## 5 Joint Optimization of FeICIC Parameters and Base-Station Density
### Joint Optimization of Pico CRE Bias and Power Reduction Factor
Then the distance between the transmitter and the receiver was shorted, resulting in network EE improvement. As shown in Figure 7, with the increase of UE density, the curves of network EE also rose accordingly. As the UE density increased, more UEs can be offloaded into the coverage of low power PBSs by adjusting pico CRE bias and power reduction factor via network EE optimization algorithms. Then network EE can be improved. For the theoretical simulation curve, because the network EE was not optimized and just calculated according to Equation (14) with pico CRE bias and power reduction factor being set to be fixed values 5 dB and 0.25, respectively, so it had the worst performance. The TPO algorithm and the TBO algorithm optimized power reduction factor and CRE bias, respectively. Therefore, the performances of these two algorithms with one parameter optimized were better than that of the theoretical simulation. Our proposed JBPO algorithm can jointly optimize pico CRE bias and power reduction factor together. Therefore, it can further improve the network EE and match the Monte Carlo simulation results very well. Furthermore, the performance of the TPO algorithm was far less than that of the TBO algorithm, which signifies that the influence of pico CRE bias was more than that of the power reduction factor on the network EE, especially in low PBS density. In addition, in Figure 7 the performance gap between the JBPO algorithm and theoretical simulation increases accordingly with the growth of UE density, which further indicates the importance of joint pico CRE bias and power reduction factor optimization for the heavy network load scenario. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Carrier frequency \(f\) & 2 GHz \\ Total spectrum bandwidth \(W\) & 10 MHz \\ Path loss exponent \(\alpha\) & 4 \\  & \(L=10\log\left(L_{0}\right)+\alpha 10\log\left(r\right)\), \\ Path loss \(L\) & where \(L_{0}=\left(4\pi f/c\right)^{2}\), \\  & \(c=3\times 10^{8}\) m/s \\ MBS transmission power \(P_{m}\) & 43 dBm \\ PBS transmission power \(P_{p}\) & 30 dBm \\ 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 2: Network scenario parameters. Then, the performances of our proposed JBPO algorithm were compared with that of the TBPO algorithm in Figures 8 and 9 from different aspects, respectively. The relationship between network EE and \(\lambda_{p}\) with different \(\lambda_{u}\) are shown in Figure 8. We can see that the performance of our proposed JBPO algorithm was just slightly worse than that of the TBPO algorithm, but the computational complexity of JBPO was much lower than that of the TBPO algorithm. In addition, all curves of network EE increased first and then fell down slightly with PBS density increase, which illustrates that increasing PBS density can improve the network EE significantly within a certain network load. Nonetheless, when the PBS density exceeded a certain limit, further increasing will cause more complex interference and more power consumption, which will result in the network EE deterioration. Figure 6: The network energy efficiency (EE) versus \(\lambda_{p}\) with fixed \(\lambda_{u}=0.0018\). Figure 7: The network EE versus \(\lambda_{u}\) with fixed \(\lambda_{p}=10\lambda_{m}\). The relationship between network EE and \(\lambda_{u}\) with different \(\lambda_{p}\) are depicted in Figure 9. Due to the curves cross with each other under different UE densities, the PBS density should be carefully adjusted according to the network load fluctuation. In addition, for a given PBS density, we can see that the network EE become greater with a higher network load. Referring to Figures 8 and 9 together, although the network EE performance of the TBPO algorithm is just slightly better than that of the JBPO algorithm, the computational complexity of it is \(O(n_{B_{p}}\times n_{p})\), which is much higher than that of the JBPO algorithm.