## 5 Numerical Results and Discussion  
In this section, we present numerical studies of the coherent THz links on turbulent conditions from weak to strong, as well as the different propagation path distances. The effects of varying turbulence strengths (from weak to strong) composited with pointing errors on coherent THz links are considered, and the error performance of such links is studied. Figure 3 shows atmospheric attenuation at frequencies up to 1 THz due to dry air and moisture under clear weather conditions using the ITU-R model. In addition, at a propagation path length of 1000 m, the FSPL with transmitter and receiver gain of 60 dBi is shown in Figure 3. The total deterministic loss \(h_{l}\) is the sum of the atmospheric loss and FSPL. Figure 3 gives the attenuation of Earth's atmosphere in the frequency range of 1 GHz to 350 GHz at sea level, the FSPL link path of 1 km at a pressure of 1013 hPa, temperature of 20 \({}^{\circ}\)C, and water vapor density of 7.5 g/m\({}^{3}\). We select a 300 GHz fixed frequency link and use an emerging high-gain LOS parabolic offset reflector at the transmitter and receiver. The basic system parameters of the THz link are summarized in Table 1. It is worth noting that since the THz transmitter receiver is affected by the half-power beam width, the corresponding beam width \(\omega_{z}\) on the receiver side is much larger than the receiver aperture diameter. Without loss of generality, one can assume 2.1 mrad beam divergence and 1 mrad pointing error. The performance of coherent THz wireless links is influenced by weather conditions, which can be characterized by refractive index structure parameter \(C_{h}^{2}\) and attenuation \(h_{l}\). Given that the LN channel model is appropriate only for weak turbulence conditions, a relatively short link distance of \(z=200\) m is considered to compare the BER performance between the LN and GG composite channels as depicted in Figure 4. In a separate analysis of the GG composite channel, BERs for weak (\(\delta_{R}^{2}=0.35\)), moderate (\(\delta_{R}^{2}=1.26\)), and strong (\(\delta_{R}^{2}=24.15\)) turbulence conditions are presented for a THz link distance of \(z=1000\) m.  
In Figure 4, the pointing error effects on the BER performance of coherent THz links are clearly shown. The BER performance decreases with the addition of a pointing error. Though not shown in the figures, our results have been confirmed by Monte Carlo simulations. Excellent agreement is found between our series (with \(J=30\)) and the exact BER solutions, which demonstrate the high accuracy of our approximate BER solutions. In addition, the exact BER and the asymptotic BER show a matching consistency at high SNR regions. Compared to the GG composite model, the LN composite model represents lower turbulence and therefore has better BER performance at the same transmission distance. From Figure 4, a less than 1 dB SNR difference can be found between LN and GG composite models at a BER of \(10^{-6}\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Frequency & 0.3 THz \\ Receiver diameter \(D(2a)\) & 300 mm for 60 dBi \\ Noise standard deviation \((\sigma_{n})\) & \(10^{-7}\) A/Hz \\ Link distance & \(z\) m \\ Half-angle beam divergence & 2.1 mrad \\ Corresponding beam radius \((\omega_{z})\) & 2.1 mrad \(\times\)\(z\) \\ Jitter angle & 1 mrad \\ Corresponding jitter standard deviation \((\sigma_{s})\) & 1 mrad \(\times\)\(z\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic system parameters with values. Figure 3: Atmospheric decay due to molecular absorption and FSPL losses in the frequency ranges of 1 GHz to 350 GHz. In Figure 5, BERs for weak (\(\delta_{R}^{2}=0.35\)), moderate (\(\delta_{R}^{2}=1.26\)), and strong (\(\delta_{R}^{2}=24.15\)) composite GG channels are given for coherent BPSK THz links. It is evident that BER performance degrades significantly as the turbulence strength increases.