# Power Control Method for Energy Efficient Buffer-Aided Relay Systems
## 1 Introduction  
Initiated by the information theoretical perspective research on the cooperative communications using a relay node (RN) [1; 2; 3; 4; 5], various cooperative communication techniques have been studied to improve communication reliability, such as spectral efficiency (SE) and bit-error-rate (BER), and/or enlarge the coverage of the communications [6; 7]. For example, in works by the authors of [2; 3], SE was considered as a key performance metric of the cooperative networks, and in the work by the authors of [4], source precoder, relaying matrices, and destination decoder were iteratively optimized to improve BER performance. There are various retransmission strategies and duplex methods for the relaying. Amplify-and-forward (AF) relays simply amplify and forward (retransmit) the received signal [8; 9; 10; 11; 12], while decode-and-forward (DF) relays decode, encode, and forward the signal under certain conditions [2; 13]. Full-duplex (FD) relay can transmit and receive the signal simultaneously, while a half-duplex (HD) relay receives and transmits separately [2]. Recently, unmanned aerial vehicles (UAV) have been rigorously studied as RN or base station (BS) [14; 15; 16; 17]. If the UAV is employed as a relay, i.e., RN, it can forward the ground BS signals to other UAVs in the air. Here, a highly limited resource, i.e., energy, should be carefully managed to prolong the battery life of the RN. To this end, energy efficiency (EE) of the cooperative system has to be emphasized in resource management. For example, in the work by the authors of [18], a resource allocation strategy including power allocation was studied for a relay system to enhance the EE of the cooperative system. In the work by the authors of [19], a near-optimal iterative subcarrier pairingalgorithm and power allocation was proposed to improve EE of DF relay networks. For a mobile RN, SE and EE are considered [20]. Based on the observation that the same achievable rate can be achieved with lower transmit power of the RN compared to an RN without the buffer, it was shown that the achievable rate can be increased by employing a buffer at the RN (see works by the authors of [21; 22; 23; 24] and the references therein). In the work by the authors of [24], the frequency and power resources were optimally allocated for multiple nodes to improve the EE of the buffer-aided relay networks. Adapting the buffer at RN allows the opportunistic retransmission, and the average achievable rate performance can thus be improved. Moreover, the packet delay and outage probability can also be reduced by using the buffer [25]. In this study, the EE of a buffer-aided fixed RN system is investigated under the assumption that the transmit power of the source node (SN) is also fixed. Here, we assume that SN and HD-DF RN are located at the fixed positions as shown in Figure 1. The RN serves the SN and destination node (DN) as a signal repeater that forwards the received signals from the SN to DN. This scenario is similar to the conventional cellular communication scenario using a repeater that forwards the outdoor base station (i.e., SN) signals to an indoor mobile user (i.e., DN) in a building [26]. Thus, the assumption of the fixed SN and RN are reasonable and many of studies regarding the cooperative communications has been performed for the fixed RN [27; 28; 29; 30]. For the buffer-aided fixed RN, we propose a method to control the transmit power of RN based on the RN power consumption model and the distance between RN and DN to improve the network EE. The achievable rate is derived, and using it and an RN power consumption model, the EE of the network is formulated. Since it is intractable to derive the derivative of the EE function with respect to the transmit power and EE is a function of various power consumption parameters, analytical design of the optimal power control strategy is formidable.