Algorithm 2 Beamspace WMMSE Precoding

Input: ${\{{\widehat{\mathbf{g}}}_k,{\gamma }_k,{\sigma }_k,{\beta }_k\}}_{\forall k}$, $P_{\mathrm{T}}$, $I_{max}$, $\chi$.   1: Initialize:    1-a: $i\leftarrow 0$.    1-b: ${\overline{R}}_k\leftarrow 0$, $\forall k\in \mathcal{K}$.   2: while $i<I_{max}$ do   3:      $i\leftarrow i+1$.   4:      ${\overline{R}}_k^{\prime }\leftarrow {\overline{R}}_k$, $\forall k\in \mathcal{K}$.   5:      Update $u_k^{★}$ as in (32).   6:      Update $m_k^{★}$ as in (34).   7:      Update $p_k^{★}$ as in (37).   8:      Calculate ${\overline{R}}_k$ as described in (14).   9:      if ${\displaystyle \frac{{\sum }_{k=1}^K{\beta }_k({\overline{R}}_k-{\overline{R}}_k^{\prime })}{{\sum }_{k=1}^K{\beta }_k{\overline{R}}_k^{\prime }}}\le \chi$ then 10:         break 11:      end if 12: end while Output:  $\mathbf{P}$.