## 4 Analytical Results  
In this section, proper analytical results obtained by the derived closed-form expressions are presented. These results mainly aim to reveal the individual impact of each of the above-mentioned major impairments as well as their joint influence on the total ABER and the coverage area of a typical THz system which may employ multiple hops. In more detail, the THz system under investigation may consist of \(N=\{1,2,3\) or \(4\}\) hops. Each of the \(n=1,2,..N\) hops are assumed to have the same, equal to \(z_{n}=150\) m, link length. The refractive index structure parameter is assumed to be \(C_{n}^{2}=5\times 10^{-14}\) m\({}^{-2/3}\) for weak or \(C_{n}^{2}=2.3\times 10^{-9}\) m\({}^{-2/3}\) or strong turbulence, similarly to the experimental measurements in [14]. Additionally, the system may operate with frequency equal to \(f=f_{n}=0.3\) THz or \(f=f_{n}=0.35\) THz, while in terms of the antenna characteristics, they have either aperture radius \(r_{n}=0.15\) m with gain \(G=G_{t}=G_{r}=55\) dBi or aperture radius \(r_{n}=0.7\) m with gain \(G=G_{t}=G_{r}=70\) dBi [19]. Note that unless otherwise stated, the \(f=f_{n}=0.3\) THz and \(r_{n}=0.15\)m with gain \(G=G_{t}=G_{r}=55\) dBi transmitter and receiver pair is utilized in the following figures and results. Such transceiver antennas can practically support up to several hundreds of meters propagation distances which is consistent with the THz hop length of the investigated system. Specifically, the selected antenna gain can be practically achieved by employing high-gain Cassegrain antennas which are commonly used in the THz frequency regime of the selected central frequency [27], while the 55 dBi antennas are also already manufactured and tested with success [77]. Consequently, we have selected the above operation frequency values for the examined link because they are appropriate for the operation of the practically applicable transmitter and receiver antenna terminals mentioned above, while they also are within the proper frequency regime in which Equation (6) is valid. In terms of the stochastic influence of the generalized pointing errors, different practical boresight and jitter component values have been assumed for each hop transmission, i.e., \(w_{n}/r_{n}=\)9 with \(\left(\mu_{x,n}/r_{n},\mu_{y,n}/r_{n},\sigma_{x,n}/r_{n},\sigma_{y,n}/r_{n} \right)=\left(0,0,5,5\right)\) or \(\left(0,0,6,6\right)\) for weak-to-strong ZB pointing errors and \(\left(\mu_{x,n}/r_{n},\mu_{y,n}/r_{n},\sigma_{x,n}/r_{n},\sigma_{y,n}/r_{n} \right)=\left(1,2,5,5\right)\) or \(\left(1,2,6,6\right)\) for weak-to-strong NZB pointing errors, respectively [69]. Furthermore, it is assumed that in accordance with the practical channel and environmental circumstances, the surface temperature is equal to 20 \({}^{\circ}\)C, the air pressure is equal to 1 atm, while \(\rho=\rho_{n}=7.5\) g/m\({}^{3}\) or \(\rho=\rho_{n}=10\) g/m\({}^{3}\) for moderate-to-strong molecular attenuation due to water vapor along each THz hop, respectively [19; 27; 60]. Regarding the impact of weather effects, with the exception of a clear sky along the THz channel, two different and realistic scenarios are examined. More precisely, the impact of fog attenuation is determined by an additional attenuation factor \(a_{w,n}=0.6\) dB/km, while rain attenuation is determined, in turn, by an additional attenuation factor \(a_{w,n}=3\) dB/km at a precipitation rate of 2 mm/h [5; 34], (Figure 1). It is worth noting that unless otherwise stated, clear weather conditions are assumed and OOK modulation is utilized. Finally, \(\sigma_{n}=10^{-7}\) A/Hz in all link configurations [19; 41], while Monte Carlo simulations are marked below with solid dots, which have been generated by Matlab software for values lower than \(10^{-6}\). In this way, we further validate the corresponding analytical results obtained.