# Outage Performance of Wireless Powered Decode-and-Forward Relaying Networks in Rician Fading
## Appendix A Derivation of Formula (13)  
\[P_{\text{out\_D}} =P_{\text{r}}\left(\sum_{j=1}^{N_{\text{S}}}\left|h_{\text{S}_{ \text{SR}}}\right|^{2}<\frac{\gamma_{\text{th}}}{\varphi\gamma_{0}Xd_{\text{ SR}}^{-m}d_{\text{RD}}^{-m}}\right)=\int_{0}^{\Theta_{1}}F_{\text{Y}}\left(\frac{ \gamma_{\text{th}}}{\varphi\gamma_{0}Xd_{\text{SR}}^{-m}d_{\text{RD}}^{-m}} \right)f_{\text{X}}(x)dx\] (A1) \[=1-\int_{0}^{\Theta_{1}}\sum_{f=0}^{\Theta_{1}}\sum_{g=0}^{f+N_{ \text{S}}-1}e^{-N_{\text{S}}K_{\text{SR}}-\frac{(1+K_{\text{SR}})\gamma_{0}}{ \varphi\gamma_{0}x\lambda_{\text{SR}}^{-m}d_{\text{SR}}^{-m}}}\] \[\quad\times\left(\frac{(1+K_{\text{SR}})\gamma_{\text{th}}}{ \varphi\gamma_{0}x\lambda_{\text{SR}}d_{\text{SR}}^{-m}d_{\text{SR}}^{-m}d_{ \text{RD}}^{-m}}\right)^{g}(N_{\text{S}}K_{\text{SR}})^{f}\ \times a\sum_{l=0}^{\Theta_{2}}\frac{(bK_{\text{RD}})^{l}x^{l}}{(l!)^{2}e^{bx}}dx\] \[=1-\int_{0}^{\Theta_{1}}\sum_{f=0}^{\Theta_{1}}\sum_{g=0}^{f+N_{ \text{S}}-1}\sum_{l=0}^{\Theta_{2}}\frac{a(bK_{\text{RD}})^{l}(N_{\text{S}}K_{ \text{SR}})^{f}}{f!g!(l!)^{2}e^{N_{\text{S}}K_{\text{SR}}}\varphi\delta^{g}}\] \[\quad\times\left(\frac{\Psi}{d_{\text{SR}}^{-m}d_{\text{RD}}^{-m} }\right)^{g}x^{l-g}e^{-\frac{\Psi}{\varphi\pi\frac{\Psi}{\pi\frac{\Psi}{\pi \frac{\Psi}{\pi\frac{\Psi}{\pi\frac{\Psi}{\pi\frac{\Psi}{\pi\frac{\Psi}}{\pi \frac{\Psi}{\pi\frac{\Psi}}{\pi\frac{\Psi}{\pi\frac{\Psi}}{\pi\frac{\Psi}}{\pi \frac{\Psi}}{\pi\frac{\Psi}{\pi\frac{\Psi}}{\pi\frac{\Psi}}{\pi\frac{\Psi}}{\pi \frac{\Psi}}{\pi\frac{\Psi}}{* [PERSON] (2008) [PERSON] Transporting information and energy simultaneously. In Proceedings of the International Symposium on Information Theory ISIT, Toronto, ON, Canada, 6-11 July 2008; [PERSON], [PERSON], Eds. ; IEEE: Piscataway, NJ, USA, 2008; pp. 1612-1616. [CrossRef]
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