## 3 Multipath Interference Suppression
The proposed method can theoretically meet the needs of target detection, but in practice the working environment of target detection is more complicated; therefore, it is necessary to further connect with the actual environment, and carry out the verification and improvement of the algorithm and system through the measured data. In addition, since the suppression performance of direct wave interference and multipath interference will have a direct impact on the subsequent target detection and parameter estimation, it is necessary to further explore the improvement of the suppression performance of various interferences. [PERSON] conceptualized and performed the algorithm and wrote the paper; [PERSON] and [PERSON] analyzed the experiment data; [PERSON] helped improve the language; [PERSON] is the research supervisor. The manuscript was discussed by all co-authors. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (62071364), the Aeronautical Science Foundation of China (2020Z073081001), the Fundamental Research Funds for the Central Universities (JB210104), the Shaanxi Provincial Key Research and Development Program (2019 GY-043), and the 111 Project (B08038). Not applicable. The authors declare no conflict of interest. ## Appendix A Proof of Lemma 1

In (24), the real part \(\text{Re}\{L(u)\}\) of the LCT under assumption \(H_{1}\) is expressed as

\[ \begin{split}\text{Re}\{L(u)\}&=\text{Re}\Bigg{\{} \int_{-\frac{T}{2}}^{\frac{T}{2}}x(t)K_{A}(u,t)dt\Bigg{\}}\\ &=\text{Re}\Bigg{\{}\int_{-\frac{T}{2}}^{\frac{T}{2}}A_{T}s_{r}( t)K_{A}(u,t)dt\Bigg{\}}\\ &+\text{Re}\Bigg{\{}\int_{-\frac{T}{2}}^{\frac{T}{2}}w(t)K_{A}(u,t)dt\Bigg{\}}.\end{split}  \tag{25}\]

The first term of (25) is the real part of the LCT of the echo signal, which belongs to the determined sensing statistics and is expressed as: \(\text{Re}\Bigg{\{}\int_{-\frac{T}{2}}^{\frac{T}{2}}A_{T}s_{r}(t)K_{A}(u,t)dt \Bigg{\}}\). The second term represents the real part of the LCT of noise, subject to Gaussian distribution, which is

\[\text{Re}\Bigg{\{}\int_{-\frac{T}{2}}^{\frac{T}{2}}w(t)K_{A}(u,t)dt\Bigg{\}} \sim N\Big{(}0,\sigma_{nn}^{2}\Big{)}. \tag{26}\]

In summary, under the assumption \(H_{1}\), \(\text{Re}\{L(u)\}\) subject to the Gaussian distribution of the following statistical characteristic

\[\text{Re}\{L(u)\}\sim N\Bigg{(}\text{Re}\Bigg{\{}\int_{-\frac{T}{2}}^{\frac{ T}{2}}A_{T}s_{r}(t)K_{A}(u,t)dt\Bigg{\}},\sigma_{nn}^{2}\Bigg{)}. \tag{27}\]In (25), the imaginary part \(\text{Im}\{L(u)\}\) of the LCT under assumption \(H_{0}\) is expressed as

\[ \begin{split}\text{Im}\{L(u)\}&=\text{Im}\left\{ \int_{-\frac{\Gamma}{2}}^{\frac{\Gamma}{2}}x(t)K_{A}(u,t)dt\right\}\\ &=\text{Im}\left\{\int_{-\frac{\Gamma}{2}}^{\frac{\Gamma}{2}}A_{T} s_{r}(t)K_{A}(u,t)dt\right\}\\ &+\text{Im}\left\{\int_{-\frac{\Gamma}{2}}^{\frac{\Gamma}{2}}w(t) K_{A}(u,t)dt\right\}.\end{split}  \tag{10}\]

Similarly, under the assumption \(H_{1}\), \(\text{Im}\{L(u)\}\) follows a Gaussian distribution with

\[\text{Im}\{L(u)\}\sim N\left(\text{Im}\left\{\int_{-\frac{\Gamma}{2}}^{\frac{ \Gamma}{2}}A_{T}s_{r}(t)K_{A}(u,t)dt\right\},\sigma_{nn}^{2}\right). \tag{11}\]

From (12) and (11), the distribution of the detection based on LCT under \(H_{1}\) is

\[(l|H_{1})\sim CN\left(\int_{-\frac{\Gamma}{2}}^{\frac{\Gamma}{2}}A_{T}s_{r}(t )K_{A}(u,t)dt,\sigma_{nn}^{2}\right), \tag{12}\]

where \(CN(\cdot)\) represents the complex Gaussian process. In (24), the real part \(\text{Re}\{L(u)\}\) of the LCT under \(H_{0}\) is expressed as

\[ \begin{split}\text{Re}\{L(u)\}&=\text{Re}\Bigg{\{} \int_{-\frac{\Gamma}{2}}^{\frac{\Gamma}{2}}x(t)K_{A}(u,t)dt\Bigg{\}}\\ &=\text{Re}\Bigg{\{}\int_{-\frac{\Gamma}{2}}^{\frac{\Gamma}{2}}v( t)K_{A}(u,t)dt\Bigg{\}},\end{split}