## 4 Special Cases  
As discussed above, the \(\kappa-\mu\) shadowed fading model contains some known fading models, namely, Rician, Rician-shadowed, \(\kappa-\mu\) Nakagami-\(\hat{m}\), and Rayleigh fading, as special cases [26]. Owing to these special cases, our obtained expressions in analytic form are general, and we can reduce them into asymmetric and symmetric fading conditions. For the sake of brevity, different scenarios, for asymmetric and symmetric fading conditions, are summarized in Table 2. We discuss special cases and the relation between previous works and new contributions for the outage probability and average capacity using adaptive transmission techniques in the following subsections.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**First Hop/Second Hop** & \(\kappa_{1}\) & \(\mu_{1}\) & \(\kappa_{2}\) & \(\mu_{2}\) & \(m_{1}\) & \(m_{2}\) \\ \hline \(\kappa-\mu\) shadowed/\(\kappa-\mu\) & \(\kappa_{1}\) & \(\mu_{1}\) & \(\kappa_{2}\) & \(\mu_{2}\) & \(m_{1}\) & \(\infty\) \\ \(\kappa-\mu\) shadowed/Rician-shadowed & \(\kappa_{1}\) & \(\mu_{1}\) & \(K_{2}\) & \(1\) & \(m_{1}\) & \(m_{2}\) \\ \(\kappa-\mu\) shadowed/Rician & \(\kappa_{1}\) & \(\mu_{1}\) & \(K_{2}\) & \(1\) & \(m_{1}\) & \(\infty\) \\ \(\kappa-\mu\) shadowed/Nakagami-\(\hat{m}\) & \(\kappa_{1}\) & \(\mu_{1}\) & \(0\) & \(\hat{m}_{2}\) & \(m_{1}\) & \(\infty\) \\ \(\kappa-\mu\) shadowed/[PERSON] & \(\kappa_{1}\) & \(\mu_{1}\) & \(0\) & \(1\) & \(m_{1}\) & \(\infty\) \\ \(\kappa-\mu\)/\(\kappa-\mu\) & \(\kappa_{1}\) & \(\mu_{1}\) & \(\kappa_{2}\) & \(\mu_{2}\) & \(\infty\) & \(\infty\) \\ \(\kappa-\mu\)/\(\kappa-\mu\) shadowed & \(\kappa_{1}\) & \(\mu_{1}\) & \(\kappa_{2}\) & \(\mu_{2}\) & \(\infty\) & \(m_{2}\) \\ \(\kappa-\mu\)/Rician-shadowed & \(\kappa_{1}\) & \(\mu_{1}\) & \(K_{2}\) & \(1\) & \(\infty\) & \(m_{2}\) \\ \(\kappa-\mu\)/Rician & \(\kappa_{1}\) & \(\mu_{1}\) & \(K_{2}\) & \(1\) & \(\infty\) & \(\infty\) \\ \(\kappa-\mu\)/Nakagami-\(\hat{m}\) & \(\kappa_{1}\) & \(\mu_{1}\) & \(0\) & \(\hat{m}_{2}\) & \(\infty\) & \(\infty\) \\ \(\kappa-\mu\)/Rayleigh & \(\kappa_{1}\) & \(\mu_{1}\) & \(0\) & \(1\) & \(\infty\) & \(\infty\) \\ Rician-shadowed/Rician-shadowed & \(K_{1}\) & \(1\) & \(K_{2}\) & \(1\) & \(m_{1}\) & \(m_{2}\) \\ Rician-shadowed/\(\kappa-\mu\) & \(K_{1}\) & \(1\) & \(\kappa_{2}\) & \(\mu_{2}\) & \(m_{1}\) & \(\infty\) \\ Rician-shadowed/Rician & \(K_{1}\) & \(1\) & \(K_{2}\) & \(1\) & \(m_{1}\) & \(\infty\) \\ Rician-shadowed/Nakagami-\(\hat{m}\) & \(K_{1}\) & \(1\) & \(0\) & \(\hat{m}_{2}\) & \(m_{1}\) & \(\infty\) \\ Rician-shadowed/Rayleigh & \(K_{1}\) & \(1\) & \(0\) & \(1\) & \(m_{1}\) & \(\infty\) \\ Rician/Rician & \(K_{1}\) & \(1\) & \(K_{2}\) & \(1\) & \(\infty\) & \(\infty\) \\ Rician/\(\kappa-\mu\) shadowed & \(K_{1}\) & \(1\) & \(\kappa_{2}\) & \(\mu_{2}\) & \(\infty\) & \(m_{2}\) \\ Rician/\(\kappa-\mu\) & \(K_{1}\) & \(1\) & \(\kappa_{2}\) & \(\mu_{2}\) & \(\infty\) & \(\infty\) \\ Rician/Rician-shadowed & \(K_{1}\) & \(1\) & \(K_{2}\) & \(1\) & \(\infty\) & \(m_{2}\) \\ Rician/Nakagami-\(\hat{m}\) & \(K_{1}\) & \(1\) & \(0\) & \(\hat{m}_{2}\) & \(\infty\) & \(\infty\) \\ Rician-shadowed/Rayleigh & \(K_{1}\) & \(1\) & \(0\) & \(1\) & \(\infty\) & \(\infty\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Special cases obtained from general analyses for \(\kappa-\mu\) shadowed fading channels with different parameter settings [33].