# Energy Efficiency Optimization in Massive MIMO Secure Multicast Transmission
## 4 Simulation Results  
To illustrate the performance of the energy efficiency optimization for massive MIMO secure multicast transmission with known statistical CSI. A series of assumptions about the simulation environment, transmission channel and antenna configuration are made in our work [48]. The major parameters related to simulation, such as the power consumption, are listed in Table 1.  
First of all, we evaluate our proposed algorithm convergence performance. In order to observe the convergence of the whole algorithm, we choose the outer iteration to draw Figure 1, which plots energy efficiency versus the number of iterations under different SNR. From Figure 1, it can be observed that our algorithm exhibits fast convergence performance. Besides, the lower the SNR regime is, the quicker the iteration converges. Thus, we can indicate that power allocation might perform better under the high SNR regime on optimizing secure multicast energy efficiency. In the regime of Figure 1, with the SNR increasing, the gain of energy efficiency increases faster, which shows that the secure multicast rate is growing rapidly. Next, we evaluate the energy efficiency performance of the proposed algorithm with a lower bound of secure multicast rate and the original optimization problem with the secure rate obtained by the Monte Carlo Method. It is shown in Figure 2 that the solutions of the two are quite tight. Therefore, we can handle the approximation problem to obtain the desired energy efficiency but significantly reduce the algorithm complexity. Then, we compare the energy efficiency performance optimized by the proposed algorithm with the traditional rate maximization one. In addition, the deterministic equivalent results are compared with those of the Monte Carlo method. According to Figure 2, it is not difficult to find that the gap between the deterministic equivalent and the Monte Carlo methods is almost zero. Besides, under the low transmit power regime, our proposed energy efficiency maximization and the traditional rate maximization algorithms have similar energy efficiency performance. It is also proved that the inference in Figure 1 is correct. However, under the high transmit power regime, the energy efficiency maximization algorithm is obviously superior to the traditional rate maximization one. It also shows that we can find a compromise power allocation to meet the two requirements at the same time in the goal of maximum rate and maximum energy efficiency for massive MIMO secure multicast transmission. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Channel model & 3 GPP SCM \\ Array topology & ULA with half wavelength antenna spacing \\ Propagation scenario & Suburban macro-cell \\ The numbers of BS antennas & \(M=64\) \\ The numbers of UTs & \(K=8\) \\ The numbers of UTs antennas & \(N_{\text{r}}=4\) (\(\forall k\)) \\ The numbers of eavesdropper antennas & \(N_{\text{e}}=4\) \\ Bandwidth & \(W=10\) MHz \\ Amplifier inefficiency factor & \(\xi=5\) \\ Static power consumption & \(P_{\text{s}}=40\) dBm \\ Hardware dissipated power per antenna & \(P_{\text{c}}=30\) dBm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Major simulation parameters of massive multiple-input multiple-output (MIMO) secure multicast transmission. Figure 1: The convergence performance of outer iteration of Algorithm 1 under different signal-to-noise-ratios (SNRs). Figure 2: The lower bound of energy efficiency by energy efficiency maximization and rate maximizations algorithm via using the deterministic equivalent and Monte Carlo methods, compared with the original energy efficiency. Finally, we study the energy efficiency performance of our algorithm versus the numbers of antennas at the BS and show the results in Figure 3. With the number of BS antennas increasing, the change of energy efficiency performance tends to be flat, which shows that the power consumption dominates the performance of energy efficiency when the number of BS antennas is large.