## 3 Proposed Jamming Suppression Method
### Analysis of Performance Degradation Under a Unified Suppression Strategy
During satellite signal acquisition, the maximum correlation peak occurs when the parameters of the real signal match those of the local replica signal. Deception signals also exhibit peak characteristics when they meet the same parameter matching conditions. When the power of the deception signals is significantly higher than that of real signals, their correlation peaks will dominate, leading to the risk of false locking by the receiver. Under conditions where the deception interference and BDS signals coexist at the same frequency, the statistical characteristics of the mixed signal detection can be represented as a superposition model of the real signal component and the interference component. \[V_{t}=G\cdot\text{sinc}(\pi\Delta fT_{d})\cdot\sqrt{\frac{P}{2}[R_{\varepsilon }^{2}(\tau_{k}-\hat{\tau})+k^{2}R_{\varepsilon}^{2}(\delta_{k}-\hat{\tau})]+2k \cdot R_{\varepsilon}(\tau_{k}-\hat{\tau})R_{\varepsilon}(\delta_{k}-\hat{\tau })\text{cos}(\Delta\phi_{m})} \tag{13}\]  
where \(G=f_{s}T_{d}\) is the gain factor, \(P\) is the true signal power, \(\Delta f\) is the estimated frequency difference, \(\hat{\tau}\) is the estimated delay, \(\Delta\phi_{m}\) is the phase difference between the spoofing and true signals, \(R_{\varepsilon}(\cdot)\) denotes the correlation function, and \(k\) is the interference relative power factor. Figure 4 simulates the two-dimensional search results of a GNSS receiver under spoofing interference. Under conditions where the spoofing signal power dominates, the amplitude of its main correlation peak significantly exceeds the true signal peak, causing the receiver to produce a false lock phenomenon. When the receiver captures a spoofing interference signal with a power higher than that of the true signal, it will incorrectly adopt the initial code phase and Doppler shift of the spoofing signal into the tracking loop, causing the spoofing signal to interfere with the DLL and PLL. Under conditions where spoofing interference and true signals coexist, the outputs of the in-phase and quadrature branches of the GNSS receiver's tracking loop correlator can be represented as three coherent integral values, E, P, and L, where the P branch is  
\[ \begin{array}{l}I_{P}\approx\frac{\sqrt{2P}}{2}R(\tau_{c}-\tau_{k})cos(\phi_ {k}-\phi_{c})+\frac{\sqrt{2P}}{2}kR(\tau_{c}-\delta_{k})cos(\psi_{k}-\phi_{c}) \\ Q_{P}\approx\frac{\sqrt{2P}}{2}R(\tau_{c}-\tau_{k})\text{sin}(\phi_{k}-\phi_{ c})+\frac{\sqrt{2P}}{2}kR(\tau_{c}-\delta_{k})\text{sin}(\psi_{k}-\phi_{c}) \end{array}  \tag{14}\]  
where \(\tau_{c}\) and \(\phi_{c}\) represent the delay and phase of the local code, respectively. A non-normalized power difference DLL phase detector is used, with the following discrimination function:  
\[D_{D}(\varepsilon)=\frac{1}{2}\Big{[}\Big{(}I_{E}^{2}+Q_{E}^{2}\Big{)}-\Big{(} I_{L}^{2}+Q_{L}^{2}\Big{)}\Big{]}=\frac{P}{4}\Big{[}R^{2}\Big{(}\varepsilon+ \frac{D}{2}\Big{)}-R^{2}\bigg{(}\varepsilon-\frac{D}{2}\Big{)}\Big{]} \tag{15}\]  
Figure 4: Two-dimensional search results when GNSS receivers are subject to spoofing interference. where \(D\) is the distance between correlators. In steady-state operation, \(D_{D}(\epsilon)=0\) is satisfied. In the case of spoofing interference, there exists  
\[ \begin{array}{ll}D_{D}^{{}^{\prime}}(\epsilon)=&D_{D}(\epsilon)+\frac{p}{4}k^ {2}\Big{[}R^{2}\Big{(}\epsilon+\frac{D}{2}-\tau_{m}\Big{)}-R^{2}\Big{(} \epsilon-\frac{D}{2}-\tau_{m}\Big{)}\Big{]}\\ &+\frac{p}{2}k\cos(\phi_{m})\Big{[}R\Big{(}\epsilon+\frac{D}{2}\Big{)}R\Big{(} \epsilon+\frac{D}{2}-\tau_{m}\Big{)}-R\Big{(}\epsilon-\frac{D}{2}\Big{)}R\Big{(} \epsilon-\frac{D}{2}-\tau_{m}\Big{)}\Big{]}\end{array}  \tag{16}\]  
In the equation, \(\tau_{m}\) and \(\phi_{m}\) represent the time delay difference and phase difference between the spoofing signal and the real signal, respectively.