# Power Control and Link Selection for Wireless Relay Networks with Hybrid Energy Sources
## 1 Introduction  
In order to expand the coverage of wireless networks and improve the communication quality of edge users, relay has been widely used in wireless networks such as long term evolution (LTE) and 5G [1; 2]. However, dense deployment of relays can lead to problems such as high energy consumption and greenhouse gas emissions [3; 4]. Energy harvesting technology is the most promising technology to solve the economic and environmental problems caused by the dense deployment of relays, which can collect and utilize renewable energy such as solar and wind energy [5; 6; 7; 8; 9]. In addition, energy harvesting technology can reduce the dependence of wireless networks on grid energy. Deploying green relays in areas where grid energy is scarce can effectively expand the coverage of wireless communication networks. However, the intermittent and random nature of the renewable energy may cause a decline in network performance. Therefore, it is critical to establish a renewable energy allocation and link selection mechanism to ensure the performance of wireless relay networks. Optimal power control strategies to alleviate network performance degradation caused by the lack of renewable energy have been proposed in [10; 11; 12; 13]. In [10], both the source and relay nodes are powered by renewable energy, and an off-line power control strategy is made to minimize data transmission time with throughput constraints. It was also proved that the power control strategy has water injection structure. Differing from [10], literature [11] considered how the source node is powered by the grid while the relay node is powered by renewable energy. An off-line power control strategy is proposed to maximize the grid energy efficiency of the source node. In [12], the research was extended to a Gauss fading channel, with both off-line and on-line power control schemes are proposed. In addition to the traditional relay, the literature [13] considers the relay with cache function. Off-line and on-line power control strategies are developed to maximize network throughput. All ofthe above studies have developed off-line or on-line power control strategies under the constraints of user's quality of service (QoS). Besides power control schemes, link selection strategies are also critical. In [14], the source node is powered by grid energy while the relay is powered by renewable energy. With causal side information, a link selection strategy is made to maximize the average throughput of all time slots. In [15], the relay is powered by radio frequency (RF) energy with a finite battery capacity, and only one data packet needs to be transmitted in each slot. A link selection scheme based on battery level is proposed to minimize the outage probability of the relay. Further, literature [16] jointly optimizes power and link selection to reduce outage probability of the relay. In [17], the research was extended to multi-relay with data caching, Under the constraints of battery capacity, on-line and off-line power allocation and link selection mechanisms were developed to minimize data transmission time. Most previous studies on hybrid energy supply (HES) wireless relay systems assume that the amount of data transmitted by the source node are fixed in each slot, and then optimize the outage probability or transmission time. However, in practical applications, the source node needs to serve a lot of different users and deliver unfixed data bits in each slot. So, data bits should be transmitted as much as possible to reduce the network congestion with grid energy consumption constraints. Consequently, in this paper, we consider that the source node has available bits to be transmitted all the time. Our goal is to maximize network throughput while minimizing grid energy consumption. The rest of this paper is organized as follows. Section 2 describes the system model. In Section 3, the Markov decision process (MDP) problem is formulated, for which a low-complexity algorithm is proposed. Simulations are shown in Section 4.