and can be expressed as $$\label{eq_g_0}\mathbf{G}=\mathbf{D}^{1/2}\mathbf{H}\mathbf{R}^{1/2},$$ where $\mathbf{H}\in\mathbb{C}^{K\times M}$ is the SSF matrix with independent and identically distributed (i.i.d.) $\mathcal{CN}(0,1)$ entries, and the diagonal matrix $\mathbf{D}\in\mathbb{R}^{K\times K}$ contains the LSF coefficients $\beta_k$ along its main diagonal. We model the LSF of the $k$-th active-UE as[^3] $\beta_k=cd_k^{-\alpha},k=1,\dots,K$, in which $d_k$ is the distance from the $k$-th active-UE to the BS, $\alpha$ is the pathloss exponent and $c$ is the pathloss at the reference distance. The transmit correlation matrix at the BS is modeled by the widely used $\delta$-Kac-Murdock-Szeg? matrix $\mathbf{R}$, in which $\delta$ is the antenna correlation coefficient[@Zelst02asingle].

The system operates in the TDD mode and the BS obtains the SSF CSI relying on the training-based channel estimation. The estimation $\hat{\mathbf{H}}$ of the SSF CSI matrix $\mathbf{H}$ is modeled as $$\label{eq_h_0}\mathbf{H}=\hat{\mathbf{H}}+\tilde{\mathbf{H}},$$where the $K\times M$ dimensional estimated channel matrix $\hat{\mathbf{H}}=[\hat{\mathbf{h}}_1^T,\cdots,\hat{\mathbf{h}}_K^T]^T$ and the $K\times M$ dimensional error matrix $\tilde{\mathbf{H}}=[\tilde{\mathbf{h}}_1^T,\cdots,\tilde{\mathbf{h}}_K^T]^T$ can be expressed as $$\label{eq_ce_0}\hat{\mathbf{H}}=\sqrt{1-\rho}\mathbf{Z}_1,\quad\tilde{\mathbf{H}}=\sqrt{\rho}\mathbf{Z}_2,\quad 0\leq\rho\leq 1.$$$\hat{\mathbf{h}}_k\in\mathbb{C}^{1\times M}$ and $\tilde{\mathbf{h}}_k\in\mathbb{C}^{1\times M}$ are the $k$-th rows of $\hat{\mathbf{H}}$ and $\tilde{\mathbf{H}}$, respectively. Both $\mathbf{Z}_1\in\mathbb{C}^{K\times M}$ and $\mathbf{Z}_2\in\mathbb{C}^{K\times M}$ are composed of i.i.d. $\mathcal{CN}(0,1)$ entries, and the two matrices are independent with each other[^4]. We assume that the LSF CSI of each UE and the transmit correlation 