Algorithm 1: The IROPE algorithm for phase compensation

Input: The range-aligned echo $e\left(r\right)$, $[Nr,Na]=size\left(e\right(r\left)\right)$, $p=0$, number of iterations l, threshold value T

1: I. Preliminary Phase Compensation

2: for $i=1:Na-1$

3: $e_{i+1}\left(r\right)=e_{i+1}\left(r\right).\ast e^{j\phi }$

4: end

5: IV. Iteration

6: for $l=1:l$ (Image entropy is further applied to control the iteration process)

7:  II. Two-step Convergence

8:  III. Circular Shifting

9:  while ${\widehat{\epsilon }}_k^{\left(p\right)}-{\widehat{\epsilon }}_k^{(p-1)}$> T

10:   for $k=1:Na-1$

11:    Update ${\widehat{\epsilon }}_k^{\left(p\right)}$ calculated by Equation (19)

12:   end

13:   for $j=1:N_r$

14:    Update ${\omega }_j^{\left(p\right)}$ calculated by Equation (19)

15:   end

16:   $p=p+1$

17:  end while

18:  $\widehat{\epsilon }={\sum }_{k=1}^K{\widehat{\epsilon }}_k^{\left(p\right)}$

19:  $e\left(r\right)=e\left(r\right).\ast exp(-1i\ast \widehat{\epsilon })$

20: end

Output: Compensated range-Doppler echo $e\left(r\right)$, phase error $\widehat{\epsilon }$