# Dual-Frequency Signal Enhancement Method of Moving Target Echoes for GNSS-S Radar
## 2 Methodology
### Signal Model  
The GNSS signal structure is Code Division Multiple Access (CDMA), which is composed of navigation messages, pseudorandom noise (PRN) code, and signal carriers [30]. The signal expression is shown as Equation (3). \[s_{d}(t)=A_{1}\cdot D(t)\cdot C(t)\cdot\cos(2\pi f_{c}t+\phi) \tag{3}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Gain of the direct receiving antenna & 3 dBi \\ Gain of the scattering receiving antenna & 15 dBi \\ Working Frequency & 1561.098 MHz and 1268.52 MHz \\ Working Bandwidth & 4.092 MHz and 20.46 MHz \\ Beam angle of the scattering receiving antenna & \(\pm 13^{\circ}\) \\ Sampling rate & 200 MSPS \\ Number of channels & 4 \\ Storage capacity & 1 TB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main parameters of the system. Figure 3: GNSS-S system configuration. where \(s_{d}(t)\) denotes the direct GNSS signal, and \(A_{1}\) denotes the signal amplitude. \(D(t)\) and \(C(t)\) represent navigation messages and PRN codes, respectively, with a value range of \(\pm 1\). \(f_{c}\) and \(\phi\) are carrier frequency and initial phase, respectively. According to the geometric configuration of the GNSS-S system given in Figure 3, the scattering signal model is expressed as Equation (4). \[s_{\text{s}}(t)=A_{2}\cdot D(t-\Delta t)\cdot C(t-\Delta t)\cdot\cos[2\pi(f_{ c}+f_{d})\cdot(t-\Delta t)+\phi] \tag{4}\]  
where \(s_{\text{s}}(t)\) denotes the scattering signal, \(f_{d}\) is the Doppler frequency shift caused by the target motion, and \(\Delta t\) is the time difference in Equation (2). Firstly, the scattering signal is quadrature demodulated to remove the carrier frequency \(f_{c}\), and the phase \(\phi\) can be adjusted to 0 by a phase-lock loop. The demodulated signal can be obtained as shown in Equation (5). Due to the motion of the target, the demodulated signal has a residual Doppler shift \(f_{d}\). \[s_{\text{s}}^{\prime}(t)=A_{2}^{\prime}\cdot D(t-\Delta t)\cdot C(t-\Delta t) \cdot\exp\{-j\cdot 2\pi\cdot f_{d}\cdot(t-\Delta t)\,\} \tag{5}\]  
Then, a PRN code correlation operation is performed on the demodulated signal \(s_{\text{s}}^{\prime}(t)\) to realize signal compression and obtain spread spectrum gain. Then, the modulated navigation messages are removed by the direct navigation message information. The compressed signal is shown in Equation (6). \[s_{\text{c}}(t)=A_{3}\cdot X(t-\Delta t)\cdot dec(f_{d})\cdot\exp\{-j\cdot 2 \pi\cdot f_{d}\cdot(t-\Delta t)\,\} \tag{6}\]  
where \(s_{\text{c}}(t)\) denotes the compressed echo signal, \(X(\cdot)\) denotes the autocorrelation function (ACF) of the PRN code, and \(dec(\cdot)\) denotes the attenuation function of the ACF, which is caused by the target motion Doppler \(f_{d}\). The image of the ACF of the PRN code is a sharp triangle. The peak of the ACF function under different \(f_{d}\) is shown in Figure 4. When the Doppler frequency shift is above 200 Hz, the correlation value will be significantly attenuated. What is more severe is that the GNSS signal power is inherently very weak. Taking the BDS signal as an example, the signal power reaching the ground is \(-130\) dBm, while the noise power is \(-101\) dBm (bandwidth is 20 MHz). When there is a residual Doppler frequency after carrier demodulation, the compressed signal energy will be attenuated. In reality, the GNSS signal is submerged under the noise, and the demodulated and compressed GNSS signal value is shown in Figure 5. It can be seen that when the frequency  
Figure 4: Influence of residual Doppler shift on correlation values. shift reaches 300 Hz, the signal energy attenuates to the noise level, and the signal cannot be detected. In order to facilitate further coherent accumulation of the compressed signal, the compressed signal is intercepted in blocks according to the code period and arranged vertically, which is converted into a \"\(\tau\)-tm\" two-dimensional signal, as shown in Equation (7). The specific process is described in reference [26].