# Dual-Frequency Signal Enhancement Method of Moving Target Echoes for GNSS-S Radar
## 2 Methodology
### Dual-Frequency Processing Methods  
Because the GNSS signal is extremely weak, it is still not enough to detect the echo signal of the target after the quadrature demodulation and code autocorrelation of the scattering signal. In order to improve the SNR of the echo signal, it is necessary to further accumulate the signal over a long time, which requires long-term coherent accumulation of the signal along the slow time \(t_{m}\). However, it can be seen from Equation (7) that the amplitude of the compressed signal is attenuated due to the residual Doppler frequency \(f_{d}\), and the signal phase fluctuates along the slow time \(t_{m}\), which limits the effect of coherent accumulation. This paper proposes a dual-frequency differential processing method that uses GNSS dual-frequency echoes for signal enhancement. The processing flow is shown in Figure 6.  
Firstly, the GNSS signals at F1 and F2 frequencies are demodulated and compressed to obtain carrier frequencies \(f_{c1}\) and \(f_{c2}\), as well as 2D data blocks. The amplitudes and phases of the compressed two frequencies signals are denoted as \((A_{1},\varphi_{1})\) and \((A_{2},\varphi_{2})\), respectively. Secondly, calculate the phase correction factor k according to the phase relationship model of the \(f_{c1}\) and \(f_{c2}\) echo signals and perform phase difference on the dual-frequency signals to obtain the differential phase \(\Delta\varphi\). Thirdly, accumulate the amplitude of the dual-frequency signal to obtain the additive amplitude, which is denoted as AA, and combine it with the dual-frequency differential phase \(\Delta\varphi\) to form a new dual-frequency differential signal \(\Delta s\), whose amplitude and phase are \((AA,\Delta\varphi)\). Finally, coherent accumulation is performed on the dual-frequency differential signal \(\Delta s\) to further improve the SNR of echo signals, and a continuous target motion track diagram can be obtained. Figure 5: Influence of residual Doppler shift on real GNSS signal compression. Generally, the GNSS system simultaneously transmits multiple signals at different frequencies. Taking BDS as an example, it simultaneously transmits signals at three frequencies: B1, B2, and B3. The signals of any two frequencies can be used as signal illumination sources for radar detection, and the signal propagation paths and frequency relationship are shown in Figure 7. The carrier frequency of the navigation satellite signal is \(f_{c}\), which can be removed after quadrature demodulation with the help of a direct signal. The main residual frequency of the 2D data block after demodulation and compression is the Doppler shift \(f_{d}\) caused by the target motion, which is related to the target velocity and carrier frequency. Considering that the height from the satellite to the ground is much greater than the distance between the target and receiver and that the Doppler caused by satellite motion has been resolved by the direct signals, when the radial velocity between target and receiver is v, the bistatic angle is \(\alpha\), and the wavelengths of the dual-frequency carrier signals are \(\lambda_{1}\) and \(\lambda_{2}\), respectively; the resulting Doppler \(f_{d1}\) and \(f_{d2}\) can be expressed as Equations (8) and (9). \[f_{d1}=\frac{v}{\lambda_{1}}(1+\cos\alpha) \tag{8}\]  
Figure 6: Processing flow of dual-frequency signals. Figure 7: Frequency relationship of dual-frequency signals. \[f_{d2}=\frac{v}{\lambda_{2}}(1+\cos\alpha) \tag{9}\]  
Substituting the above equations into Equation (7), the echo signal model can be obtained, as shown in Formulas (10) and (11). It can be seen that the phase of the echo signal is related to the moving speed v of the target and the wavelength \(\lambda\) of the carrier wave. When performing coherent accumulation directly, the effect of long-term accumulation will be affected due to the change in the signal phase. \[