Algorithm 3: Design algorithm of the digital beamforming matrix and the analog beamforming matrix.

Main algorithm: MM-AltOpt algorithm. Input: Hybrid beamforming matrix $\mathit{F}$, initial: ${\mathit{F}}_{RF}^{\left(n=0\right)}\in \mathbb{F}$, iteration index $n=0$, threshold ${\epsilon }_3={10}^{-3}$, the solution of the objective function of the problem $P_1$ in the $n\mathrm{th}$ iteration is ${\delta }^{\left(n\right)}$. 1. while $\left|{\delta }^{\left(n\right)}-{\delta }^{\left(n-1\right)}\right|\ge {\epsilon }_3$ 2.   Based on ${\mathit{F}}_{RF}^{\left(n\right)}$, calculate ${\mathit{F}}_{BB}^{\left(n+1\right)}$ according to ${\mathit{F}}_{BB}={\left({\mathit{F}}_{RF}^{\left(n\right)H}{\mathit{F}}_{RF}^{\left(\left(n\right)\right)}\right)}^{-1}{\mathit{F}}_{RF}^{\left(n\right)H}\mathit{F}$. 3.   Based on ${\mathit{F}}_{BB}^{\left(n+1\right)}$, calculate ${\mathit{F}}_{RF}^{\left(n+1\right)}$ according to the inner algorithm. 4.   Set $n=n+1$. 5. end Output: ${\mathit{F}}_{RF}$,${\mathit{F}}_{BB}$, normalize ${\mathit{F}}_{BB}=\frac{\sqrt{P_T}}{{‖{\mathit{F}}_{{}_{RF}}{\mathit{F}}_{BB}‖}_{\mathit{F}}}{\mathit{F}}_{BB}$. Inner algorithm: Algorithm for solving the analog beamforming matrix. Input: Hybrid beamforming matrix $\mathit{F}$, ${\mathit{F}}_{BB}^{\left(n\right)}$, ${\mathit{F}}_{RF}^{\left(q=0\right)}\in \mathbb{F}$, iteration index $q=0$, threshold ${\epsilon }_4={10}^{-3}$, the solution of the objective function of the problem $P_5$ in the $q\mathrm{th}$ iteration is ${\delta }_1^{\left(q\right)}$. 1. while $\left|{\delta }^{\left(n\right)}-{\delta }^{\left(n-1\right)}\right|\ge {\epsilon }_4$ 2.     Calculate $C^{\left(q\right)}={\mathit{F}}_{BB}^{\left(n\right)}{\mathit{F}}^H-\left({\mathit{F}}_{BB}^{\left(n\right)}{\mathit{F}}_{BB}^{\left(n\right)}{}^H-{\lambda }_{\max }\left({\mathit{F}}_{BB}^{\left(n\right)}{\mathit{F}}_{BB}^{\left(n\right)}{}^H\right)\mathit{I}\right){\mathit{F}}_{RF}^{\left(q\right)H}$. 3.     Calculate ${\mathit{F}}_{RF}^{}=e^{-j\arg \left(C^{\left(q\right)T}\right)}$. 4.     Set $q=q+1$. 5. end Output: ${\mathit{F}}_{RF}^{\left(n\right)}$.