## 5 Numerical Results
### The Impact of User Location and Deployment Dimensions  
We start by analyzing the impact of the user location on the spectral efficiency of the system presented in Figure 7 for several values of \(x_{0}\), different duration, initial \(Oy\) coordinate \(y_{0}=0\), mean displacement due to macro-mobility speed of approximately 0.8 m/s corresponding to the diffusion constant of \(D_{M}=D_{x}=D_{y}=100\), mean displacement due to micro-mobility of around 2 \({}^{\circ}\)/s corresponding to the diffusion constant of \(D_{\gamma}=0.05\), compartment size \(L=100\) m, and BS antenna \(15\times 15\) elements. Note that due to \(y_{0}=0\), the initial \(Oy\) coordinate \(x_{0}\) characterized the distance between UE and BS. By analyzing the presented results, one may observe that the mean time-dependent spectral efficiency does converge to the same values as time increases (see Figure 7a), confirming the correctness of the developed model. This time-averaged value can be obtained using conventional stochastic geometry methods for 5G/6G mmWave/THz system analysis [17]. Specifically, this time-averaged point corresponds to the expected distance from a user randomly moving inside the square of size \(L\times L\) to the BS. One of the critical observations is that the time-dependent spectral efficiency does not decrease drastically as one may expect. The rationale is two-fold. First of all, the considered dimensions of the compartment size are rather limited (i.e., \(100\times 100\) m). Most importantly though is that the presented spectral efficiency represents the spatially averaged value over the macro- and micro-mobility range. In spite of the considered metric not capturing rapid random fluctuations, it demonstrates that the communications are feasible opportunistically at rather high spectral efficiency, even when UE and BS antennas are not perfectly synchronized at all times. Figure 7: Spectral efficiency as a function of the user location with respect to the BS. (**a**) Within 120 s. (**b**) Within 20 s. (**c**) Within 5 s. (**d**) Within 1 s.  
By taking a look at the fine-grained dynamics of the time-dependent spectral efficiency presented in Figure 7b-d for 20 s, 5 s, and 1 s, respectively, we observe that there are rapid fluctuations in the time-dependent spectral efficiency. These fluctuations are caused by the interplay between micro- and macro-mobilities and utilized antenna radiation patterns. Specifically, by observing Figure 7d, we notice that due to micro-mobility, the spectral efficiency quickly drops and eventually reaches a local minimum. This minimum corresponds to the first local minimum of the radiation pattern. As time goes on, the overall decreasing trend induced by the macro-mobility persists and several other local minima are reached. These conclusions are further illustrated in Figure 8, where we show the mean time-dependent beam misalignment as a function of the micro- and macro-mobility for corresponding mean displacement speeds of 2 \({}^{\circ}\)/s and 0.8 m/s. Here, we see that the impact of micro-mobility is expectedly more dominant as compared to macro-mobility. Another important parameter is the deployment dimensions that we call compartment size in this work. The impact of this parameter on the time-varying spectral efficiency is demonstrated in Figure 9 for the mean macro-mobility displacement 0.8 m/s, mean displacement due to micro-mobility of around 2 \({}^{\circ}\)/s, compartment size of \(L=100\) m, and BS antenna \(15\times 15\). Here, the initial distance from the BS was always chosen to be \(x_{0}=L/2\), and \(y_{0}\) was set to zero. By analyzing the presented data, one may observe that the principal difference between the considered deployment dimensions is in the time- and spatially-averaged value serving as a convergence plateau for the considered metric. The absolute drop between the initial value of spectral efficiency corresponding to the perfect BS and UE antenna alignment and the average value is approximately the same and corresponds to around 3 bit/Hz/s.