## 5 Numerical Results and Discussions
Figure 4 exhibits the average channel capacity of the OPRA technique against the average SNR per hop for the distinct channel models, viz., the Rician/Rician, \(\kappa-\mu/\kappa-\mu\), Rayleigh/Rayleigh, Rician-shadowed/Rician-shadowed, and Nakagami-\(\hat{m}\)/Nakagami-\(\hat{m}\) fading links. As discussed before, the generalized \(\kappa-\mu\) shadowed fading model contains these channel models as special cases, as listed in Table 2. Note that the parameter \(m\) (\(m_{1}\), \(m_{2}\)) is set as \(m_{1}=m_{2}=100\) for non-shadowing environments, \(m_{1}=m_{2}=0.5\) for shadowing environments, and the accuracy is confirmed through simulation. Furthermore, it is clear, from Figure 4, that \(\kappa-\mu/\kappa-\mu\) outperforms the other fading models, whereas the Rician/Rician shows the lowest performance, owing to shadowing. In Figure 5, the capacity performance is shown with respect to the number of antennas. We notice that the capacity performance increases with the increasing number of antennas at \(S\) and \(D\) nodes for all adaptive policies. It can also be seen that the ORA policy obtains a larger capacity, as compared to OPRA, when the number of antennas is low, but the performance gap between ORA and OPRA reduces with the increasing number of antennas. Additionally, a gap in the capacities of the TIFR and CIFR techniques is also observed with a lower number of antennas, but it is unnoticeable when the number of antennas is increased. Figure 4: Average channel capacity of OPRA scheme for some channel models, viz., the Rician (when \(K_{1}=K_{2}=5\)), \(\kappa-\mu\) (when \(\kappa_{1}=\kappa_{2}=4\) and \(\mu_{1}=\mu_{2}=2\)), Rician-shadowed (when \(K_{1}=K_{2}=8\) and \(m_{1}=m_{2}=0.5\)), Rayleigh fading, and Nakagami-\(\hat{m}\) (when the shaping factor of the Nakagami-\(\hat{m}\) is set to 2 for each link). Figure 6 shows the average channel capacity for the parameter, \(m\) (\(m_{1}\), \(m_{2}\)), in the considered environment of \(\kappa-\mu\) shadowed fading. It can be noticed that the capacity performance improves with the increasing value of the parameter \(m\). The shadowing parameter \(m\) is the degree of fluctuation in the dominant component of the signal, owing to shadowing. For the larger parameter \(m\), the power of the dominant component is more stable and thus causes less shadowing. Figure 7 exhibits the average channel capacity of the ORA technique as a function of the fading parameter \(\kappa\) (\(\kappa_{1}\), \(\kappa_{2}\)) for the different shadowing parameter \(m\). An improvement in the system performance is observed for the higher value of \(m\) (i.e., light shadowing conditions), as compared to the smaller value of \(m\) (i.e., strong shadowing conditions). Additionally, the capacity performance decreases in a strong shadowing environment as \(\kappa\) increases and _vice versa_. Figure 5: Average channel capacity of four adaptive transmission policies for different arrangements of antennas, \(N\) (\(N_{1}\), \(N_{2}\)), when \(\overline{7}_{1}=\overline{7}_{2}=8\) dB, \(\kappa_{1}=\kappa_{2}=1\), \(\mu_{1}=\mu_{2}=1\), and \(m_{1}=m_{2}=1\). Figure 6: Average channel capacity under different adaptive transmission techniques for different shadowing parameter, \(m\) (\(m_{1}\), \(m_{2}\)), when \(\overline{7}_{1}=\overline{7}_{2}=10\), \(N_{1}=N_{2}=2\), \(\kappa_{1}=\kappa_{2}=1\), and \(\mu_{1}=\mu_{2}=1\). The \(\kappa-\mu\) shadowed distribution contains Nakagami-\(\hat{m}\) distribution as a particular case (when \(\kappa\to 0\), \(\mu=\hat{m}\), and \(m\to\infty\)). It is known that the Hoyt (Nakagami-\(q\)) distribution can be approximated by the Nakagami-\(\hat{m}\) distribution by setting a relation between the Nakagami-\(q\) parameter \(q\) and the Nakagami-\(\hat{m}\) parameter \(\hat{m}\), as \(m=(1+q^{2})^{2}/2(1+2q^{4})\) when \(m\leq 1\)[48] (Equation (2.25)).