## 3 Proposed Algorithm
By substituting \(\mathbf{w}_{j}\triangleq\tilde{\mathbf{w}}_{j}+\Delta\mathbf{w}_{j}\), \(\mathbf{z}\triangleq\tilde{\mathbf{z}}+\Delta\mathbf{z}\) and \(\mathbf{v}_{m}\triangleq\tilde{\mathbf{v}}_{m}+\Delta\mathbf{v}_{m}\) into the LHS of (24) and (25), we have  
\[s.t.\ \log\left(1+\frac{\rho_{k}\mathbf{h}_{e,k}^{H}\mathbf{w}_{k} \mathbf{w}_{k}^{H}\mathbf{h}_{c,k}}{\rho_{k}\big{(}\mathbf{h}_{c,k}^{H}(\sum_ {j\
eq k}\mathbf{w}_{j}\mathbf{w}_{j}^{H}\mathbf{+z}\mathbf{z}^{H})\mathbf{h} _{c,k}\mathbf{+}\mathbf{g}_{c,k}^{H}\sum_{m=1}^{M}(\mathbf{v}_{m}\mathbf{v}_{ m}^{H})\mathbf{g}_{c,k}\mathbf{+}\sigma_{a,k}^{2}\big{)}\mathbf{+}\delta_{p,k}^{2}}\right)\]7 \[s.t.\ \log\left(1+\frac{\rho_{k}\mathbf{h}_{e,k}^{H}\mathbf{w}_{k} \mathbf{w}_{k}^{H}\mathbf{h}_{c,k}}{\rho_{k}\big{(}\mathbf{h}_{c,k}^{H}(\sum_ {j\
eq k}\mathbf{w}_{j}\mathbf{w}_{j}^{H}\mathbf{+z}\mathbf{z}^{H})\mathbf{h} _{c,k}\mathbf{+}\mathbf{g}_{c,k}^{H}\sum_{m=1}^{M}(\mathbf{v}_{m}\mathbf{v}_{ m}^{H})\mathbf{g}_{c,k}\mathbf{+}\sigma_{a,k}^{2}\big{)}\mathbf{+}\delta_{p,k}^{2}}\right)\]8 \[s.t.\ \log\left(1+\frac{\rho_{k}\mathbf{h}_{e,k}^{H}\mathbf{w}_{k} \mathbf{w}_{k}^{H}\mathbf{h}_{c,k}}{\rho_{k}\big{(}\mathbf{h}_{c,k}^{H}(\sum_ {j\
eq k}\mathbf{w}_{j}\mathbf{w}_{j}^{H}\mathbf{+z}\mathbf{z}^{H})\mathbf{h} _{c,k}\mathbf{+}\mathbf{g}_{c,k}^{H}\sum_{m=1}^{M}(\mathbf{v}_{m}\mathbf{v}_{ m}^{H})\mathbf{g}_{c,k}\mathbf{+}\sigma_{a,k}^{2}\big{)}\mathbf{+}\delta_{p,k}^{2}}\right)\]9 \[\qquad-\log\left|\mathbf{I}+\big{(}\sigma_{e,l}^{2}\mathbf{I}+ \mathbf{H}_{e,l}^{H}\big{(}\sum_{j\
eq k}\mathbf{w}_{j}\mathbf{w}_{j}^{H} \mathbf{+z}\mathbf{z}^{H}\big{)}\mathbf{H}_{e,l}\mathbf{+}\mathbf{G}_{e,l}^{ H}\sum_{m=1}^{M}\big{(}\mathbf{v}_{m}\mathbf{v}_{m}^{H})\mathbf{G}_{e,l}\big{)}^{-1} \mathbf{H}_{e,l}^{H}\mathbf{w}_{k}\mathbf{w}_{k}^{H}\mathbf{H}_{e,l}\right| \geq\bar{R}^{c},\]0  
