# Energy-Efficient Multicast Precoding for Massive MIMO Transmission with Statistical CSI
## 4 Numerical Results  
Extensive numerical results are provided in this section to corroborate the performance of the proposed energy-efficient multicast precoding for massive MIMO transmission with only statistical CSI available at the BS. In the simulation, we adopt the 3 GPP SCM channel model and the suburban macro-cell propagation scenario [30]. In addition, both the BS and the UTs are equipped with the uniform linear arrays (ULAs) where the antennas are spaced with half wavelength. We list the major simulation parameters in Table 1.  
Firstly, the convergence performance of the proposed energy-efficient multicast power allocation algorithm is evaluated in Figure 1. We can observe from Figure 1 that the proposed energy-efficient multicast power allocation algorithm converges very rapidly for different values of multicast power budget \(P_{\max}\). Usually, the proposed algorithm converges after very few iterations. In addition, we can observe that the proposed multicast power allocation algorithm achieves near-optimal EE performance.  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Value** \\ \hline Channel model & 3 GPP SCM \\ Propagation scenario & Suburban macro-cell \\ Pathloss & \(-120\) dB (\(\forall k\)) \\ Array topology & ULA with half wavelength antenna spacing \\ Number of antennas at the BS & \(M=128\) \\ Number of UTs & \(K=8\) \\ Number of antennas at the UTs & \(N_{k}=4\) (\(\forall k\)) \\ Bandwidth & \(W=10\) MHz \\ Amplifier inefficiency factor & \(\zeta=5\) \\ Hardware dissipated power per antenna & \(P_{\rm c}=30\) dBm \\ Static power consumption & \(P_{\rm s}=40\) dBm \\ Noise variance & \(\sigma^{2}=-131\) dBm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation Setup Parameters.  
Figure 1: Convergence performance of the proposed energy-efficient multicast power allocation algorithm for different values of multicast power budget \(P_{\max}\).  
We then compare the EE performance of the proposed EE maximization approach with that of the rate maximization approach which aims to maximize the achievable ergodic multicast rate in Figure 2. We can observe from Figure 2 that the proposed EE maximization approach and the conventional rate maximization approach achieve similar EE performance in the low transmit power regime, which indicates that using the maximum power budget is almost EE optimal. Meanwhile, in the high transmit power regime, our proposed EE maximization approach significantly outperforms the conventional rate maximization approach. In addition, we can also observe that the proposed DE result is quite accurate compared with the Monte-Carlo results in a wide range of power budget values.  
Finally, the EE performance of our proposed approach versus the number of BS antennas is evaluated in Figure 3. We can observe from Figure 3 that the EE performance of our proposed approach will reduce as the number of BS antennas \(M\) increases, which indicates that power consumption dominates the EE performance in the case with large numbers of antennas.  
Figure 2: Comparison of the EE performance between the proposed EE maximization approach and the conventional multicast rate maximization approach. The depicted results are shown versus the multicast power budget \(P_{\text{max}}\). The DE results of both approaches are also depicted.