Skip to main content

Table 2 2D CGLS Algorithm

From: Two-dimensional SLIM with application to pulse Doppler MIMO radars

Initialization:
U 0 = 0, G 0 = 0, T 0 = − η 1/2 Y, R 0 = − Y, P 0 = Y
1 W l  = Σ (A H P l Θ H)
2 V l  = η 1/2 P l
3 \( {\alpha}_l={\left\Vert {\boldsymbol{R}}_l\right\Vert}_F^2/\left({\left\Vert {\boldsymbol{W}}_l\right\Vert}_F^2+{\left\Vert {\boldsymbol{V}}_l\right\Vert}_F^2\right) \)
4 U l + 1 = U l  + α l P l
5 G l + 1 = G l  + α l W l
6 T l + 1 = T l  + α l V l
7 R l + 1 = A(ΣG l + 1)Θ + η 1/2 T l + 1
8 \( {\beta}_l={\left\Vert {\boldsymbol{R}}_{l+1}\right\Vert}_F^2/{\left\Vert {\boldsymbol{R}}_l\right\Vert}_F^2 \)
9 P l + 1 = − R l + 1 + β l P l
Go to Step 1 until \( \frac{1}{K}{\left\Vert \boldsymbol{A}\left(\boldsymbol{\Gamma} \odot \left({\boldsymbol{A}}^H\boldsymbol{U}{\boldsymbol{\Theta}}^H\right)\right)\boldsymbol{\Theta} +\eta \boldsymbol{U}-\boldsymbol{Y}\right\Vert}_F<\varepsilon \)
Final result U = U l + 1