# Power Control Method for Energy Efficient Buffer-Aided Relay Systems
## 6 Numerical Results and Discussion  
In this section, EE is evaluated by varying \(P_{c}\) and \(d_{rd}\). We compare five power control (PC) schemes:  
* EE-based PC w/ a buffer: The proposed RN system with a buffer. The RN transmit power is controlled by a one-dimensional numerical search. This method can be interpreted as a numerical approach of the optimal strategy in the work by the authors of [24], for a single pair of RN and DN. This is optimal yet impractical approach as stated in the previous section.
* EE-based PC w/ a buffer: The proposed RN system with a buffer. The RN transmit power is controlled by Equation (10).
* EE-based PC w/o a buffer: The conventional RN system without a buffer. The RN transmit power is controlled by Equation (11). The PC method is designed in this study, yet it is employed to the conventional RN for the sake of comparison. This method can be interpreted as an EE-based power control method in [18].
* SE-based PC w/ a buffer: PC is performed to maximize SE [2; 3]. Here, the RN employs a buffer.
* SE-based PC w/o a buffer: PC is performed to maximize SE [2; 3]. Here, the RN does not employ a buffer.  
In Figure 8, each subfigure shows EE by varying \(P_{c}\) for fixed \(d_{rd}\). From the results, the proposed PC is verified that it can achieve the near-optimal EE regardless of the power consumption model, i.e., \(P_{c}\), and the distance \(d_{rd}\). Clearly, EE decreases as \(P_{c}\) increases. It is also observed that the proposed PC can also significantly improve EE for the relay system without a buffer. On the other hand, SE-based PC methods do not provide comparable EE to the relay system with EE-based PC. Here, note that the transmit power of RN of SE-based PC methods is fixed as it is independent of the power consumption model. The fixed parameters of power are as follows: \(P_{r}=13\) dBm and \(P_{r}=20\) dBm for RN with and without a buffer, respectively, when \(d_{rd}=0.3\) km in Figure 8a; \(P_{r}=22\) dBm and \(P_{r}=30\) dBm for RN with and without a buffer, respectively, when \(d_{rd}=0.5\) km in Figure 8b; \(P_{r}=27\) dBm and \(P_{r}=35\) dBm for RN with and without a buffer, respectively, when \(d_{rd}=0.7\) km in Figure 8c; and \(P_{r}=32\) dBm and \(P_{r}=40\) dBm for RN with and without a buffer, respectively, when \(d_{rd}=0.9\) km in Figure 8d. This is because, as previously shown in Figure 6, the transmit power of RN is needed to increase to improve EE as \(P_{c}\) or \(d_{rd}\) increases. The SE-based fixed PC may achieve the best EE, e.g., when \(P_{c}\) is high. However, the fixed PC strategies are inefficient since \(P_{c}\) may vary in time due to the external environment variation, such as temperature and humidity. Moreover, even \(P_{c}\) is fixed, \(d_{rd}\) may vary and accordingly the optimal \(P_{r}\) also varies. To clarify it, the next simulation is performed for fixed \(P_{c}\) by varying \(d_{rd}\).  
In Figure 9, each subfigure shows EE by varying \(d_{rd}\) for fixed \(P_{c}\). Clearly, EE decreases as \(d_{rd}\) increases. The proposed PC can achieve the near-optimal EE regardless of the power consumption model, i.e., \(P_{c}\), and the distance \(d_{rd}\). It is also observed that the proposed EE-based PC can also improve EE for the RN system without a buffer, especially, when \(P_{c}\) is small. However, the EE gap between RN with and without a buffer increases as \(P_{c}\) increases. From this results, we see that the buffer is more efficient when \(P_{c}\) is large. Though the SE-based PC methods optimize \(P_{r}\) according to \(d_{rd}\), their EE performance is not comparable to the EE of the proposed EE-based PC methods for RN with a