## 2 System Model  
The GPS waveforms-based forward scatter system is shown in Figure 1. Since the bistatic angle is close to 180\({}^{\circ}\), the signals received by the receiving antenna include direct wave signals, forward scatter signals, multipath interference, and noise. Thus, it requires direct wave suppression and multipath interference suppression for target sensing and target parameter estimation. The geometry of the forward scatter system is shown in Figure 2. In Figure 2, multipath refers to the propagation of radio signals from the transmitting antenna to the receiving antenna through multiple paths. The scattering of radio waves by the atmosphere, the reflection and refraction of radio waves by the ionosphere, and the reflection of radio waves by surface objects, such as mountains and buildings, will all cause multipath propagation. The system uses GPS as the illuminator, and the receiver is located at the \(O\) point of the coordinate system. It is assumed that the satellite transmitter is located on the \(xOz\) plane, and that the target moves at a speed \(v\) and height \(H\) in a plane parallel to the ground. \(\theta_{SV}\) denotes the angle between the baseline and the \(z\) axis, and \(\theta_{v}\) represents the projection angle between the target trajectory on the ground and the axis. Assuming that the target crosses the baseline, or is near the baseline, \(R_{D}\), \(R_{T}\), \(R_{R}\) are the distances from the transmitter to the receiver, from the transmitter to the target, from the receiver to the target, respectively. \(\theta\) represents the angle between \(R_{D}\) and \(R_{R}\). Compared with conventional radar, the main difference of FSR is its scattering characteristics. In the FSR configuration, the received signal includes the direct wave signal \(s_{d}(t)\) from the transmitter, the forward scatter signal \(s_{t}(t)\) due to the presence of the aerial target, the multipath interference and noise; therefore, the signal received by the receiver can be described as  
\[ \begin{split} x(t)&=A_{d}s(t-\tau_{d}(t))+A_{T}s(t -\tau_{t}(t))e^{\mathrm{i}\varphi_{r}}+\sum_{j=1}^{H}\omega_{j}s\big{(}t-\tau_{ \eta j}(t)\big{)}+n(t)\\ =&\sqrt{P_{d}}c^{k}(t-\tau_{d}(t))D^{k}(t-\tau_{d}(t) )e^{2\pi f_{0}(t-\tau_{d})}\\ +&\sqrt{P_{t}}C^{k}(t-\tau_{t}(t))D^{k}(t-\tau_{t}(t) )e^{2\pi f_{0}(t-\tau_{t})}e^{\mathrm{i}\varphi_{r}}\\ &+\sum_{j=1}^{H}\omega_{j}s\big{(}t-\tau_{\eta j}(t)\big{)}+n(t), \end{split}  \tag{1}\]  
where \(A_{d}\) denotes the amplitude of the direct wave signal, \(A_{T}\) represents the amplitude of the forward scatter signal, \(\varphi_{r}\) is the scatter phase, and \(H\) stands for the order of the multipath channel. \(\omega_{j}\) is the amplitude of the direct wave signal after passing through the \(j\)th multipath, \(\tau_{\eta j}(t)\) represents the delay of the direct wave signal after passing through the \(j\)th multipath, and \(n(t)\) is stationary Gaussian white noise with mean zero. \(C^{k}\) is the C/A code of the satellite signal and \(D^{k}\) is the satellite navigation data. \(P_{d}\) denotes the power of the direct wave signal and \(P_{t}\) represents the power of the forward scatter signal. In addition, \(\tau_{d}(t)\) and \(\tau_{t}(t)\) indicate delays in the direct and target channels as  
\[\tau_{d}(t)=\frac{R_{D}(t)}{c}, \tag{2}\]  
Figure 1: GPS waveforms-based forward scatter system model. \[\tau_{t}(t)=\frac{R_{T}(t)+R_{R}(t)}{c}, \tag{3}\]  
where \(c\) denotes the velocity of light. As the target moves, the scattered signal \(s_{t}(t)\) exhibits a Doppler change, and its amplitude modulation is specified by the forward scatter mode and the propagation loss. In the forward scatter scenario, it is assumed that the arrival time of the direct wave and forward scatter signal are nearly the same. In this case, there is no distance offset between the two signals, so the effect of the delay difference in the C/A code and the navigation code can be ignored; therefore, the received signal can be rewritten as  
\[