Algorithm 1 Beam-forming Algorithm for A Given Cluster

Require:  ${\mathbf{U}}_{\mathbf{n}}$ Ensure:  $\mathrm{\Phi }$ 1:Initialize T, $\eta$. 2:${\mathbf{Y}}_{\mathbf{n}}$ = Ø, ${\mathbf{S}}_{\mathbf{n}}$ = Ø, ${\mathbf{R}}_{\mathbf{n}}$ = Ø. 3:Randomly initialize $\mathrm{\Phi }$. 4:${\mathbf{g}}_{\mathbf{pre}}$← the gradient of f at $\mathrm{\Phi }$. 5:Calculate the updating direction $\mathbf{y}$= −${\mathbf{g}}_{\mathbf{pre}}$. 6:Obtain the optimal step size $\mu$ based on the Armijo rule. 7:$\mathbf{y}\leftarrow \mu \mathbf{y}$, $\mathrm{\Phi }\leftarrow \mathrm{\Phi }+\mathbf{y}$. 8:${\mathbf{g}}_{\mathbf{cur}}$← the gradient of f at $\mathrm{\Phi }$. 9:$\mathbf{s}\leftarrow {\mathbf{g}}_{\mathbf{cur}}-{\mathbf{g}}_{\mathbf{pre}}$. 10:$\rho \leftarrow {\mathbf{y}}^H\mathbf{s}$. 11:while  $\left|{\mathbf{g}}_{\mathbf{cur}}\right|\ge \eta$  do 12:   ${\mathbf{g}}_{\mathbf{pre}}\leftarrow {\mathbf{g}}_{\mathbf{cur}}$. 13:   Insert $\mathbf{y}$ to ${\mathbf{Y}}_{\mathbf{n}}$. 14:   Insert $\mathbf{s}$ to ${\mathbf{S}}_{\mathbf{n}}$. 15:   Insert $\rho$ to ${\mathbf{R}}_{\mathbf{n}}$. 16:   L← the number of the elements in ${\mathbf{Y}}_{\mathbf{n}}$. 17:   if $L>T$ then 18:     Pop the first element in ${\mathbf{Y}}_{\mathbf{n}}$. 19:     Pop the first element in ${\mathbf{S}}_{\mathbf{n}}$. 20:     Pop the first element in ${\mathbf{R}}_{\mathbf{n}}$. 21:     L←$L-1$. 22:   end if 23:   (Back Propagating) 24:   for i = L:−1:1 do 25:     $\mathbf{s}\leftarrow$ the i-th element in ${\mathbf{S}}_{\mathbf{n}}$. 26:     $\mathbf{y}\leftarrow$ the i-th element in ${\mathbf{Y}}_{\mathbf{n}}$. 27:     $\rho \leftarrow$ the i-th element in ${\mathbf{R}}_{\mathbf{n}}$. 28:     ${\chi }_i\leftarrow \rho {\mathbf{s}}^H{\mathbf{g}}_{\mathbf{cur}}$. 29:     ${\mathbf{g}}_{\mathbf{cur}}\leftarrow {\mathbf{g}}_{\mathbf{cur}}-{\chi }_i\mathbf{y}$. 30:   end for 31:   (Forward Propagating) 32:   $\mathbf{res}\leftarrow {\mathbf{g}}_{\mathbf{cur}}$. 33:   for i = 1:L do 34:     $\mathbf{s}\leftarrow$ the i-th element in ${\mathbf{S}}_{\mathbf{n}}$. 35:     $\mathbf{y}\leftarrow$ the i-th element in ${\mathbf{Y}}_{\mathbf{n}}$. 36:     $\rho \leftarrow$ the i-th element in ${\mathbf{R}}_{\mathbf{n}}$. 37:     ${\beta }_i\leftarrow \rho {\mathbf{y}}^H\mathbf{res}$. 38:     $\mathbf{res}\leftarrow \mathbf{res}+({\chi }_i-{\beta }_i)\mathbf{s}$. 39:   end for 40:   $\mathbf{y}=-\mathbf{res}$. 41:   steps (6)–(10) 42:end while