## 1 Introduction  
Deploying picocells in traditional macrocells to build hierarchical heterogeneous networks (HetNets) can effectively solve problems, such as uneven distribution of users and insufficient coverage of hotspot areas [1]. Due to the different deployment methods of different networks in HetNets, there are some problems with co-tier interference and cross-tier interference in HetNets. Therefore, inter-cell interference coordination technology is one of the hot spots in the research of heterogeneous cellular networks. Therefore, inter-cell interference coordination technology is one of the hotspots in the research of heterogeneous cellular networks. Among them, enhanced inter-cell interference coordination (eICIC) [2] includes cell range expansion (CRE) and almost blank subframe (ABS) and has been widely used in two-tier heterogeneous cellular networks. Firstly, because the transmit power of the macrocell base station (MBS) is much larger than that of the picocell base station (PBS) in the downlink of HetNets, most users choose to access the MBS for the larger transmit power; which will cause unbalanced load distribution. Secondly, the macrocell users who are located near the picocell and are far away from the MBS need to increase transmit power to communicate with the MBS in the uplink of HetNets. At the same time, this will cause serious uplink interference in the PBS. In order to solve the above problems, CRE technology [2] has been proposed in 3 GPP. The basic principle is to add a positive bias value on the basis of the reference signal receiving power (RSRP) from the PBS so that more macrocell users are off-loaded to the picocell to balance the network load and reduce the uplink interference. However, the users who access the PBS through CRE will suffer severe interference from the MBS and the downlink performance of the network will be affected. ABS technology [2] is effective in addressing this interference problem. The basic principle is that the MBS stops transmission in a specific subframe to protect the users which suffer severe interference from the MBS. Then these users can communicate in a specific subframe to reduce the interference from the tier of macrocell. The reference [3] realizes the self-optimized networking based on CRE and ABS and evaluates the gains of real network data. Moreover, the eICIC technology has been combined with coordinated multipoint (CoMP) in [4] to satisfy the requirement of the users. A novel joint user association with the eICIC scheme [5] was proposed to solve the max-min fairness optimization problem by the optimal ABS ratio. Moreover, a novel user throughput estimation method [6] where ABS and a proportional fairness scheduler are applied was proposed to maximize cell user throughput by adjusting the ABS ratio. The interaction among the base stations was modeled as a near-potential game [7] and uses distributed learning algorithms to achieve better load balancing. In [8], the author performed the eICIC configuration with multiple coexisting services and designed an optimization algorithm based on the alternating direction method which adapts CRE bias at the service layer and the ABS ratio at the base station (BS) layer. Moreover, an adaptive ABS configuration scheme [9] was proposed to dynamically match the real-time users and combines the power control of MBS to improve the performance of edge users. Because of the downlink/uplink decoupling, a novel method for the load balancing of downlink and uplink [10] was proposed to improve the throughput and rate gain based on ABS configuration. The energy efficiency (EE) with interference coordination in HetNets has been considered in [11] and a max-min energy efficient algorithm with eICIC was proposed to improve the performance of the network. Moreover, reference [12] proposed an energy efficient optimized strategy to balance the load, reduce the interference and increase the system EE and fairness at the same time.