# Optimal Energy Efficiency Fairness of Nodes in Wireless Powered Communication Networks
## 1 Introduction  
With the wide use of smartphones, tablets, and machine-to-machine (M2M) devices for various applications and services, the amount of mobile data traffic has grown dramatically in recent years [1]. The deployment of low-power small base stations (BSs) in hotspot areas is a potential solution to cope with the increase in traffic and devices [2]. In particular, with the density of low-power small BSs, heterogeneous cellular networks (HetNets) could enhance area spectral efficiency, increase the capacity of communication, and reduce transmission delay [3]. Therefore, a high dense heterogeneous network is one of the preeminent technologies in the racetrack towards fulfilling the requirements of next generation mobile networks [4]. In practice, low-power small BSs have advantages on both devices and networks in terms of energy efficiency. On the one hand, low-power small BSs serving wireless devices with short communication distances results in a lower power consumption. On the other hand, the BSs of a macrocell can reduce power consumption by offloading part of the traffic to small BSs. As a result, various energy-efficient designs have been proposed [5; 6; 7; 8; 9] to exploit the potential performance gains brought by deployment of low-power small BSs. A novel approach for joint power control and user scheduling has been proposed in [5] for optimizing energy efficiency (EE) while ensuring user QoS in ultra-dense small cell networks (UDNs). An algorithm is proposed in [6] to enable small cells activation/deactivation adaptively with respect to the dynamically fluctuating traffic loads to fullfil the data rate requirement. The user association problem is investigated in [7] for maximizing the energy efficiency of a network considering the capacity and energy consumptionand a low-complexity algorithm achieving near-optimal performance is proposed. A non-convex optimization problem is formulated for power control of small BSs to maximize their EE in [8] and a distributed power control scheme is proposed to achieve the Nash equilibrium with the minimum information exchange. The energy efficiency of the uplink transmission in HetNets, where the user equipments (UEs) apply a flexible power control scheme subject to maximum transmit power constraint, is investigated in [9]. Meanwhile, there has also been growing interest in studying various techniques for the nodes to improve the energy efficiency of the network [10; 11; 12]. With the aid of learning automata, an energy efficient barrier coverage algorithm is proposed to select minimum number of required nodes to monitor barriers in deployed network [10]. An energy-efficient adaptive resource scheduler for Networked Fog Centers is proposed in [11] for real-time vehicular cloud services to meet quality-of-service (QoS) requirements. An energy-efficient stable election routing algorithm is presented in [12] to maintain balanced energy consumption of nodes in a wireless sensor network. Despite the fruitful research on the deployment of low-power small BS, several open issues remain unsolved which are the obstacles for achieving high energy-efficient multi-tier HetNets. One of the fundamental challenges is the energy limitation of sensors. In general, most of the nodes are powered by battery with limited energy storage and lifetime. Hence, wireless powered communication networks (WPCNs), where BSs in HetNets can use energy harvest (EH) and wireless power transfer (WPT) technique, is a promising solution to prolong the lifetime of energy-limited nodes [13; 14; 15; 16; 17; 18]. In [13], power allocation is designed for the maximization of energy efficiency of an energy harvesting system relying on renewable natural energy sources such as solar and wind. However, renewable energy sources are intermittent and the communication devices may not always be able to harvest sufficient energy for supporting their energy consumptions.