## 4 Simulation and Analysis  
In this paper, the scenario of massive MIMO enabled HetNets is considered, where the coverage radius of MBSs and SBSs are 500 m and 50 m, respectively. The network simulation parameters are shown in Table 1[13]. Assumed that all the SBSs and users distribute evenly within the coverage area of the center MBS and each SBS is at least 40 m away from the center MBS. The number of antennas installed on the macro-BS and the maximum data streams supported by the macro-BS are supposed to be 100 and 20, respectively. In addition, the maximum transmit power of the MBS and each SBS are 43 dBm and 23 dBm, respectively. All the simulation results are obtained by 5000 Monte Carlo runs. Due to the characteristic of channel hardening in the massive MIMO system, the effects of fast fading can be eliminated. Then, we can suppose the channel fading only includes path loss, shadow fading and frequency selective Rayleigh fading. The path loss model can be found in _Model A.2.1.1.2-3 for outdoor RRH or hotspot area model 1[43]_, as shown in Table 2, where the unit of \(d\) is km. The Rayleigh fading channel gains are modeled as i.i.d. unit-mean exponentially distributed random variables. The variance of the lognormal shadowing from the associated BS to each user is considered to be 10 dB. Figure 2 shows the convergence in term of different initial values of each BS's transmit power for Algorithm 3 versus the number of iterations, where \(p_{j}=p_{j,\max},\forall j\) and \(p_{j}=p_{j,\max}/2,\forall j\), respectively. The simulation setting of the number of users and the number of antennas installed on the MBS are 30 and 100, respectively. The ordinate in Figure 2 represents the change number of the convergence flag \(\xi^{n}=\max\limits_{jk}\Delta\gamma_{jk}^{n}\) in Algorithm 3. Obviously, we can find Algorithm 3 converges after a limited number \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(J\) & 10 & \(B\) & 10 MHz \\ \(R_{MBS}\) & 500 m & \(R_{SBS}\) & 50 m \\ \(M\) & 100 & N & 20 \\ \(p_{1,\max}\) & 43 dBm & \(p_{j,\max,j}>1\) & 23 dBm \\ \(p\) & 0.02 W & \(\varepsilon_{j}\) & 0.38 \\ \(\xi_{1}\) & 10 W & \(\xi_{j}/j>1\) & 0.2 W \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. \begin{table}
\begin{tabular}{c c} \hline \hline
**Channel** & **Path Loss Model** \\ \hline From MBS to users & \(PL=128.1+37.6 log_{10}\left(d\right)\) \\ From SBS to users & \(PL=140.7+36.7 log_{10}\left(d\right)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Path loss model. Figure 5 shows the relationship between the network EE and the weight coefficient \(\omega\) in Algorithm 2, where the numbers of users \(K\) has different values. The simulation setting of the number of antennas \(M\) and the initial value of each BS's transmit power \(p_{j}\), \(\forall j\) are 100 and \(p_{j,\max}\), respectively. The vertical axis of Figure 5 is the value of the network EE calculated by Algorithm 2 with different values of given weight coefficient \(\omega\). We can find two interesting points in Figure 5. The first point is that the network EE is a concave function on the weight coefficient \(\omega\). In addition, it can be concluded that the network EE has no change irrespective of the different numbers of users. Then, we analyze and discuss the two points as follows. Firstly, the weight coefficient can denote the degree of preference for energy consumption. With the weight coefficient increasing, the energy consumption increases and the network capacity reduces, correspondingly. Then, the network EE is a concave function on \(\omega\). Secondly, the energy consumption of users can be almost neglected in the wireless downlink transmission system. In the OFDMA system, the distribution and the number of users have little effects on the spectrum efficiency after enough number of Monte Carlo run. Based on the above discussion, it can be concluded that the number of users has a negligible impact on the network EE.