# A Wideband Non-Stationary 3D GBSM for HAP-MIMO Communication Systems at Millimeter-Wave Bands
## 2 Channel Model
### Large-Scale Parameters  
HAP is located at the altitude of the stratosphere, and its propagation environment is very different from traditional ground communication or low altitude communication systems. The complex propagation environment requires large-scale parameters to characterize it. Due to the relatively long propagation distance between HAP and ground terminals, path loss increases with distance, and free space loss is the most basic part, which can help us accurately evaluate signal attenuation. The weather conditions in the stratosphere can also have a significant impact on signal propagation, and our HAP channel is located in the mmWave band with a high frequency, so rainfall attenuation is also an important factor that we need to consider. Therefore, it is important to consider large-scale parameters, such as free space loss and rainfall attenuation, in HAP channel modeling.  
When wireless signals propagate through the atmosphere, they encounter various atmospheric components that affect their transmission. The primary atmospheric components contributing to this attenuation are dry air molecules and water molecules in the atmosphere. To calculate the attenuation caused by atmospheric absorption on transmission signals, we can refer to the ITU-R P.676 [37], which provides an atmospheric molecular absorption attenuation prediction model. The oblique path gas attenuation can be estimated by dividing the atmosphere into exponentially increasing layers, determining the specific attenuation (dB/km) of each layer and the path length (km) passing through each layer. The product of the specific attenuation of each layer and the path length passing through each layer can be summed up to provide a very approximate estimation. The molecular absorption loss is represented by [37]  
\[A_{gas}=\sum_{i=1}^{i_{\text{max}}}\omega_{i}H_{i}, \tag{21}\]  
where \(H_{i}\) denotes the distance of the path and \(\omega_{i}\) denotes the ratio decline, which relates to dry air pressure, water vapor partial pressure, and ambient temperature. We use the simulation data of the global annual average reference atmosphere in the ITU-R P.835 [38].  
The rainfall process introduces a significant complexity to the attenuation of the HAP channel. To compute the attenuation caused by rainfall on transmission signals in the HAP channel, we can refer to the rainfall attenuation prediction model provided in the ITU-R P.618 [39]. This prediction model incorporates factors such as the actual propagation distance, rainfall rate, and height of the rainfall in the HAP channel. This model can replace the path loss caused by rainfall in the HAP communication environment with an equivalent tilted path and unit kilometer attenuation. The rainfall attenuation can be expressed as [39]  
\[A_{rain}=\gamma_{R}\times L_{E}, \tag{22}\]  
which can be derived from the ITU-R P.618 recommendation. Where \(\gamma_{R}\) denotes unit kilometer ratio fading. It is related to rainfall rate and communication frequency. \(L_{E}\) denotes effective inclined path length. The length of the tilted path is related to the communication elevation and orbit height and requires frequency correlation coefficient correction to obtain an effective tilted path length.