Algorithm 1. Iterative mismatch approximation method.

Input: $ϵ, \varphi ,{\overline{\mathit{a}}}_q,{\widehat{\mathit{R}}}^{-1}$ Output: ${\tilde{\mathit{a}}}_q,pwr$ 1:  Initialize $\mathit{a}={\overline{\mathit{a}}}_q$ 2:  for $it1=1\dots M$ 3:   ${\tilde{\Theta }}_{\mathit{\alpha }}=\left[{\alpha }_{ql},{\alpha }_{qh}\right]=\left[1-ϵ, 1+ϵ\right]$,${\tilde{\Theta }}_{\mathit{\beta }}=\left[{\beta }_{ql},{\beta }_{qh}\right]=\left[{\mathit{e}}^{j\left(-\varphi \right)},{\mathit{e}}^{j\left(\varphi \right)}\right]$ 4:   for$it2=1\dots d\mathit{e}pth$ 5:    ${\mathit{E}}_{ap}={\tilde{\Theta }}_{\mathit{\beta }}\otimes {\tilde{\Theta }}_{\mathit{\alpha }}, {\mathit{E}}_{ap}\in {ℂ}^{1\times 4}$ 6:    ${\mathit{a}}_i\left(it1\right)={\overline{\mathit{a}}}_q\left(it1\right){\mathit{E}}_{gp}\left(i\right),i=1,\dots ,4$ 7:    Calculate $p\left(i\right)$ by substituting ${\mathit{a}}_i$ into Equation (10) 8:    $\left(pwr,idx\right)=max\left(p\right)$ 9:    Zoom out of the amplitude/phase error area built by ${\tilde{\Theta }}_{\mathit{\alpha }}$ and ${\tilde{\Theta }}_{\mathit{\beta }}$ to $E_{ap}\left(idx\right)$ 10:    Update ${\tilde{\Theta }}_{\mathit{\alpha }}$ and ${\tilde{\Theta }}_{\mathit{\beta }}$ 11:   end 12:    ${\tilde{\mathit{a}}}_q\left(it1\right)={\overline{\mathit{a}}}_q\left(it1\right){\mathit{E}}_{ap}\left(idx\right)$ 13:  end