## 3 Proposed Algorithms
### The BCD Method for the CP Scheme
To address the non-convex QoS constraints, method of SOCP is employed to effectuate a further transformation of the constraint condition (6e) into:  
\[\mathfrak{I}\Big{\{}\Big{(}\mathbf{h}_{Bl}^{H}+\boldsymbol{\theta }^{H}H_{l}\Big{)}\mathbf{w}_{l}\Big{\}} =0, \tag{9}\] \[\sqrt{1+\frac{1}{\Gamma_{min}}}\mathfrak{R}\Big{\{}\Big{(} \mathbf{h}_{Bl}^{H}+\boldsymbol{\theta}^{H}H_{l}\Big{)}\mathbf{w}_{l}\Big{\}} \geq\Big{\|}\Big{(}\mathbf{h}_{Bl}^{H}+\boldsymbol{\theta}^{H}\mathbf{H}_{l} \Big{)}\mathbf{W}\;\sigma^{2}\Big{\|}, \tag{10}\]  
where \(\mathbf{W}=[\mathbf{w}_{T},\mathbf{w}_{R}]\). Upon holding constant any value within the set of parameters \(\mathbf{w}_{l}\) or \(\boldsymbol{\theta}_{l}\), the aforementioned constraint assumes the form of an elliptical constraint. Based on the above equation, with fixed \(\boldsymbol{\theta}_{l}\) we can reformulate (6a)-(6f) as  
\[\min_{\boldsymbol{\theta}_{l},\mathbf{w}_{l}}\sum_{l}\phi_{l}R_{l} ^{SEC}\] (11a) \[d_{l}^{2} =\frac{d_{l}^{1}\Big{|}\Big{(}\mathbf{h}_{Bl}^{H}+\boldsymbol{ \theta}_{l}^{{}^{H}H}\mathbf{H}_{l}\Big{)}\mathbf{w}_{l}^{*}\Big{|}^{2}}{\Big{|} \Big{(}\mathbf{h}_{Bl}^{H}+\boldsymbol{\theta}_{l}^{{}^{H}H}\mathbf{H}_{l} \Big{)}\mathbf{w}_{l}^{*}\Big{|}^{2}+\Big{|}\Big{(}\mathbf{h}_{Bl}^{H}+ \boldsymbol{\theta}_{l}^{{}^{H}H}\mathbf{H}_{l}\Big{)}\mathbf{w}_{l^{\prime} }^{*}\Big{|}^{2}+\sigma^{2}},\]0 (11b) \[\eqref{eq:eq:eq:eq:eq:eq:eq:eq:eq:eq:eq:eq:eq:eq:eq:eq:eq:eq:eq:eq:eq:eq:eq: eq  
Nextly, we define \(\widetilde{\mathbf{\vartheta}}_{l}=diag\Big{(}\widetilde{\mathbf{\psi}}_{l}^{H}\Big{)}(- \mathbf{\theta}_{l}+\rho\lambda_{l})\), \(a_{n}=\bigg{|}\widetilde{\mathbf{\vartheta}}_{T}^{*}\Big{|}cos\Big{(}\angle \widetilde{\mathbf{\vartheta}}_{T}^{*}\Big{)}\), \(b_{n}=\bigg{|}\widetilde{\mathbf{\vartheta}}_{R}^{*}\Big{|}\)\(sin\Big{(}\angle\widetilde{\mathbf{\vartheta}}_{R}^{*}\Big{)}\), \(\xi_{n}=sgn(b_{n})arccos\Big{(}\frac{a_{n}}{\sqrt{a_{n}^{2}+b_{n}^{2}}}\Big{)}\), then, for any given \(\widetilde{\mathbf{\psi}}_{T}\) and \(\widetilde{\mathbf{\psi}}_{R^{\prime}}\), the optimal solutions for the elements of \(\widetilde{\mathbf{\beta}}_{T}\) and \(\widetilde{\mathbf{\beta}}_{R}\) are given by  
\[\left\{ \begin{array}{l}\widetilde{\mathbf{\beta}}_{T,m}^{*}=sin(\omega_{n}),\\ \widetilde{\mathbf{\beta}}_{R,m}=cos(\omega_{n}).\end{array} \right. \tag{16}\]  
where  
\[\omega_{n}=\left\{ \begin{array}{l}-\frac{1}{2}\pi-\xi_{n},\quad\text{if }\xi_{n} \in\left[-\pi,-\frac{1}{2}\pi\right),\\ 0,\quad\quad\text{if }\xi_{n}\in\left[-\frac{1}{2}\pi,\frac{1}{4}\pi \right),\\ \frac{1}{2}\pi,\quad\quad\text{otherwise}.\end{array} \right. \tag{17}\]  
Finally, in accordance with the PDD framework, the dual variables \(\{\lambda_{T},\lambda_{R}\}\) and the penalty factor \(\rho\) are subject to iterative updating. The overall procedure is given in Algorithm 1, where \(R^{(q)}\) denotes the obtained WSSR in the \(q\)-th iteration, and \(\eta\) denotes the stopping threshold, \(\delta=max\Big{\{}\bigg{\|}\mathbf{\theta}_{T}-\widetilde{\mathbf{\theta}}_{T}\bigg{\|},\bigg{\|}\mathbf{\theta}_{R}-\widetilde{\mathbf{\theta}}_{R}\bigg{\|}\Big{\}}\) denotes the constraint violation function. ```
1:Set feasible variables \(\left\{\mathbf{\mathrm{w}}_{l}^{(0)},\mathbf{\theta}_{l}^{(0)}\right\}\) and \(q=0\). 2:repeat
3:repeat
4: (a) Obtain \(\left\{\mathbf{\mathrm{w}}_{T}^{(q)},\mathbf{\mathrm{w}}_{R}^{(q)}\right\}\) via solving (11a) and (11b) using CVX, with fixed \(\left\{\mathbf{\theta}_{l}^{(q-1)},\mathbf{\mathrm{w}}_{l}^{(q-1)}\right\}\). 5: (b) Obtain \(\left\{\mathbf{\mathrm{\theta}}_{T}^{(q)},\mathbf{\mathrm{\theta}}_{R}^{(q)}\right\}\) via solving (12a)-(12c) using CVX, with fixed \(\left\{\mathbf{\mathrm{w}}_{l}^{(q)},\mathbf{\mathrm{\theta}}_{l}^{(q-1)}\right\}\). 6: (c) update \(\widetilde{\mathbf{\psi}}_{l}\) by (14). 7: (d) update \(\widetilde{\mathbf{\beta}}_{l}\) by (16). 8: (e) \(q\gets q+1\). 9: (f) Calculate WSSR \(R^{(q)}\) by (6a). 10: until\(R^{(q)}-R^{(q-1)}<\kappa\).