# Energy-Efficient Subcarrier Pairing and Power Allocation for DF Relay Networks with an Eavesdropper
## 1 Introduction  
The enormous growth of energy consumption in wireless communication networks has recently drawn significant attention from both academics and industry. The energy consumption in telecommunication networks is predicted to surge rapidly due to the increasing escalation of data rates and the use of numerous smart devices [1]. Improving the energy efficiency (EE) of networks is of paramount importance in striving towards green 5G radio [2]. Accordingly, investigation on energy-aware system design and power and subcarrier allocation techniques that provide significant energy savings [3] is inevitable in the research of future wireless communications systems. Cooperative communications have been proven to be promising technologies for enhancing the throughput, extending the coverage, and enhancing the link reliability. Various relaying protocols have been proposed, among which amplify-and-forward (AF) and decode-and-forward (DF) are two main protocols [4]. In the AF protocol, the relay retransmits the amplified signal to the destination, while in the DF protocol, the relay decodes the received signals and retransmits the re-encoded information bits to the destination. While in terms of implementation complexity the AF protocol has an advantage over others, when the channel quality of the source-to-relay (SR) link is good, the DF protocol performs better than the AF protocol. Furthermore, different channel coding can be used at the source and the relay nodes for the DF protocol, which is another advantage of it. With regard to the power consumption in wireless networks, dynamic power consumption due to transmit power, which is allocated in response to the instantaneous channel conditions, and static power consumption due to signal processing at each node, site cooling, battery backup, etc., are the two main sources of power dissipation [5]. Further, for DF relay networks, the EE performance is highly dependent on these two sources [6]. Accordingly, in this paper, through a joint optimization of the subcarrier pairing and transmit power allocation, we will maximize the EE of a dual-hop DF relay network in the presence of an eavesdropper. Of late, resource allocation has been studied in literature for enhancing the throughput of DF relay networks. In [7; 8], the optimal power allocation schemes were investigated to maximize the rate in DF networks under total transmit power or individual power constraints. Similarly, the authors in [9; 10] studied the optimization problems for joint subcarrier pairing and power allocation with a total network power constraint or with individual power constraints for the source and the relay nodes. In particular, to overcome the interference problem, the authors in [10] performed a joint optimization of relay selection, power allocation, and subcarrier assignment. Further, in these existing works [7; 8; 9; 10; 11], the throughput maximization was the main design goal. However, similar resource allocation schemes cannot be directly used when the network EE is considered to be the objective function. In this regard, in [12], an energy-efficient resource allocation algorithm was proposed for downlink network with a large number of transmit antennas. However, instead of worst-case EE maximization, the authors of [12] focused on maximizing the total EE for downlink networks. Moreover, the scheme described in [12] cannot be easily applied to multi-hop scenarios. Additionally, due to the broadcasting nature of wireless channels, a secure exchange of information between mobile users is required. In [13], a secure cooperative communications scheme was investigated for cognitive radio networks, and a joint destination-aided cooperative jamming and precoding technique for dual-hop AF MIMO relay networks was proposed. Further, [PERSON] et al. in [14] comprehensively analyzed secrecy performance for multiuser regenerative relay wiretap networks, while the authors in [15] proposed an artificial-noise (AN)-aided relay selection scheme to enhance the security of DF relay networks.