## 2 System Model  
We consider coordinated multicast precoding for multi-cell massive MIMO transmission, as shown in Figure 1. The number of cells in the considered coordinated multi-cell massive MIMO transmission is \(U\) and each cell includes several multiple antenna UTs and a BS, which is equipped with \(M\) antennas. We focus on the case where there is only one multicast group in each cell. Denote by \((k,u)\) the \(k\)th UT in cell \(u\), equipped with \(N_{k,u}\) antennas, and \(\mathcal{K}_{u}\) the UT set in cell \(u\). Let \(\mathbf{x}_{u}\in\mathbb{C}^{M\times 1}\) be the multicast transmitted signal for all the UTs in cell \(u\) by the BS in cell \(u\), then the received signal of UT \((k,u)\) can be written as  
\[\mathbf{y}_{k,u}=\mathbf{H}_{k,u,u}\mathbf{x}_{u}+\sum_{ \begin{subarray}{c} \ell\
eq u\\ \text{inter-cell interference}\end{subarray} }+\mathbf{z}_{k,u}\in\mathbb{C}^{N_{ k,u}\times 1}, \tag{1}\]  
where \(\mathbf{H}_{k,u,\ell}\in\mathbb{C}^{N_{k,u}\times M}\) is the downlink channel matrix between the BS in the \(\ell\)th cell and UT \((k,u)\), and \(\mathbf{z}_{k,u}\in\mathbb{C}^{N_{k,u}\times 1}\) represents the additive complex-valued white Gaussian noise distributed as \(\mathcal{CN}\left(\mathbf{0},\mathbf{I}_{\mathbf{N}_{k,u}}\right)\). Assume that the multicast signal \(\mathbf{x}_{\ell}\) sent by the BS in the \(\ell\)th cell satisfies \(\mathsf{E}\left\{\mathbf{x}_{\ell}\right\}=\mathbf{0}\) and \(\mathsf{E}\left\{\mathbf{x}_{\ell}\mathbf{x}_{\ell}^{H}\right\}=\mathbf{Q}_{ \ell}\in\mathbb{C}^{M\times M}\) where \(\mathbf{Q}_{\ell}\) is the multicast transmit covariance matrix. In this paper, we adopt the jointly correlated Rayleigh fading MIMO channel model [27] (also referred to as [PERSON]'s channel model [28]). Different from the conventional independent and identically distributed MIMO channel model, the adopted jointly correlated MIMO channel model can capture the joint correlation properties of the channels between the transmitter and the receiver. Specifically, the downlink channel matrix from the BS in the \(\ell\)th cell to UT \((k,u)\) is given by  
\[\mathbf{H}_{k,u,\ell}=\mathbf{U}_{k,u,\ell}\mathbf{G}_{k,u,\ell}\mathbf{V}_{k,u,\ell}^{H}, \tag{2}\]  
where \(\mathbf{U}_{k,u,\ell}\in\mathbb{C}^{N_{k,u}\times N_{k,u}}\) and \(\mathbf{V}_{k,u,\ell}\in\mathbb{C}^{M\times M}\) are deterministic unitary matrices, and \(\mathbf{G}_{k,u,\ell}\in\mathbb{C}^{N_{k,u}\times M}\) is a random matrix with independently distributed zero-mean elements. Note that \(\mathbf{G}_{k,u,\ell}\) is referred to as the beam domain channel matrix [29]. The statistics of the beam domain channel matrix \(\mathbf{G}_{k,u,\ell}\) can be described by the following matrix  
\[\mathbf{\Omega}_{k,u,\ell}=\mathbb{E}\left\{\mathbf{G}_{k,u,\ell}\odot\mathbf{ G}_{k,u,\ell}^{*}\right\}\in\mathbb{R}^{N_{k,u}\times M}, \tag{3}\]  
where the elements of \(\mathbf{\Omega}_{k,u,\ell}\) represent the average power of the corresponding beam domain channel elements. Statistical CSI \(\mathbf{\Omega}_{k,u,\ell}\) varies much more slowly than instantaneous CSI \(\mathbf{G}_{k,u,\ell}\). In addition, the channel statistics have been shown to stay constant over a wide frequency interval [30; 31]. Therefore, statistical CSI can be obtained via averaging over time and frequency in a wideband wireless transmission system with guaranteed accuracy and can be adopted to facilitate practical wideband transmission. In massive MIMO systems, when the number of BS antennas \(M\) goes to infinity, the eigenvector matrices of the BS correlation matrices for different links tend to be equal, which only depends on the array topology adopted at the BS [23]. For example, it has been shown in [23] that for the case where the BS is equipped with the uniform linear array (ULA), the eigenvector matrices of the BS correlation matrices will tend to be a discrete Fourier transform (DFT) matrix.