## 3 Multipath Interference Suppression
\begin{split}& P_{D}=\int_{\lambda}^{+\infty}p(l|H_{1})dl\\ =&\int_{\lambda}^{+\infty}\frac{2l}{\sigma_{nn}^{2} }\text{exp}\Bigg{(}\frac{l^{2+}\Big{|}\int_{-\frac{T}{2}}^{\frac{T}{2}}A_{T}s_ {r}(t)K_{A}(u,t)dt\Big{|}^{2}}{\sigma_{nn}^{2}}\Bigg{)}\\ &\times I_{0}\Bigg{(}\frac{2l\cdot\Big{|}\int_{-\frac{T}{2}}^{ \frac{T}{2}}A_{T}s_{r}(t)K_{A}(u,t)dt\Big{|}}{\sigma_{nn}^{2}}\Bigg{)}dl\\ &=Q\Bigg{(}\sqrt{\frac{2\Big{|}\int_{-\frac{T}{2}}^{\frac{T}{2}} A_{T}s_{r}(t)K_{A}(u,t)dt\Big{|}^{2}}{\sigma_{nn}^{2}}},\sqrt{2\ln\frac{1}{P_{ fa}}}\Bigg{)},\end{split}  \tag{26}\]

where \(p(l|H_{1})\) represents the probability density function of \((l|H_{1})\) and \(Q(\cdot,\cdot)\) denotes the Marcum Q function [26]. The false alarm probability \(P_{fa}\) is

\[ \begin{split} P_{fa}&=\int_{\lambda}^{+\infty}p(l|H _{0})dl\\ &=\int_{\lambda}^{+\infty}\Big{(}2l\Big{/}\sigma_{nn}^{2}\Big{)} \exp\Big{(}l^{2}\Big{/}\sigma_{nn}^{2}\Big{)}dl\\ &=\exp\Big{(}\lambda^{2}\Big{/}\sigma_{nn}^{2}\Big{)},\end{split}  \tag{27}\]where \(p(l|H_{0}\,)\) represents the probability density function of \((l|H_{0}\,)\). The threshold \(\lambda\) of false alarm probability detection can be expressed as

\[\lambda=\sqrt{-\sigma_{nn}^{2}\ln P_{fa}}. \tag{28}\]

## 6 Aerial Target Parameter Estimation

### Parameter Estimation Based on LCT+MF

When the target gradually approaches and then moves away from the baseline at a constant speed, the sum of the distances from the transmitter to the target and from the target to the receiver changes. Linear frequency modulation (LFM) signal increases the transmission bandwidth of the signal by modulating the carrier frequency, and realizes pulse compression at reception. The forward scatter system does not have a reference signal, but when the moving speed of the target is slow, the Doppler frequency shift is small and the frequency change is slow. At this time, the echo signal can be approximated as a chirp signal with frequency change. Based on this, the feature function is constructed, and the speed and flight altitude can be estimated through the matched filtering (MF). The target parameter estimation system diagram based on LCT+MF is shown in Figure 10.

The LCT-based method can effectively separate the signal and the interference, thereby reduce the influence of interference and improve the accuracy of parameter estimation. By designing the four parameters \((a,b,d,u)\) in the LCT domain, the spectral peak information is obtained in the LCT domain. The corresponding parameters at the spectral peak include the target parameter information \(H_{\text{max}},v_{\text{max}},\theta_{v_{\text{max}}}\) of the moving target. One has

\[|l|\underbrace{ \begin{subarray}{c}H_{1}\\ H_{0}\end{subarray} }_{<}T_{d}. \tag{29}\]

The relationship between the target parameters can be estimated according to the characteristics of the parameter \(\left(\hat{a},\hat{b},\hat{d},\hat{u}\right)\) at the peak and the forward scattered signal as

\[|l|\underbrace{ \begin{subarray}{c}H_{1}\\ H_{0}\end{subarray} }_{<}T_{d}. \tag{30}\]

The coordinates \((a,b,d,u)\) corresponding to the peak can be effectively extracted using the following peak extraction methods summarized in Algorithm 2. Figure 10: Target parameter estimation system diagram based on LCT+MF. The target parameters are related through \(v^{2}\cos\theta_{SV}(1-\cos^{2}\theta_{v}\sin^{2}\theta_{SV})\)\(=\)\(-\frac{\hat{a}}{2\hat{b}}\frac{2 cH}{2\pi\ell_{c}}\). The steps of parameter estimation based on LCT+MF are as follows:

Step 1: Construct the feature function as

\[f(t)=a_{F}e^{\jmath 2\pi\ell_{c}q(v,H)t^{2}}, \tag{31}\]

where \(a_{F}\) represents the amplitude of the characteristic function, \(f_{c}\) stands for the carrier frequency, and \(q(v,H)\) is a function of the parameters \(v\) and \(H\) with \(q(v,H)=\frac{v^{2}\cos\theta_{SV}(1-\cos^{2}\theta_{v}\sin^{2}\theta_{SV})}{2 cH}\).