expected to have different attenuation levels as the signal passes through different tropospheric layers' thicknesses. One related methodology for atmospheric attenuation calculations in the ITU recommendations in [27] considers only the atmospheric path loss for elevated stations below 10 km altitude which is not suitable for the aircraft-SB network. Therefore, in this section, we will extend this model to calculate the atmospheric attenuation that fits the proposed system based on the numerical methodology in [27] for slant paths. Assuming that the atmospheric slant range between an aircraft and SB can be divided into very small thickness  
Figure 6: A complete aircraft flight profile model. layers where in the \(n\)th layer, the signal has a path segment \(\rho_{n}\) along the aircraft-SB line of sight as shown in Figure 7 with an incident angle \(\gamma_{n}\) with the \((n+1)\)th layer, the refraction angle of the \(n\)th layer is \(\beta_{n}\), and the new elevation angle of the \((n+1)\)th layer is \(\alpha_{n+1}\). According to the layer altitude, the atmospheric parameters such as pressure and temperature change correspondingly, and hence each layer has its own refractive index which will determine the values of \(\alpha_{n}\), \(\beta_{n}\), and \(\gamma_{n}\).