## 5 Numerical Results  
This section presents the analytical and simulated results of the considered HSTS model using M-PSK, M-QAM and M-PAM modulation formats over generalized fading channels. We demonstrate the usefulness of the expressions derived in Sections 3 and 4 using numerical examples and study the effects of interference on the system's performance. The simulated results are obtained by generating \(10^{7}\) channel realizations for the M-PSK, M-QAM and M-PAM symbols. It is assumed that relay-destination and interferer-relay channels follow the Nakagami-\(m\) fading with parameters adopted from [29]. The satellite-relay LMS channel is changed according to different practical shadowing conditions. The parameters of the shadowed Rice LMS model are shown in Table 1; see Section 2 for more details on these channel parameters. Figure 2 shows the average SER versus SNR of the considered HSTS, for infrequent light shadowing (in satellite-relay LMS channel), with multiple values of CCI (\(-5\) dB, \(0\) dB and \(5\) dB) using different M-PSK modulation schemes: BPSK, QPSK and \(8\)-PSK. It is assumed that \(\sigma_{1}^{2}=\sigma_{2}^{2}\); and on the x-axis of Figure 2, SNR denotes \(\overline{\gamma}\); in the plots, CCI represents \(\overline{\gamma}_{int}\). We consider the situation when relay is interfered by a single dominant interferer; we assume that the interferer can operate in a range of different transmit power levels. The value of total CCI \(\overline{\gamma}_{int}\) experienced by the source to relay link is varied in increasing order as: \(-5\) dB, \(0\) dB and \(5\) dB. An arrow shown in Figure 2 traversing the plots represents the direction of increasing CCI, i.e., from \(-5\) dB to \(+5\) dB. The analytical average SER for M-PSK is plotted by using Equation (28), and that for M-QAM and M-PAM is evaluated by employing the corresponding expressions given in Section 3. Figure 3 shows the average SER versus SNR of the considered HSTS, for average shadowing (in satellite-relay LMS channel), with multiple values of CCI (\(-5\) dB, \(0\) dB and \(5\) dB) using different M-PSK modulation schemes: BPSK, QPSK and \(8\)-PSK. Figure 4 shows the average SER versus SNR of the considered HSTS, for frequent heavy shadowing (satellite-relay LMS channel), with multiple values of CCI (\(-5\) dB, \(0\) dB and \(5\) dB) using different M-PSK modulation schemes: BPSK, QPSK and \(8\)-PSK. Figure 5 shows the average SER versus SNR of the considered HSTS, for infrequent light shadowing (in satellite-relay LMS channel), with multiple values of CCI (\(-5\) dB, \(0\) dB and \(5\) dB) using different M-QAM modulation schemes: \(8\)-QAM and \(16\)-QAM. Figure 6 shows the average SER versus SNR of the considered HSTS, for average shadowing \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Shadowing** & \(\mathbf{b_{i}}\) & \(\mathbf{m_{i}}\) & \(\mathbf{\Omega_{i}}\) \\ \hline Frequent heavy & \(0.063\) & \(0.739\) & \(8.97\times 10^{-4}\) \\ Average & \(0.126\) & \(10.1\) & \(0.835\) \\ Infrequent light & \(0.158\) & \(19.4\) & \(1.29\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: LMS channel parameters [21]. (satellite-relay LMS channel), with multiple values of CCI (\(-5\) dB, \(0\) dB and \(5\) dB) using different M-QAM modulation schemes: 8-QAM and 16-QAM. Figure 7 shows the average SER versus SNR of the considered HSTS, for infrequent light shadowing (in satellite-relay LMS channel), with multiple values of CCI (\(-5\) dB, \(0\) dB and \(5\) dB) using different M-PAM modulation schemes: 4-PAM and 8-PAM. The above discussion about the values of network and interference parameters for Figure 2 is also applicable for Figures 3-7. We observe from Figures 3-7 that the simulated SER very closely follows the analytical SER for all shadowing conditions of the LMS channel and modulations considered in the figures; indicating the correctness of the approximations taken in deriving the performance analysis framework of Section 3.