Algorithm 2 AMP Algorithm in mmWave Channels

Require:      sensing matrix $\mathbf{A}$, measurement vector $\mathbf{y}$, and the number of iterations T    1:$\mathbf{Initialize}{\widehat{\mathbf{h}}}_0=0,{\mathbf{v}}_{-1}=0$, and $b_0=0$    2:$\mathbf{for}$$t=0,1,\cdots ,T-1$$\mathbf{do}$    3:${\mathbf{v}}_t=\mathbf{y}-\mathbf{A}{\widehat{\mathbf{h}}}_t+b_t{\mathbf{v}}_{t-1}$    4:${\mathbf{r}}_t={\widehat{\mathbf{h}}}_t+{\mathbf{A}}^T{\mathbf{v}}_t$    5:${\lambda }_t=\frac{1}{\sqrt{M}}{∥{\mathbf{v}}_t∥}_2$    6:${\widehat{\mathbf{h}}}_{t+1}={\mathit{\eta }}_{\mathbf{s}\mathbf{t}}\left({\mathbf{r}}_t;\alpha ,{\lambda }_t\right)$    7:$b_{t+1}=\frac{1}{M}{\sum }_{i=1}^N\frac{\partial {\eta }_{\mathrm{st}}\left({\mathbf{r}}_t;\alpha ,{\lambda }_t\right)}{\partial r_{t,i}}$    8:$\mathbf{end}\mathbf{for}$    9:return$\widehat{\mathbf{h}}={\widehat{\mathbf{h}}}_T.$