## 6 Data Fitting and Simulation Analysis  
In this section, we first find the expression of the MISR for the MHCP network. It should be noted that the theoretical derivation of the MISR expression for the non-PPP network is too complex to implement. Thus, we use simulation and data fitting to get the expression of MISRMTCP. Then, a series of numerical simulations are carried out to verify the accuracy of our derived coverage and energy efficiency expressions. In order to keep the derivation tractable, we do not consider the MUEs' QoS requirements and we assume that each BS equally allocates the frequency resource among its associated MUEs. Furthermore, the downlink channel capacity is calculated based on the preset target SIRs, and the target SIRs for MBSs and PBSs are set to be the same in the simulation. For the power consumption model, we refer to the statistics proposed in [48]. The simulation parameters are shown in Table 1.  
Figure 2 shows the relationship between \(\text{MISR}_{\text{MHCP}}\) and path loss. We use the fitting toolbox cftool in MATLAB to obtain the mathematical model of MISR about path loss as  
\[\text{MISR}_{\text{MHCP}}(\alpha)=a\cdot a^{b}+c \tag{22}\]  
The correlation coefficients fitted for each tier of the MHCP network are given in Table 2.  
Then we can use \(\text{MISR}_{\text{MHCP}}\) to calculate \(\text{G}_{\text{MHCP}}\) according to Equation (4), and then substitute \(\text{G}_{\text{MHCP}}\) into Equation (9) to obtain the approximate coverage of the two-tier MHCP-MHCP network. It should be noted that the fitting results in Table 2 are related to the repulsion radius. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters Name** & **Values** \\ \hline Bandwidth & \(10^{7}\) Hz \\ MHCP-MHCP network area & \(1000\times 1000\) m\({}^{2}\) \\ density of MUs, \(\lambda\)u & \(0.15\) m\({}^{-2}\) \\ density of MBSs, \(\lambda_{1\text{-MHCP}}\) & \(2\)* \(10^{-5}\) m\({}^{-2}\) \\ density of PBSs, \(\lambda_{2\text{-MHCP}}\) & \(2\)* \(10^{-4}\) m\({}^{-2}\) \\ repulsion radius of MBSs & \(100\) m \\ repulsion radius of PBSs & \(50\) m \\ path-loss exponent, \(\alpha\) & [3, 5] \\ circuit power consumption of MBS, \(P_{\text{C1}}\) & \(130\) W \\ transmit power of MBS, \(P_{\text{T1}}\) & \(20\) W \\ number of transmit antenna elements of MBS, \(N_{\text{TR1}}\) & \(6\) \\ slope of power consumption depends on load of MBS, \(\theta_{1}\) & \(4.7\) \\ circuit power consumption of PBS, \(P_{\text{C2}}\) & \(6.8\) W \\ transmit power of PBS, \(P_{\text{T2}}\) & \(0.13\) W \\ number of transmit antenna elements of PBS, \(N_{\text{TR2}}\) & \(2\) \\ slope of power consumption depends on load of PBS, \(\theta_{2}\) & \(4.0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Coefficients Name** & **a** & **b** & **c** \\ \hline
1-th tier network (MBSs) & \(5.917\) (\(5.55\), \(6.285\)) & \(-1.551\) (\(-1.641\), \(-1.461\)) & \(0.001449\) (\(-0.04122\), \(0.04412\)) \\ \hline
2-th tier network (PBSs) & \(18.09\) (\(16.82\), \(19.36\)) & \(-2.602\) (\(-2.678\), \(-2.527\)) & \(0.1721\) (\(0.1558\), \(0.1883\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fitted correlation coefficients (with 95% confidence bounds). Figure 2: Mean interference-to-signal ratio (MISR) simulation for a single-tier MHCP network. Figure 3 compares the coverage probabilities of the MHCP-MHCP network with that of the PPP-PPP network, and both simulation and theoretical approximations of coverage are given. The target SIRs for MBSs and PBSs are set to be the same. It can be seen from Figure 3 that the theoretical results are in good agreement with the simulation results, which further verifies the effectiveness of the proposed ET-ASAPPP method. It can also be seen that the approximate coverage of MHCP-MHCP is the lower bound of simulation coverage. What is more, the coverage performance of the MHCP-MHCP network is significantly better than that of the PPP-PPP network.