## 2 Related Works  
Early literatures mainly focused on pico CRE bias, ABS ratio, and ABS power optimization for the network capacity maximization [15; 16; 17; 18] and recent works began to investigate the network EEimprovement from different perspectives including resource management [19; 20; 21; 22; 23], FeICIC parameters optimization [24; 25; 26; 27; 28; 29; 30; 31] and BS deployment strategy [32; 33; 34; 35; 36; 37; 38; 39]. As for resource management, centralized resource allocation algorithms based on convex-optimization [19; 20], graph-theory [21] or even game-theory [22; 23] were proposed to achieve the maximum EE gain.  
As for FeICIC parameter optimization, the ABS ratio dynamical optimization algorithm based on network load was proposed to enhance the network EE in [24]. For improving the network capacity and EE, pico CRE bias optimization problem was further developed combined with power control in [29]. Using the stochastic geometric approach, the expressions for SE and cell-edge throughputs have been derived as a function of the power reduction factor of low power ABS in [30]. To move one step further, pico CRE bias, ABS ratio and ABS power are jointly optimized by a robust EE optimization framework in [25]. In [31], it was proved that FeICIC can achieve a better gain in view of network EE, cell-edge throughput and user fairness compared with eICIC. In addition, the distributed algorithms based on the exact potential game framework for both eICIC and FeICIC optimizations were proposed to offer better network performance. The authors of [26] deducted and analyzed the EE coverage performance of FeICIC with extra pico CRE bias. In [28], FeICIC technique was applied to mitigate the inter-tier interference in HetNets deployed with unmanned aerial vehicles (UAVs). In such a scenario, the locations of UAVs, pico CRE bias and inter-cell interference coordination parameters were jointly optimized by using a genetic algorithm. In [27], the EE of HetNets with joint FeICIC and adaptive spectrum allocation was analyzed by the stochastic geometric approach. The research on FeIC parameters optimization on the basis of stochastic geometry is relatively few in the existing literatures.  
As for BS deployment strategy, general linear power consumption models were developed by means of linear regression in [38]. Meanwhile, the effects of MBS transition power and on/off switching on instantaneous MBS power consumption were analyzed. A threshold of SBS density in ultra-dense HetNets was investigated in consideration of the backhaul network capacity and network EE in [32]. In [33], the authors came up with an approximation algorithm to solve the intractable user association problem by controlling the PBS density dynamically. The relationship between PBS density and network EE was analyzed under different UE density in [34]. It was proved that both PBS density and MBS density have a notable impact on the network EE in [35]. In [36; 37], PBS density and MBS density were jointly optimized based on traffic-aware sleeping strategies and stochastic geometry to enhance the network EE, respectively. In [39], taking the traffic pattern variations into account, the BSs can not only adaptively switch on/off states but also can dynamically scale its transmit power according to network capacity demands. In this way, network energy consumption is reduced.  
Despite the aforementioned research works, few works in the literatures focused on FeICIC parameters and PBS density joint optimization for network EE improvement in HetNets, which will be investigated and developed in this paper.