# Application Research of Multi-Mode Relay in Future Heterogeneous Networks
## 4 Theoretical Calculation and Simulation Analysis  
In Section 4, we verify above theoretical analysis by data simulation. The simulation diagram and parameters are shown in Figure 4 and Table 1. The hierarchical heterogeneous network model is shown in Figure 5, where the green squares represent macro cells, the red squares represent randomly distributed micro cells, and the blue squares represent users. The network also provides two user connection modes: (a) Both users access a random macro cell; (b) Both users access a random micro cell. It is possible to simulate the access mode of two users and perform system performance studies in the selected mode. Figure 4: System simulation diagram. Figure 5: Hierarchical heterogeneous network model (7 macro cells, 70 micro cells, 140 users). In Figure 6, with the variance of channel estimation errors, we set up the number of interferers \(N=4\) and the powers of N interferers \(u_{1}=2.1\), \(u_{2}=0.5\), \(u_{3}=6\), \(u_{4}=1.4\), respectively. The target threshold \(f_{th}\) is 5 dB. Consequently, the comparison of the outage probability results of the analytical Equation (19) in [13], the aforementioned Equation (29), and the data simulation are illuminated in Figure 4. It is obvious to see that the theoretical results of Equations (19) and (29) are very approximate at low relay power, and as the relay power increases, their performance shows some difference; even though the simulation results have similar trends to theoretical analysis, there is a gap in comparison with theoretical values. Figure 7 displays the system outage probability results with different power ratios, i.e., the \(p_{r2}\) equals to 9/10, 1/2, 1/3, 1/4, 1/5 times \(p_{r1}\), respectively. As we see in results, there is little difference between the analytical results of different emission power \(p_{r2}\) size. Then with the increase of \(p_{s}\), there are differences between them, but they all show some differences gradually, which means that \begin{table}
\begin{tabular}{l l} \hline Environmental Deployment & 10 Micro Cells Randomly Distributed Around Macro Cell \\ \hline Cell Connection Plan & RSRP and CL \\ \hline Bandwidth & 10 MHz \\ \hline Carrier Frequency & 2 GHz \\ \hline Path Loss Model & 3 GPP TR 36.814 Model 1 \\ \hline Distance between Macro cells & 250 m \\ \hline Maximum Macro Cell Transmit Power & 46 dBm \\ \hline Maximum Micro Cell Transmit Power & 30 dBm \\ \hline Noise Figure & 9 dB \\ \hline Macro cell eNodeB Antenna Model & 3D Antenna Model \\ \hline Micro Cell eNodeB Antenna Model & Omnidirectional Antenna, 2D Antenna Model \\ \hline Macro Cell Antenna Gain & 14 dBi \\ \hline Micro Cell Antenna Gain & 5 dBi \\ \hline Antenna Configuration & 2 Cross-polarized Transmit Antennas for eNodeBs \\ \hline Receiver Type & Minimum Mean Square Error Receiver \\ \hline Minimum Distance Between Micro cell and Macro cell & 75 m \\ \hline Minimum Distance Between Micro Cells & 40 m \\ \hline Minimum Distance Between Macro cell and user & 25 m \\ \hline Minimum Distance Between Micro cell and user & 10 m \\ \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 6: Outage probability of HHWN with MMR of different emission powers. the multiplicative between two emission powers (\(p_{r1}\) and \(p_{r2}\)) will not have significant influence on the outage probability. Figure 8 depicts the system spectral efficiency (SE) with different power ratios. The solid, dashed, triangle, rhombus, square, and star lines indicate SE of \(p_{r2}=\lambda*p_{r1}\), \(\lambda=1,9/10,1/2,1/3,1/4,1/5\), respectively. As shown in the figure, the base line is \(p_{r2}=p_{r1}\) and the other SEs of HHWN system decreases when the power gap grows. When SE is more than 4 bits/s/Hz, the gap between \(p_{r2}=p_{r1}\) and \(p_{r2}=0.25*p_{r1}\) reaches 3 dB. Consequently, to avoid 3 dB loss of SE, the power ratio should be higher than 0.25.