## 4 Clutter Suppression Method
### Identification of Clutter Position  
Since the clutter is the side lobe of the echo signal, its energy is much weaker than that of the main lobe. In through-wall detection, the energy of the human target's echo signal is very small, in which means that its side lobes can be neglected. In this case, the main causes of clutter are the directly coupled wave from the transceiver antenna, the reflected echo from the wall and the reflected wave from a strongly reflected stationary target. The energy of these three waves is strong, so their side lobes, i.e., the clutter on their sides, are pronounced. As shown in Figure 8, \(T\) represents the transmitting antenna and \(R\) represents the receiving antenna. They are all placed against the outer wall. Paths \(l_{1}\), \(l_{2}\), \(l_{3}\) and \(l_{4}\) correspond to different echoes: the direct coupling of the transceiver antenna, reflection from the inner wall, reflection from a strong stationary target, and reflection from a human target, respectively. Except for the echo of the human target, the other three exhibit strong energy resulting in significant clutter on either side. This seriously interferes with the detection of the human target. Since the location of the clutter is unknown, it should first be distinguished from the signal of human target before removal. The process of identifying the position of the clutter requires using long delay lines and cross-correlation. Figure 7: Results of closed-loop experiments. (**a**) The clutter in experiments with optical fibers of different lengths; (**b**) Changes in the amplitude and position of the clutter. Four points on the same folded line correspond from left to right to the length of the fiber as 12 m, 16 m, 24 m and 40 m.  
* The use of long delay lines. The symmetry of the left and right clutter of the main lobe is analyzed in Section 2.2 and verified in Section 3. It is critical to distinguish it from the signal of the human target. Moreover, the clutter located on both sides of the main lobe is at a certain distance from the main lobe of the signal. The forward-most signal of the echo is the direct coupling of the transceiver antenna. Its main lobe itself is very close to the zero point of distance. The left clutter at a certain distance in front of it appears to the left of the zero point. It is not visible in the results. Therefore, long delay lines are accessed before the transmitting antenna and after the receiving antenna to move the signal to the right overall. After that, symmetric left-side and right-side clutter all appear in the observation region. * The cross-correlation of signal. The range corresponding to the maximum value of the echo spectrum needs to be found. This range serves as the dividing line for the range-slow time matrix. In through-wall detection, the most powerful echo is the reflection from the inner wall, which is path \(l_{2}\) in Figure 8. Therefore, the range corresponding to the maximum value is the position of the inner wall. The matrix of range-slow time echoes is divided into upper and lower parts bounded by it. As shown in Figure 9, the upper matrix contains M rows and the lower matrix contains N rows. Rows and columns represent the range dimension and the slow-time dimension. The two matrices are denoted as \(\mathbf{S}_{1}\) and \(\mathbf{S}_{2}\), respectively. Row \(i\) of matrix \(\mathbf{S}_{1}\) and row \(i^{\prime}\) of matrix \(\mathbf{S}_{2}\) can be expressed as  
\[\left\{ \begin{array}{l}s_{1i}=x_{1i}+n_{1i}\\ s_{2i^{\prime}}=x_{2i^{\prime}}+s_{hi^{\prime}}+n_{2i^{\prime}}\end{array}  \right., \tag{15}\]  
where \(x_{1i}\) and \(x_{2i^{\prime}}\) are the clutter in two matrices generated by the phase-locked loop spuriousness, \(n_{1i}\) and \(n_{2i^{\prime}}\) represent background noise, and \(s_{hi^{\prime}}\) is the echo of the human target in the second matrix which does appear in the first matrix.