## 4 Joint Parameters Optimization
### _Initialization_
In addition, with the increase of UE density, the performance gap between CBO Algorithm and static pico CRE bias increase accordingly, which further signifies the importance of pico CRE bias optimization for the heavy network load scenario. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Carrier frequency \(f\) & 2 GHz \\ Path loss exponent \(\alpha\) & 4 \\  & \(L=10\log\left(L_{0}\right)+410\log\left(\tau_{l}\right)\), \\ Path Loss \(L\) & where \(L_{0}=\left(4\pi f/c\right)^{2}\), \\  & \(c=3\times 10^{8}\,\mathrm{m/s}\) \\ MBS transmit power \(P_{m}\) or \(P_{m,l}\) & 43 dBm or 20 W \\ PBS transmit power \(P_{p}\) or \(P_{p,l}\) & 30 dBm or 1 W \\ Bandwidth \(W\) & 10 MHz \\ MBS static power \(P_{m,s}\) & 800 W \\ PBS static power \(P_{p,s}\) & 130 W \\ MBS density \(\lambda_{m}\) & 0.00003 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Network scenario parameters. ### Performance Analysis for PBS Density Optimization

The performances of the optimal PBS density obtained according to PDO Algorithm are compared with those of the static PBS density (represented by the static ratio of PBS density to MBS density) and Monte Carlo simulation, which are presented in Figures 4 and 5 from different aspects, respectively. The network EE for the static ratio of PBS density to MBS density is obtained according to Equation (14) and the static ratio \(\rho_{p,m}\) is set to be 10, 15 and 20, respectively. The Monte Carlo simulation results show the maximum network EE within the value range of PBS density and are averaged over 50 times of network realizations. The relationship between the network EE and \(B_{p}\) with UE density \(\lambda_{u}=0.0018\) is depicted in Figure 4. The network EE versus \(\lambda_{u}\) with pico CRE bias \(B_{p}=5\,\mathrm{dB}\) is described in Figure 5. Both of the simulation results show that the performances of PDO Algorithm outperform those of the static PBS densities and fit those of Monte Carlo simulation precisely. Figure 4 also shows that the network EE is nonlinear with \(B_{p}\), which signifies the difficulty of \(B_{p}\) optimization by closed-form solution. As shown in Figure 5, the curves of static PBS densities cross with each other under different UE densities, which indicates that the PBS density should be carefully adjusted according to the network load fluctuation. Figure 3: The network EE versus \(\lambda_{u}\) with \(\lambda_{p}=0.0006\). This is why the performance of our proposed PDO Algorithm can always outperform those of static PBS density scheme. ### Performance Analysis for Joint Optimization of CRE Bias and PBS Density

The network EE performance of JBPDO Algorithm are compared with those of a CBO Algorithm with fixed \(\lambda_{p}=20\lambda_{m}\), PDO Algorithm with fixed \(B_{p}=5\) dBm, Traverse Algorithm and Monte Carlo simulation in Figure 6. Traverse Algorithm simulation results are obtained by traversing all the values of pico CRE bias and PBS density to find optimal CRE bias and PBS density based on Equation (14) to maximize the network EE. The Monte Carlo simulation results show the maximum network EE within the value ranges of PBS density and pico CRE bias together and are averaged over 50 times of network realizations. Clearly, due to the fact that the JBPDO Algorithm can jointly optimize pico CRE bias and PBS density together to achieve these two parameters global optimization, the number of UEs offloaded from macro cells can be further optimized and eventually the JBPDO Algorithm can further enhance the network EE compared with CBO Algorithm and PDO Algorithm. Monte Carlo simulation results once again illustrate the accuracy and effectiveness of our proposed JBPDO Algorithm. The network EE increments of JBPDO Algorithm compared with CBO Algorithm and PDO Algorithm are depicted in Figure 7 under different user densities. As shown in Figure 7, due to the fact

Figure 4: The network EE versus \(B_{p}\) with \(\lambda_{u}=0.0018\).