# Wireless Energy Harvesting Two-Way Relay Networks with Hardware Impairments
## 5 Numerical Results  
### Effects of Various Parameters on Ergodic Capacity  
The purpose of this set of simulations is to validate the correctness of the ergodic capacity expression derived and investigate the effect of various parameter settings on the ergodic capacities for that uses the DF protocol or AF protocols. Parameters chosen are: \(\kappa_{1}=\kappa_{2}=\kappa_{\rm ave}\), \(\sigma^{2}=10^{-6}\). The channel gains are considered as Rayleigh fading with pass loss, where the variances of the channel coefficients satisfy \(\lambda_{1}=\lambda_{2}=1\), and the pass loss exponent is set as \(m=2.7\). The transmit power \(P_{1}=P_{2}=P_{t}\), which is within the region \(P_{t}=[0,30]\) dBm. Figure 2 shows the effect of \(\kappa_{\rm ave}\) on ergodic capacities. The utilized parameter settings are: \(\rho=0.5\), \(d_{1}=d_{2}=5\) m, and \(\eta=0.8\). The ideal hardware impairment situation (\(\kappa_{\rm ave}=0\); i.e., no hardware impairments) are presented as benchmark performance. This figure shows that the ergodic capacities obtained by using the closed-form integral expressions are identical with Monte Carlo simulations. When the effects of hardware impairments are considered, the ergodic capacities tend to saturation with the increase of \(P_{t}\). And the higher the value of \(\kappa_{\rm ave}\), the more quickly the ergodic capacities saturate. This is because the distortion noises introduced by hardware impairments also increase when \(P_{t}\) increases, which will set a bound on the SNDR of each transmission link. Meanwhile, we also find that the effect of \(\kappa_{\rm ave}\) on the DF protocol is more obvious than that on AF protocol. This is because in AF protocol, the amplification of useful signal is more effective than distortion noise with the increase of \(P_{t}\), which will slow down the effect degree of the distortion noise, thus do not contribute severe distortion noises than in the DF protocol in the high SNR region. The effects of relay deployment on ergodic capacities are presented in Figure 3 for the DF protocol (left) and the AF protocol (right). The distance between \(S_{1}\) and \(S_{2}\) is fixed as \(d_{1}+d_{2}=10\) m, where \(d_{i},i\in\{1,2\}\) is the distance between \(S_{i}\) and \(R\). The utilized parameter settings are: \(\kappa_{\rm{ave}}=0.1\), \(\rho=0.5\), \(\eta=0.8\) and destination pair \((d_{1},d_{2})=\{(1,9),(3,7),(5,5),(7,3),(9,1)\}\) m. It is observed that the ergodic capacity obtained by the closed-form expressions coincide with that obtained by Monte Carlo simulations (Simu). It is evident that the ergodic capacities when \((d_{1},d_{2})=\{(1,9),(3,7)\}\) m are identical with that when \((d_{1},d_{2})=\{(9,1),(7,3)\}\) m for both protocols, which infers that the ergodic capacities of both protocols are symmetric with the increase of \(d_{1}\). This is because when set \(P_{1}=P_{2}\) and fix the distance between \(S_{1}\) and \(S_{2}\), the system is symmetric, and thus contribute to a symmetric performance. We also find that the DF protocol have the minimum ergodic capacities when the distance pair are set as \((d_{1},d_{2})=(5,5)\) m, the minimum ergodic capacities of AF protocol is obtained when \((d_{1},d_{2})=(5,5)\) m in the low SNR region, and varies to different destination pairs when setting the transmit power \(P_{t}\) to some certain values. This abnormal phenomenon of AF is due to the amplification process. The effect of energy efficient conversion ratio \(\eta\) on ergodic capacities are presented in Figure 4 for the DF protocol (left) and the AF protocol (right) with parameters \(\kappa_{\rm{ave}}=0.1\), \(\eta=0.5\), \((d_{1},d_{2})=(5,5)\) m, \(\eta=[0.2,0.4,0.6,0.8]\). It can be noticed that the ergodic capacities of  
Figure 3: The effect of \(d_{1}\) on Ergodic Capacity for DF (left) and AF (right) Protocols. Figure 2: The effect of \(\kappa_{\rm{ave}}\) on Ergodic Capacity for DF (upper) and AF (lower) Protocols. both protocols obtained by the closed-form expressions are in accordance with that obtained via Monte Carlo simulations (Simu).