# A Wideband Non-Stationary 3D GBSM for HAP-MIMO Communication Systems at Millimeter-Wave Bands
## 4 Results and Analysis  
In our simulation process, we consider HAP-MIMO communication scenarios. Unless otherwise specified, the following parameters are selected: \(f=38\) GHz, \(n_{T}=64\), \(n_{R}=2\), \(\beta_{T}=60^{\circ}\), \(\theta_{T}=\theta_{R}=45^{\circ}\), \(\psi_{R}=0^{\circ}\), \(H_{T}=20\) km, \(H_{R}=10\) m, \(k=4\), \(\mu=0^{\circ}\), \(H=100\) m, \(R=200\) m; we refer to a typical densely built area in London and set the average height of scatterers as \(H_{mean}=17.6\) m and \(\sigma=0.31\), \(K=3\) dB, \(v_{a}=50\) m/s, \(v_{b}=5\) m/s, \(\lambda_{G}=0.13\)/m, \(\lambda_{R}=0.03\)/m, \(n=40\). Figure 4 shows that the attenuation increases with increasing rainfall intensity in the HAP channel. From the table, it can be seen that our manuscript considers non-stationary characteristics from time domain, space domain, and frequency domain, and also takes into account the influence of large-scale parameters on channel attenuation. By considering these factors, our model can more accurately describe the characteristics of actual channels. Due to the mutual movement between SBS and TMS, the channel model exhibits non-stationary characteristics in the time domain. Figure 5 shows the variation of time-domain normalized ACF with time interval \(\Delta t\) at three different starting times \(t=0\) s, \(t=2\) s, and \(t=4\) s. As shown in the figure, the temporal ACF for different simulation starting times has significant differences. The theoretical results and simulation results are basically consistent. Therefore, the proposed model can characterize the non-stationary characteristics in the time domain. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Our Model** & **Model in [31]** & **Model in [32]** \\ \hline GBSM & GBSM & GBSM \\ \hline Consider birth–death process & Consider birth–death process & Not consider birth–death process \\ \hline Consider large-scale parameters & Not consider large-scale parameters & Not consider large-scale parameters \\ \hline Consider temporal ACF & Consider temporal ACF & Consider temporal ACF \\ \hline Consider spatial CCF & Consider spatial CCF & Not consider spatial CCF \\ \hline Consider FCF & Not consider FCF & Not consider FCF \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison among our model and Model in [31] and Model in [32]. Figure 4: Path loss for different rain-rates. Figure 6 depicts the variation of the temporal ACF with different elevation angles \(\beta_{\mathrm{T}}\) at \(t\) = 0 s; as shown in the figure, the increase in \(\beta_{\mathrm{T}}\) leads to a sharp decrease in temporal correlation. In the HAP system, when the elevation angle changes, the length and propagation time of the signal propagation path also change accordingly. This results in different multipath signals reaching the TMS at different phases, thereby affecting the temporal ACF of the signal. As the elevation angle increases, the signal propagation environment changes more dramatically, the diversity of signal propagation paths increases, and multipath effects become more significant. Therefore, the impact of HAP motion on time correlation is decreasing. Figure 5: Temporal ACF results at different times. Figure 6: Temporal ACF results at different elevation angles (\(t\) = 0 s). Figure 7 shows the temporal ACF between the isotropic environment \(k=0\) and the non-isotropic environment \(k=4\) and \(k=10\). It can be seen that, as \(k\) increases, the distribution of scatterers becomes more concentrated and the correlation becomes higher. Due to the drastic changes in the channel caused by the near-field effect with the antenna array, the massive MIMO channel we use exhibits non-stationary characteristics in the space domain. We calculate the changes in the space domain normalized cross-correlation function with the array element spacing \(\Delta p\) for three sets of transmitting and receiving antenna pairs \(p=1\), \(q=1\), \(p=32\), \(q=1\), and \(p=64\), \(q=2\), respectively.