## 4 Simulation Results  
Numerical results are presented to evaluate the performance of our proposed coordinated multicast precoding for multi-cell massive MIMO transmission. We adopt the WINNER II channel model in the suburban macro-cell propagation environment in the simulation [37]. We adopt the \(120^{\circ}\) tri-sector cellular model. We focus on a coordinated network which is composed \(U=3\) neighbouring sectors and assume that the user terminals are uniformly distributed in each sector. The number of multicast UTs in each sector is \(|\mathcal{K}_{u}|=4\). The BSs and UTs are all equipped with the ULAs with half wavelength antenna spacing. The numbers of antennas at the BSs and UTs are set to be \(M=128\) and \(N_{k,u}=4\left(\forall k,u\right)\), respectively. The power budgets in all cells are set to be equal as \(P_{u}=P\left(\forall u\right)\), and the signal-to-noise ratio (SNR) is defined as \(P\). The major simulation setup parameters are listed in Table 1.  
We first evaluate the convergence performance of the proposed iterative coordinated power allocation procedure in Algorithm 1. We can observe from Figure 2 that the proposed algorithm exhibits very fast convergence performance under different values of SNRs. We then compare the performance of the proposed coordinated multi-cell multicast precoding approach with that of the conventional uncoordinated approach, where the BSs do not coordinate and the inter-cell interference is not taken into account in precoding optimization. We consider two specific UT distribution cases. In Case A, all UTs are randomly distributed within the associated cell, as shown in Figure 3, and in Case B, all UTs are randomly distributed within a circle with a radius of 0.2 times the cell radius from the corresponding BS, as shown in Figure 4. We can observe from Figure 5 that the proposed coordinated approach outperforms the conventional uncoordinated approach, especially in the high SNR regime where the inter-cell interference dominates. In addition, the performance gain of the proposed coordinated approach over the conventional uncoordinated approach in Case A is larger than that in Case B, which shows that our proposed coordinated multicast approach is especially beneficial for cell-edge UTs. The accuracy of the DE results compared with the Monte-Carlo results in a wide range of SNRs is also verified in Figure 5. \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Value** \\ \hline Channel model & WINNER II \\ Scenario & Suburban macro-cell \\ Array topology & ULA with half wavelength antenna spacing \\ Number of Sectors & \(U=3\) \\ Number of BS antennas & \(M=128\) \\ Number of UTs in each sector & \(|\mathcal{K}_{u}|=4\) (\(\forall u\)) \\ Number of UT antennas & \(N_{k,u}=4\) (\(\forall k,u\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Setup Parameters. Figure 2: Convergence performance of Algorithm 1 for different values of SNRs. Figure 4: Illustrative schematic diagram of the UT. distributions considered in Case B where UTs are randomly distributed within a circle with a distance of 0.2 times the cell radius from the corresponding BS (unit: meter). Figure 3: Illustrative schematic diagram of the UT distributions considered in Case A where UTs are randomly distributed within each cell (unit: meter). We evaluate the performance of the proposed coordinated approach for different numbers of BS antennas in Figure 6. We can observe from Figure 6 that the coordinated multicast sum rate performance increases as the number of BS antennas increases. In addition, the DE results exhibit similar performance as the Monte-Carlo results with typical numbers of BS antennas in massive MIMO. Finally, we compare the performance of our proposed statistical CSI approach with that of the full CSI approach where the BSs can know the instantaneous CSI of all the UTs in the coordinated network. We can observe from Figure 7 that there exits a performance gap between our proposed approach and the full CSI approach.