## 3 Multipath Interference Suppression  
Since the received signal is inevitably affected by the direct wave and multipath interference, the power of the direct wave and multipath interference is higher than the power of the echo signal containing the target. This will affect the sensing. Thus it is necessary to suppress the direct wave and multipath interference. Linear canonical transform (LCT) is a generalized form of Fourier transform, which has multiple free parameters. Compared with the traditional Fourier transform, it has great flexibility. The traditional method of separating signal and noise is only carried out in either the time domain or the frequency domain, but it is difficult to obtain good filtering and interference separation effect in time domain or frequency domain if there is strong time-frequency coupling between signal components and between signal and noise. In this case, the LCT provides a more suitable filtering and interference separation scheme in another transform domains. For the problem of multipath interference in the receiving channel, using the reversibility of the linear canonical transform and its suppression of Gaussian noise, the Gaussian noise and multipath interference in the channel can be removed by the rectangular window function in its linear regular domain. Thus, the signal after noise suppression is obtained through inverse linear regular transformation. In contrast, Fourier transform can only remove noise and cannot effectively suppress multipath interference; therefore, we choose the linear canonical transform with better filtering and interference separation performance to process the signal. The signal distribution before the multipath interference suppression in the LCT domain is shown in Figure 6. In Figure 6, \(u\) represents the LCT domain. Fourier transform and fractional Fourier transform are special forms of LCT, so LCT domain can be regarded as the unity of time domain, frequency domain, and fractional Fourier domain, and contains the information of signal in time domain and frequency domain. Since most of the energy of the echo signal is concentrated in a narrow band centered at the peak point of the linear canonical transform domain, the Gaussian noise does not have good energy concentration in the LCT domain. It can also be seen that the energy distribution of multipath interference is on both sides of the LCT domain; therefore, the peak point can be used as the center of the rectangular window function to filter out the noise and interference. Figure 5: Output signal after symbol elimination. The steps to design the bandwidth of the rectangular window function are summarized in Algorithm 1. According to the above analysis, the window function can be constructed to extract the echo signal. The rectangular window function in the linear canonical domain can be expressed as  
\[\ell[f(t)](u)=\left\{ \begin{array}{ll}1&u\in[a,b],\\ 0&else.\end{array} \right. \tag{7}\]  
By applying the reversibility of the LCT algorithm to transform the separated signal, the suppression of direct wave and multipath interference can be achieved. The suppressed signal is subject to LCT again, and the suppression effect is determined by observing whether there is a corresponding peak in the LCT domain. The effect of interference suppression on the signal is shown in Figure 7. From Figure 7, we can see that the multipath interference have been well suppressed. ```
1:Perform LCT on the signal to obtain the LC spectrum of the signal \(P_{L}(w)\);
2:Perform least squares polynomial fitting to obtain a smooth power spectrum curve;
3:Derivative the smoothness power spectrum curve, and extract the positions of the maximum and minimum points of the slope derivative value near the center point of the LC domain from \(a\) and \(b\), respectively. Further, use the difference \(|b-a|\) as the bandwidth estimation;
4:Design the number of cycles and repeat the above operation to obtain the statistical average.