## 1 Introduction
### Motivation  
In HetNets consisting of MBSs and PBSs, as shown in Figure 1, the great difference of transmitter power leads to load imbalance between macro tier and pico tier. To address this issue, PBSs adopt cell range expansion (CRE) technology to enlarge the PBS coverage area by adding a positive bias on the reference signal received power (RSRP) of PBSs without increasing transmission power [5,6]. Unfortunately, CRE user equipments (UEs) located in the pico CRE region will suffer serious downlink interference from dominating MBSs, even causing the outage of control signals. As a result, it is important to mitigate the downlink interference to improve the wireless link quality between transmitter and receiver. Then the network EE can be improved.  
To mitigate the downlink inter-tier interference for HetNets, further enhanced inter-cell interference coordination (FeICIC) scheme has been specified in 3 GPP Release 11 [7]. In FeICIC scheme, MBSs can transmit data to macro center UEs with low transmission power over certain subframes, termed as low power almost blank subframes (ABS), over which PBSs can schedule CRE UEs with reduced interference [8]. On the basis of FeICIC technique, for user association, the pico CRE bias will directly affect the value of user received RSRP from PBSs, which will eventually affect the number of CRE UEs associated to PBSs. As CRE UEs are scheduled in the subframes corresponding to the ABS of MBSs, the transmission power of MBSs in ABS, i.e., ABS power, will decide the interference degree suffered by CRE UEs. Therefore, pico CRE bias and ABS power are two important factors for  
Figure 1: The network scenario.  
the wireless link quality of UEs, especially for CRE UEs, which eventually have significant effect on the network EE performance.  
To meet the super-large capacity demand in 5G wireless communication networks, more and more base stations (BSs), especially small base stations (SBSs), are deployed in HetNets [9; 10]. On the one hand, irregular deployment of massive BSs causes additional and intractable inter-tier interference. On the other hand, although high-density PBSs are deployed to satisfy the peak traffic volume, highly dynamic wireless traffic may deteriorate EE if the capacity gains of numerous PBSs are utilized insufficiently. In short, the BSs deployment strategy based on network load is also one of the key issues to realize 5G green cellular network [11].  
In addition, the network EE of HetNets is also affected by some other aspects of factors. For instance, it is proved that the reasonable adjustments of BS transmit power, inter-site distances and the number of MBSs or SBSs contribute to the improvement of EE of HetNets [12]. In [13], assuming that SBSs have performed traffic offloading from MBS, the authors investigated the MBS and SBS power allocation scheme to improve network EE. In [14], the authors investigated the user scheduling and resource allocation method to optimize the network EE for HetNets.  
To sum up, for complex HetNets, network EE is affected by many different aspects of factors, e.g., MBS transmit power in low power ABS, MBS transmit power in non-ABS, MBS density, ABS ratio, pico CRE bias, PBS density, PBS transmit power in low power ABS, PBS transmit power in non-ABS, etc. Thus, it will be a very challenging work to analyze the effects of all of these factors together on network EE. In this paper, for HetNets deployment in reality with inter-tier interference coordination by adopting FeICIC scheme, the pico CRE bias, the power reduction factor of low power ABS, and the density of PBSs are three more related factors for the network EE improvement compared with others. Therefore, the above three factors are focused and jointly optimized for the network EE maximization in this paper.