## 1 Introduction  
Heterogeneous networks (HetNets) [1, 2] are proposed in long-term evolution-advanced (LTE-A) systems by the 3 rd Generation Partnership Project (3 GPP) to not only meet the rapidly increasing demands of mobile data traffic, but also to reduce the huge energy consumptions caused by data transmissions. A HetNet is a hierarchical network where low-power access points (APs, also named small cell sites [3, 4]) are included in a macro-cell, in order to provide highly qualified services. Typical small cell sites include pico, femto, relay and so forth. Femto [5] is mainly for indoor transmissions, while pico [6] is used outdoors in a crowded place, such as a university. Relay [7] is usually built in a remote area far from the macro-cell site (named the Evolved Node B, or eNodeB, in LTE-A HetNet) to extend the coverage of the macro-cell. Figure 1 presents a simple example of a HetNet. Although HetNets are widely considered as the main trend in the development of mobile communication systems [3], several challenges should be dealt with before implementation in the real world. One of the major challenges is severe intercell interference aggravated by the dense deployment, which crucially affects the performance of HetNets. As a promising measurement to deal with intercell interference, coordinated multiple point (CoMP) [8] techniques are considered to be helpful for HetNets. The basic idea of CoMP techniques is to coordinate coordinated neighboring cells, so that intercell interference can be reduced to a large extent. According to the different ways to cooperate, CoMP techniques are classified into two categories, coordinated scheduling/coordinated beamforming (CS/CB) and joint processing (JP) [9]. CS/CB CoMP makes neighboring cells jointly pre-code according to global channel state information (CSI) to avoid potential interference, while JP CoMP allows neighboring cells to jointly process signals intended for a specific user in the overlapping area. Joint transmission (JT) is a typical JP CoMP technique that requests of cooperating cells to transmit the same data packets to a user independently and simultaneously. In this paper, we take JT CoMP as an example to discuss the performance of CoMP-based HetNet, and the study can also be extended to other CoMP techniques. To fulfill the requirements of the future mobile networks, CoMP-based HetNets need to provide qualified services as much as possible while maintaining acceptable energy consumption. According to report [10], energy consumption caused by information and communications technology (ICT) has contributed up to 5% of the world-wild power supply at present. To avoid the further increase of energy consumption, mobile networks are required to significantly improve the utility efficiency of power resources. Radio resource management (RRM), which adaptively allocates radio resources, such as frequency and power, according to CSIs, is beneficial for CoMP-based HetNets to enhance the energy efficiency. In this paper, we focus on RRM in a CoMP-based HetNet for the purpose of improving the energy efficiency while guaranteeing high data rates, as well as user fairness. An optimization problem aiming at maximizing weighted energy efficiency is formulated, where the weights are employed for maintaining the fairness of users's data rates. Several crucial constraints in practice are taken into consideration in the formulated problem. Besides the limitation on total power at each transmitter, backhaul links, which connect small cells to the eNodeB for exchanging data and control information, are considered to have restricted capacity. Additionally, the lowest data rate of each transmission is defined, in order to guarantee the quality of transmissions and avoid wasting of energy. Since the formulated problem is unsolvable mixed integer programming (MIP), we separate the whole problem into a scheduling subproblem under the assumption of equal power allocation and a power allocation subproblem with known scheduling results.