Algorithm 1: Successive refinement algorithm

Initialize: $\mathbf{\Theta }={\mathbf{\Theta }}^{\left(0\right)}$ Setup: $k=0$, $R^{(0)}={\log }_2\left(1+{\displaystyle \frac{P\Vert h_d+H_{br}\Theta h_{rv}{\Vert }^2}{N_0}}\right)$ While $|R^{(k)}-R^{(k-1)}|>ϵ$ do                   for $n=0$ to $N$ do ${\theta }_n^{*}=\arg {\min }_{\theta \in \mathcal{F}}|\theta -k_n|$ $k=k+1$ $R^{(k)}={\log }_2\left(1+{\displaystyle \frac{P\Vert {\mathbf{h}}_d+{\mathbf{H}}_{br}\mathbf{\Theta }{\mathbf{h}}_{rv}{\Vert }^2}{N_0}}\right)$ end end