## 2 System Model
### Two-Stage Precoder  
We adopt the two-stage precoder to reduce complexity and feedback overhead induced by large number of antennas [10; 19], which is illustrated in Figure 2. In this case, the linear precoder becomes \(\mathbf{F}\triangleq\mathbf{TV}\), where \(\mathbf{T}\in\mathbb{C}^{M\times S}\) is the outer precoder, which is for spatial division, while \(\mathbf{V}\in\mathbb{C}^{S\times K}\) is the inner precoder, which is for spatial multiplexing in each group. The outer and the inner precoders are given by \(\mathbf{T}\triangleq[\mathbf{T}_{1},\ldots,\mathbf{T}_{G}]\) and \(\mathbf{V}\triangleq\text{bldiag}\{\mathbf{V}_{1},...,\mathbf{V}_{G}\}\), respectively, where \(\mathbf{T}_{g}\in\mathbb{C}^{M\times s_{g}}\) and \(\mathbf{V}_{g}\in\mathbb{C}^{s_{g}\times K_{g}}\) are the outer and inner precoder of the \(g\)-th group, respectively, where \"bldiag\" denotes block-diagonalized matrix. Here, the dimension of effective channels, i.e., \(S\triangleq\sum_{g=1}^{G}s_{g}\), is a design parameter, where \(s_{g}\) is the reduced-dimension of the effective channel for the \(g\)-th group to be optimized. We denote by \(\mathbf{H}_{\mathbf{g}}\triangleq[\mathbf{h}_{g,1},\ldots,\mathbf{h}_{g,K_{g}}]\) the channel matrix of the \(g\)-th group. Then, the concatenated channel matrix is represented by \(\mathbf{H}=[\mathbf{H}_{1},...,\mathbf{H}_{G}]\). For given channel covariance matrices, the dimension-reduced effective channel after outer precoding is represented as follows:  
\[\mathbf{H}^{\text{eff}}\triangleq\mathbf{T}^{\dagger}\mathbf{H}\triangleq \begin{bmatrix}\mathbf{T}_{1}^{\dagger}\mathbf{H}_{1}&\mathbf{T}_{1}^{ \dagger}\mathbf{H}_{2}&\cdots&\mathbf{T}_{1}^{\dagger}\mathbf{H}_{G}\\ \mathbf{T}_{2}^{\dagger}\mathbf{H}_{1}&\mathbf{T}_{2}^{\dagger}\mathbf{H}_{2} &\cdots&\mathbf{T}_{2}^{\dagger}\mathbf{H}_{G}\\ \vdots&\vdots&\ddots&\vdots\\ \mathbf{T}_{G}^{\dagger}\mathbf{H}_{1}&\mathbf{T}_{G}^{\dagger}\mathbf{H}_{2} &\cdots&\mathbf{T}_{G}^{\dagger}\mathbf{H}_{G}\end{bmatrix} . \tag{4}\]  
Note that it is difficult to acquire the CDI of the whole effective channel \(\mathbf{H}^{\text{eff}}\) at the BS due to the heavy channel feedback overhead. Thus, we focus on a more practical approach with low computational complexity, which quantizes and feeds back only the dimension-reduced effective  
Figure 2: Illustration of the two-stage precoder with limited feedback. channel of each group, i.e., \(\mathbf{H}_{g}^{\text{eff}}(\triangleq\mathbf{T}_{g}^{\dagger}\mathbf{H}_{g}) \in\mathbb{C}^{s_{g}\times K_{g}}\), whose dimension is determined by \(s_{g}\). Consequently, the received signal at user \(k\) in the \(g\)-th group is given by  
\[y_{g,k}=\sqrt{\frac{\overline{P}}{K}}\mathbf{h}_{g,k}^{\dagger}\mathbf{T}_{g} \mathbf{v}_{g,k}d_{g,k}+\underbrace{\sqrt{\frac{\overline{P}}{K}}\mathbf{h}_{g,k}^{\dagger}\sum_{i\
eq k}^{K_{g}}\mathbf{T}_{g}\mathbf{v}_{g,i}d_{g,i}}_{ \text{same group interference (SGI)}}+\underbrace{\sqrt{\frac{\overline{P}}{K}}\mathbf{h}_{g,k}^{\dagger} \sum_{c\
eq g}^{G}\sum_{j=1}^{K_{g}}\mathbf{T}_{c}\mathbf{v}_{cj}d_{c,j}}_{ \text{inter-group interference (IGI)}}+n_{g,k}, \tag{5}\]  
where \(\mathbf{v}_{g,k}\) and \(\mathbf{v}_{g,i}\) are the beamforming vectors of user \(k\) and user \(j(\
eq k)\) in the \(g\)-th group, respectively, which consist of the inner precoder for the \(g\)-th group represented by \(\mathbf{V}_{g}=[\mathbf{v}_{g,1},...,\mathbf{v}_{g,K_{g}}];\mathbf{v}_{c,j}\) is the beamforming vector of the \(j\)-th user in group \(c(\
eq g)\), i.e., \(\mathbf{V}_{c}=[\mathbf{v}_{c,1},...,\mathbf{v}_{c,K_{c}}]\); \(n_{g,k}\) is a complex Gaussian noise with zero mean and variance \(\sigma^{2}\), i.e., \(n_{g,k}\sim\mathcal{CN}(0,\sigma^{2})\). Note that the second and third terms on the right-hand side of (5) are the same-group interference (SGI) and inter-group interference (IGI), respectively.