Btukfyl

begin{align} maxlimits_{bm{P}^{(k)}} & R_k(bm{P}^{(k)})=sumlimits_{jin c^{(k)}}text{log}_2left(1+frac{p_j^{(k)}g_{j,j}^{(k)}}{sigma_N^2+sumlimits_{j'=1,j'neq j}^{vert mathcal{C}^{(k)}vert}p_{j'}^{(k)}h_{j',j}^{(k)}+p_{b}^{(k)}h_{b,j}^{(k)}}right) nonumber\ text{s.t}. &C_{1}:0le p_{b}^{(k)}leq P_{b}^{max}nonumber\ &C_{2}:0leq p_{j}^{(k)}leq P_{d}^{max},~~forall jin c^{(k)}nonumber\ &C_{3}:text{log}_2(1+frac{p_b^{(k)}g_{b,n}^{(k)}}{sigma_N^2+sumlimits_{jin c^{(k)}}p_j^{(k)}h_{j,b}^{(k)}})geq R_{b,min}label{powerprob}end{align}

begin{align} maxlimits_{bm{P}^{(k)}} & R_k(bm{P}^{(k)})=sumlimits_{jin c^{(k)}}text{log}_2left(1+frac{p_j^{(k)}g_{j,j}^{(k)}}{sigma_N^2+sumlimits_{j'=1,j'neq j}^{vert mathcal{C}^{(k)}vert}p_{j'}^{(k)}h_{j',j}^{(k)}+p_{b}^{(k)}h_{b,j}^{(k)}}right) nonumber\ text{s.t}. &C_{1}:0le p_{b}^{(k)}leq P_{b}^{max}nonumber\ &C_{2}:0leq p_{j}^{(k)}leq P_{d}^{max},~~forall jin c^{(k)}nonumber\ &C_{3}:text{log}_2(1+frac{p_b^{(k)}g_{b,n}^{(k)}}{sigma_N^2+sumlimits_{jin c^{(k)}}p_j^{(k)}h_{j,b}^{(k)}})geq R_{b,min}label{powerprob}end{align}

begin{align} maxlimits_{bm{P}^{(k)}} & R_k(bm{P}^{(k)})=sumlimits_{jin c^{(k)}}text{log}_2left(1+frac{p_j^{(k)}g_{j,j}^{(k)}}{sigma_N^2+sumlimits_{j'=1,j'neq j}^{vert mathcal{C}^{(k)}vert}p_{j'}^{(k)}h_{j',j}^{(k)}+p_{b}^{(k)}h_{b,j}^{(k)}}right) nonumber\ text{s.t}. &C_{1}:0le p_{b}^{(k)}leq P_{b}^{max}nonumber\ &C_{2}:0leq p_{j}^{(k)}leq P_{d}^{max},~~forall jin c^{(k)}nonumber\ &C_{3}:text{log}_2(1+frac{p_b^{(k)}g_{b,n}^{(k)}}{sigma_N^2+sumlimits_{jin c^{(k)}}p_j^{(k)}h_{j,b}^{(k)}})geq R_{b,min}label{powerprob}end{align}

begin{align} maxlimits_{bm{P}^{(k)}} & R_k(bm{P}^{(k)})=sumlimits_{jin c^{(k)}}text{log}_2left(1+frac{p_j^{(k)}g_{j,j}^{(k)}}{sigma_N^2+sumlimits_{j'=1,j'neq j}^{vert mathcal{C}^{(k)}vert}p_{j'}^{(k)}h_{j',j}^{(k)}+p_{b}^{(k)}h_{b,j}^{(k)}}right) nonumber\ text{s.t}. &C_{1}:0le p_{b}^{(k)}leq P_{b}^{max}nonumber\ &C_{2}:0leq p_{j}^{(k)}leq P_{d}^{max},~~forall jin c^{(k)}nonumber\ &C_{3}:text{log}_2(1+frac{p_b^{(k)}g_{b,n}^{(k)}}{sigma_N^2+sumlimits_{jin c^{(k)}}p_j^{(k)}h_{j,b}^{(k)}})geq R_{b,min}label{powerprob}end{align}

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