Algorithm 3 Alternating optimization for solving Problem (30)

1:Initialize iteration index $l=0$ and the $({\mathbf{\varphi }}^{\mathit{l}},{\mathit{p}}^{\mathit{l}},{\tau }_e^l)$ satisfying the constraints in (15). 2:while The improvement of $\eta$ is higher than a predefined threshold ${ϵ}_2$ do. 3:    Solve Problem (16) given $({\mathit{p}}^{\mathit{l}},{\tau }_e^l)$ and obtain the optimal solution ${\mathbf{\varphi }}^{\mathit{l}+\mathbf{1}}$. 4:    Solve Problem (27) given $({\mathbf{\varphi }}^{\mathit{l}+\mathbf{1}},{\tau }_e^l)$ and obtain the optimal solution ${\mathit{p}}^{\mathit{l}+\mathbf{1}}$. 5:    Solve Problem (30) given $({\mathbf{\varphi }}^{\mathit{l}+\mathbf{1}},{\mathit{p}}^{\mathit{l}+\mathbf{1}})$ and obtain the optimal solution ${\tau }_e^{l+1}$. 6:    Update $l=l+1$. 7:return The optimal beamwidth ${\mathbf{\varphi }}^{*}$, transmit power ${\mathit{p}}^{*}$, and EH time ratio ${\tau }_e^{*}$.