Table 2 EIAA algorithm

Repeat:

(a) Calculate the correlation matrix by ${\widehat{\mathbf{R}}}^{\left(i\right)}=\mathbf{A}{\widehat{\mathbf{P}}}^{\left(i\right)}{\mathbf{A}}^H$;

   Let the index support set Λ⁽ⁱ⁾= ∅ and the principal spatial component set Γ⁽ⁱ⁾= ∅.

(b) While the relative residue is larger than a threshold, i.e., $\frac{{∥{\mathbf{r}}^{\left(i\right)}∥}_2^2}{{∥\mathbf{y}∥}_2^2}>\xi$

   Find the index n _l corresponding to the largest entry in the vector $\left[{\widehat{p}}_1^{\left(i\right)},{\widehat{p}}_2^{\left(i\right)},\dots ,{\widehat{p}}_K^{\left(i\right)}\right]$;

   Expand the index support set by Λ⁽ⁱ⁾= {Λ⁽ⁱ⁾, n₁};

   Expand the principal spatial component set by ${\mathrm{\Gamma }}^{\left(i\right)}=\left\{{\mathrm{\Gamma }}^{\left(i\right)},{\left|\frac{{\mathbf{a}}^H\left({\theta }_{n_l}\right)\cdot {\left({\widehat{\mathbf{R}}}^{\left(i\right)}\right)}^{-1}\cdot \mathbf{y}}{{\mathbf{a}}^H\left({\theta }_{n_l}\right)\cdot {\left({\widehat{\mathbf{R}}}^{\left(i\right)}\right)}^{-1}\cdot \mathbf{a}\left({\theta }_{n_l}\right)}\right|}^2\right\}$;

   Calculate the residue by ${\mathbf{r}}^{\left(i\right)}=\mathbf{y}-{\left({\mathbf{A}}_{{\mathrm{\Lambda }}^{\left(i\right)}}^H{\mathbf{A}}_{{\mathrm{\Lambda }}^{\left(i\right)}}\right)}^{-1}{\mathbf{A}}_{{\mathrm{\Lambda }}^{\left(i\right)}}^H\mathbf{y}$, where the matrix ${\mathbf{A}}_{{\mathrm{\Lambda }}^{\left(i\right)}}$ consists of the columns of A with indices k ∈ Λ⁽ⁱ⁾;

   Update the spatial estimate by ${\widehat{p}}_k^{\left(i\right)}=\frac{{\left|{\mathbf{a}}^H\left({\theta }_k\right){\mathbf{r}}^{\left(i\right)}\right|}^2}{{\left[{\mathbf{a}}^H\left({\theta }_k\right)\mathbf{a}\left({\theta }_k\right)\right]}^2}$, for k = 1, 2, ..., K.

   end While

(c) Restore the principal spatial components by ${\widehat{p}}_k^{\left(i\right)}={\mathrm{\Gamma }}^{\left(i\right)}\left(k\right)$, for k ∈ Λ⁽ⁱ⁾.

(d) If the norm of the difference between ${\widehat{\mathbf{P}}}^{\left(i-1\right)}$ and ${\widehat{\mathbf{P}}}^{\left(i\right)}$ is smaller than a threshold, i.e., ${\delta }^{\left(i\right)}\triangleq \sqrt{\sum _{k=1}^K{\left[{\widehat{p}}_k^{\left(i-1\right)}-{\widehat{p}}_k^{\left(i\right)}\right]}^2}<\epsilon$, the iteration is stopped; otherwise let i = i+1 and go to a).