where the inequality is achieved by removing the quadratic terms \(\sum_{j=1}^{K}\Delta\mathbf{w}_{j}^{H}\mathbf{H}_{k}\Delta\mathbf{w}_{j}\), \(\Delta\mathbf{z}^{H}\mathbf{H}_{k}\Delta\mathbf{z}\) and \(\sum_{m=1}^{M}\Delta\mathbf{v}_{m}^{H}\mathbf{G}_{c,k}\Delta\mathbf{v}_{m}\). Similarly, for the LHS of (25), it follows  
\[ \begin{split}&\sum_{j=1}^{K}\mathbf{w}_{j}^{H}\mathbf{\tilde{H}}_{e,l} \mathbf{w}_{j}+\mathbf{z}^{H}\mathbf{\tilde{H}}_{e,l}\mathbf{z}+\sum_{m=1}^{M} \mathbf{v}_{m}^{H}\mathbf{\tilde{G}}_{e,l}\mathbf{v}_{m}\\ &=\sum_{j=1}^{K}(\mathbf{\tilde{w}}_{j}+\Delta\mathbf{w}_{j})^{H} \mathbf{\tilde{H}}_{e,l}(\mathbf{\tilde{w}}_{j}+\Delta\mathbf{w}_{j})+( \mathbf{\tilde{z}}+\Delta\mathbf{z})^{H}\mathbf{\tilde{H}}_{e,l}(\mathbf{ \tilde{z}}+\Delta\mathbf{z})+\sum_{m=1}^{M}(\mathbf{\tilde{v}}_{m}+\Delta \mathbf{v}_{m})^{H}\mathbf{\tilde{G}}_{e,l}(\mathbf{\tilde{v}}_{m}+\Delta \mathbf{v}_{m})\\ &\geq\sum_{j=1}^{K}\left(\mathbf{\tilde{w}}_{j}^{H}\mathbf{\tilde {H}}_{e,l}\mathbf{\tilde{w}}_{j}+2\Re\{\mathbf{\tilde{w}}_{j}^{H}\mathbf{ \tilde{H}}_{l}\Delta\mathbf{w}_{j}\}\right)+\mathbf{\tilde{z}}^{H}\mathbf{ \tilde{H}}_{e,l}\mathbf{\tilde{z}}+2\Re\{\mathbf{\tilde{z}}^{H}\mathbf{\tilde {H}}_{e,l}\Delta\mathbf{z}\}\\ &+\sum_{m=1}^{M}(\mathbf{\tilde{v}}_{m}^{H}\mathbf{\tilde{G}}_{e, l}\mathbf{\tilde{v}}_{m}+2\Re\{\mathbf{\tilde{v}}_{m}^{H}\mathbf{\tilde{G}}_{e,l} \Delta\mathbf{v}_{m}\}).\end{split}  \tag{27}\]  
Based on (26) and (27), the linear approximations of the concave constraints (24) and (25) can be obtained as  
\[ \begin{split}&\sum_{j=1}^{K}\left(\mathbf{\tilde{w}}_{j}^{H}\mathbf{H }_{e,k}\mathbf{\tilde{w}}_{j}+2\Re\{\mathbf{\tilde{w}}_{j}^{H}\mathbf{H}_{e,k} \Delta\mathbf{w}_{j}\}\right)+\mathbf{\tilde{z}}^{H}\mathbf{H}_{c,k}\mathbf{ \tilde{z}}+2\Re\{\mathbf{\tilde{z}}^{H}\mathbf{H}_{c,k}\Delta\mathbf{z}\}\\ &\quad+\sum_{m=1}^{M}(\mathbf{\tilde{v}}_{m}^{H}\mathbf{G}_{e,k} \mathbf{\tilde{v}}_{m}+2\Re\{\mathbf{\tilde{v}}_{m}^{H}\mathbf{G}_{e,k} \Delta\mathbf{v}_{m}\})\geq\frac{\tilde{E}^{c}}{\eta_{k}(1-\rho_{k})}-\sigma_ {a,k}^{2},\forall k.\end{split}  \tag{28}\]  
\[