Algorithm 1 Sparse auto-calibration radar coincidence imaging (RCI) method

Input: $y$, $S\left(a=1,\phi =0\right)$, $I_{\max }$, $\eta$

Initialization: $i=0$, $a=1$, $\phi =0$

Iteration: While continuing, if not converged, do

Step 1: Target reconstruction ${\beta }^{i+1}=\underset{\beta }{\arg \min }J\left(\beta ,a^i,{\phi }^i\right)$

Step 2: Gain error estimation Phase error estimation $a^{i+1}=\underset{\phi }{\arg \min }J\left({\beta }^{i+1},a,{\phi }^i\right)$

Phase error estimation ${\phi }^{i+1}=\underset{\phi }{\arg \min }J\left({\beta }^{i+1},a^{i\text{+}1},\phi \right)$

Step 3: Gain-phase error compensation, update $S\left(a^{i+1},{\phi }^{i+1}\right)$

Step 4: Let $i=i+1$ and check for convergence: ${\Vert {\beta }^{i+1}-{\beta }^i\Vert }_2^2/{\Vert {\beta }^i\Vert }_2^2<\eta$ or $i=I_{\text{max}}$ end while Output: Reconstructed scattering coefficient vector