## 2 Materials and Methods
### Estimation of the Interferometric Phase of the Source of Radiation  
The most fundamental step of DCC is the estimation of the IPSR, which is denoted as \(\Delta\phi_{\text{j}}(\eta)\) in the equations above. The interferometric phase of the dual channels (IPDC) is the phase difference of the vector addition of the ground echoes and the jamming signals. On the one hand, if the jamming-to-signal ratio (JSR) is high enough, the jamming signals dominate the echoes, and IPSR dominates the interferometric phase, which means that IPSR is very close to IPDC. Since IPDC is easy to compute, in this case, IPSR is considered equal to IPDC [30]. The cost of this approximation is that IPSR is not precise and will cause residual interference after DCC. The jamming residuals after DCC with different IPSR errors are obtained by simulation, as shown in Figure 1. From Figure 1, we can see that the IPSR error decreases with the reduction of the jamming residual after DCC. Generally, cancellation with residual interference less than \(-10\) dB can be considered effective. In such a case, the IPSR error should not be greater than \(18^{\circ}\), which corresponds to the blue curve in Figure 1.  
On the other hand, if the JSR is not high enough, the estimation of IPSR will become rather intractable. The difference between IPSR and IPDC shows relatively strong ground echoes. Figures 2 and 3 show the IPDC under different JSRs, in which the color map represents the interferometric phase ranging from 0 to \(2\pi\). It is clear that a higher JSR can result in a smoother IPDC. If one examines the arbitrary azimuth bin in Figure 2, it can be found that the IPDCs along the range bins are nearly the same, which is consistent with the previous analysis. In addition, the distribution of IPDCs along the azimuth direction can be easily identified as being nearly linear. Figure 1: Jamming residual with IPSR error. However, the performance of IPDC will be seriously affected by the value of the JSR. As is clearly shown in Figure 3, when the JSR is reduced to 0 dB, the IPDC image will behave more noisily than in Figure 2, in which the IPDC distribution pattern along the azimuth direction can barely be identified. Figures 4 and 5 show the IPSR and IPDC distribution comparison along the azimuth direction under different JSRs. Figure 3: IPDC image of 0 dB JSR. Figure 2: IPDC image of 10 dB JSR. As is shown in Figure 4, when the JSR is 10 dB, there is a good match between the IPSR and IPDC, in which we can note that the IPDC is wrapped from \(0^{\circ}\) to \(360^{\circ}\). However, in Figure 5, where the JSR is 0 dB, the IPSRs are quite different from the IPDCs and will be clearly not effective in DCC. To address this problem, a traversal algorithm using cosine similarity is presented. For an arbitrary pulse repeat time (PRT), we traverse the IPSR from 0 to \(2\pi\) and perform DCC. As the interference signals are different from the SAR echoes in certain aspects (for example, in the frequency domain), then we can use the similarity of the spectrum of pure SAR echoes and that of DCC signals to determine the optimal IPSR estimation. In this method, cosine similarity is used to describe the similarity in the spectrum shapes, which is calculated as below:  
\[\gamma(IPSR)=\frac{\sum_{k=1}^{n}F_{1k}F_{2k}(IPSR)}{\sqrt{\sum_{k=1}^{n}F_{ 1k}^{2}}\sqrt{\sum_{k=1}^{n}F_{2k}^{2}(IPSR)}} \tag{8}\]  
Figure 4: IPSRs and IPDCs along azimuth (10 dB JSR). Figure 5: IPSRs and IPDCs along azimuth (0 dB JSR). where \(F_{1k}\) demotes the spectrum of the pure SAR echoes, \(F_{2k}(IPSR)\) denotes the spectrum of the DCC signal corresponding to IPSR, and \(\gamma(IPSR)\) is the cosine similarity corresponding to IPSR. When the IPSR meets the optimal value, the cosine similarity will reach its peak. Since the IPSR changes slowly along the azimuth direction, one does not need to perform the traversal algorithm for each PRT.