## 4 Joint Parameters Optimization
### _Initialization_  
Based on the aforementioned parameter optimization algorithms, each parameter is just optimized with the other one being fixed, which in fact cannot reach these parameters' global optimization due to the fact that these parameters are affected by each other. Therefore, combining the CBO Algorithm and PDO Algorithm, we further propose a heuristic pico CRE bias and PBS density joint optimization algorithm to address the objective Equation (15), which is as shown in Algorithm 3. ```
1. Initialization:

(1) Initialize the network scenario and the values \(\lambda_{u}\), \(\lambda_{m}\), \(B_{p}\) and \(\rho_{p,m}\), where \(B_{p}\in(0,25]\) and \(\rho_{p,m}\in(0,30]\). (2) Let \(EE^{*}=0\) represent the initial optimal value of the network EE. Initialize algorithm iteration number \(N_{loop}=0\). Given a tolerance \(\varepsilon>0\). (3) Denote \(B_{p}^{*}\) as the optimized

## 5 Numerical Results and Analysis

A square of \(1000\,\mathrm{m}\times 1000\,\mathrm{m}\) network coverage area is considered in the simulation. The deployment of PBSs and MBSs follows the PPP model and the typical user is placed in the origin. The detailed simulation parameters are summarized in Table 1. Monte Carlo simulation method is adopted to illustrate our proposed algorithms. In Monte Carlo simulation, the locations of MBSs, PBSs and UEs are modeled as spatial PPP for each time of the network realization, respectively. According to the network topology realized by spatial PPP model, the network EEs will be calculated for all the different combinations of pico CRE bias and PBS density values within their value ranges based on wireless link quality. Then, the maximum network EE and the optimal pico CRE bias and PBS density can be obtained by comparing all the calculated network EEs. By averaging 50 times of the network realizations, Monte Carlo simulation results can be obtained. ### Performance Analysis for Pico CRE Bias Optimization

The performances of the optimal pico CRE bias obtained according to CBO Algorithm are compared with those of the static pico CRE bias and Monte Carlo simulation, which are shown in Figures 2 and 3 from different aspects, respectively. The network EE for the static pico CRE bias is calculated according to Equation (14) and the static pico CRE bias is set to be 3 dB, 9 dB and 15 dB, respectively. The Monte Carlo simulation results show the maximum network EE within the value range of PBS density. The network EE versus \(\lambda_{p}\) with UE density \(\lambda_{u}=0.0018\) is shown in Figure 2. As shown in Figure 2, the performances of CBO Algorithm always outperform those of static pico CRE bias and agreed with those of Monte Carlo simulation very well, which illustrate on the one side the accuracy of our derived closed form of network EE and on the other side the effectiveness of our proposed CBO Algorithm. Furthermore, simulation results show that no matter what the value of pico CRE bias is, all the curves of network EE keep increasing with PBS density increasing at the initial stage, and then tend to fall down slightly with PBS density further increasing. This indicates that increasing the PBS density deployment can improve the network EE significantly with a certain UE density. Nonetheless, when the PBS density achieves a certain level, further increasing of it will not only cause a lot of interference to users, but also give rise to more power consumption, and eventually deteriorate the network EE. The network EE versus \(\lambda_{u}\) with fixed PBS density \(\lambda_{p}=0.0006\) is depicted in Figure 3, which shows that the network energy efficiencies of CBO Algorithm are always better than those of static pico CRE bias and capture the results of Monte Carlo simulation very well. This is due to the fact that the CBO Algorithm can optimize the number of UEs offloaded from macro cell on the basis of the network EE.