## 3 Multipath Interference Suppression
\begin{split} I_{ii}&=-\frac{2}{N_{0}}\int_{- \infty}^{+\infty}\bigg{(}\bigg{(}\frac{\partial a_{Tt}}{\partial\theta_{i}} \bigg{)}^{2}+(2\pi f_{0}a_{Tt})^{2}\bigg{(}\frac{\partial\Delta\tau}{ \partial\theta_{i}}\bigg{)}^{2}\bigg{)}dt\\ &=-\frac{2}{N_{0}}\Big{(}G_{ii}+(2\pi f_{0})^{2}Q_{ii}\Big{)}, \end{split}  \tag{49}\]

\[ \begin{split} I_{ij,i\
eq j}&=I_{ji,i\
eq j}\\ &=-\frac{2}{N_{0}}\int_{-\infty}^{+\infty}\bigg{(}\frac{ \partial a_{Tt}}{\partial\theta_{j}}\bigg{)}^{*}\bigg{(}\frac{\partial a_{Tt}}{ \partial\theta_{i}}\bigg{)}+(2\pi f_{0}a_{Tt})^{2}\bigg{(}\frac{\partial \Delta\tau}{\partial\theta_{j}}\bigg{)}^{*}\bigg{(}\frac{\partial\Delta\tau}{ \partial\theta_{i}}\bigg{)}\\ &+j2\pi f_{0}a_{Tt}\bigg{(}\bigg{(}\frac{\partial a_{Tt}}{ \partial\theta_{j}}\bigg{)}^{*}\frac{\partial\Delta\tau}{\partial\theta_{i}}+ \bigg{(}\frac{\partial\Delta\tau}{\partial\theta_{j}}\bigg{)}^{*}\frac{ \partial a_{Tt}}{\partial\theta_{i}}\bigg{)}dt\\ &=-\frac{2}{N_{0}}\Big{(}G_{ij}+(2\pi f_{0})^{2}Q_{ij}+j2\pi f_{ 0}R\Big{)}.\end{split}  \tag{50}\]

Then, the FIM can be expressed in (51). \[ \begin{split} I(\theta)&=\frac{-2}{N_{0}}\Bigg{[} \begin{array}{cc}G_{11}+(2\pi f_{0})^{2}Q_{11}&G_{12}+(2\pi f_{0})^{2}Q_{ 12}+j2\pi f_{0}R\\ G_{12}+(2\pi f_{0})^{2}Q_{12}+j2\pi f_{0}R&G_{22}+(2\pi f_{0})^{2}Q_{22} \end{array}\Bigg{]}\\ &=-\frac{2}{N_{0}}\bigg{[}\begin{array}{cc}A&B\\ B&C\end{array}\bigg{]},\end{split}  \tag{51}\]

The inverse of the FIM matrix, and normalized Cramer-Rao lower bound (NCRLB) of the estimation speed and height can be expressed as

\[Var(\hat{\sigma})_{NCRLB}=\frac{N_{0}C}{B^{2}-AC}, \tag{52}\]

and

\[Var(\hat{H})_{NCRLB}=\frac{N_{0}A}{B^{2}-AC}. \tag{53}\]

## 8 Numerical Results and Discussion

In order to evaluate the performance of the proposed method, the GPS satellite communication waveforms are used. The sensing performance is determined by [30; 31]

\[\delta_{H}=\frac{N_{r}}{N}\times 100\%, \tag{54}\]

where \(\delta_{H}\) represents the detection accuracy, \(N_{r}\) and \(N\) are the numbers of correct detections and the total number of detections, respectively. In the simulation, we adopt the GSM TU 6 channel model. Using this multipath fading model, the following experiments examine the performance of the proposed algorithm for target echo signal detection. In order to evaluate the influence of sampling points on the sensing performance, the parameters are set as follows: the sampling frequency is \(f_{s}=10.23\) MHz, the false alarm probability is \(P_{fa}=10^{-4}\), the GPS direct wave power is \(P_{d}=-100\) dBm, the symbol rate is \(f_{Gb}=1.023\) MHz, the carrier frequency is \(f_{c}=1.57\) GHz, the aerial target altitude is 10 km, the flight speed is 100 m/s, the average power of the echo signal is \(P_{r}=-135\) dBm; 2000 Monte Carlo simulations are used. It can be seen from Figure 12 that the target sensing performance improves as the number of sampling points increases. This is because the increase in the number of sampling points will increase the cumulative number of points in the time domain, resulting in the enhancement of the peak height in the corresponding LCT domain, thus improving the sensing performance. Although the number of sampling points is an important factor, the limited sensing range in the case of forward scatter prevents sampling points from increasing indefinitely, and the sampling points should be set reasonably. When the number of sampling points is \(5\times 10^{6}\), the sensing performance reaches 100% with SNR = \(-31\) dB. When the number of sampling points is \(10^{7}\), the sensing performance can reach 100% with SNR = \(-36\) dB, and when the number of sampling points is \(2\times 10^{7}\), the sensing performance can reach 100% with SNR = \(-37\) dB. At the same time, it can be seen that under the same number of sampling points, as the signal-to-noise ratio increases, the detection effect is better. The actual simulation performance is basically consistent with the theoretical derivation, which verifies the effectiveness of the proposed method.