## 4 Simulation and Experimental Data
### Experimental Data  
The 3D TWI experiment of a single moving target is shown in Figure 10b. The 3D through-wall imaging radar was developed by the Aerospace Information Research Institute, Chinese Academy of Sciences. The MIMO radar includes four transmitting antennas and eight receiving antennas, and the planar array is consistent with that in Figure 5. The Archimedes spiral antenna (the horizontal and vertical radiation angles are both \(-60^{\circ}\) to \(+60^{\circ}\)) is adopted in the system. The specific parameters of the radar used in the experiment are given in Table 3. A pseudo-random coded signal is used in the radar to improve the penetration performance. The radar center frequency and bandwidth are both 1 GHz. The scanning frequency of the system is three frame/s. The obstacle in the experimental scene is a red brick wall with a thickness of 37 cm. Assuming that the wall is of a homogeneous medium, the relative permittivity of the wall is approximately 5.6, measured by auxiliary equipment such as the vector network analyzer, and the conductivity \(\sigma=0.05\) Sm\({}^{-1}\). In the experiment, the starting position of the target is (\(-1.5\), 6.0 m). Based on the normal direction of the wall, the moving direction of the target is \(30^{\circ}\), and the speed is 0.8 m/s.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method Performance** & **Sidelobes** & **Position** & **Imaging** & **System** \\  & & **Deviation** & **Time** & **Complexity** \\ \hline Before & \(-1.3\) dB \#azimuth & & \(<\)1.40 m & 0.25 s & low \\ compensation & \(-6.0\) dB \#height & & & \\ RCMCA & no sidelobes & \(<\)0.30 m & 0.26 s & high \\ The proposed & no sidelobes & \(<\)0.30 m & 0.26 s & low \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance comparison of the different compensation algorithms.  
Figure 13: The position deviation. **(a)** The position deviation at different speeds; **(b)** the position deviation at different distances.  
Figure 14a-i show the 3D imaging and 2D projection with no compensation, the RCMCA, and the proposed algorithm, respectively. It is obvious that the sidelobes of the imaging are high without compensation, and the position shows deviation. After compensation using the RCMCA, the sidelobes of the target are eliminated, and the position deviation is also corrected. Figure 14g-i are the imaging results after compensation using the proposed algorithm. The problems of the target sidelobes and deviation have also been well resolved, and the imaging effect is basically the same as that of the RCMCA. The target positions before motion compensation, after the RCMCA, and after the proposed algorithm are (\(-\)1.95, 6.31 m), (\(-\)1.53, 6.16 m), and (\(-\)1.52, 6.18 m), respectively. The target position compensated using the proposed method is basically consistent with the  
**Author Contributions:** The research was performed by the authors as follows: conceptualization, J.P. and S.W.; methodology, J.P.; software, D.Z.; validation, K.Y., J.N. and B.Z.; formal analysis, J.P.; investigation, X.L. and S.W.; resources, G.F.; data curation, J.H. and B.Z.; writing\(-\)original draft preparation, J.P.; writing\(-\)review and editing, S.W. and G.F.; visualization, X.L.; supervision, B.Z.; project administration, G.F.; and funding acquisition, G.F. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported in part by the Basic Science Center Project of National Natural Science Foundation of China under grant 61988102, in part by the Key Research and Development Program of Guangdong Province under grant 2019B090917007, and in part by the Science and Technology Planning Project of Guangdong Province under grant 2019B090909011.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data sharing is not applicable to this article.  
**Conflicts of Interest:** The authors declare no conflict of interest.