## 4 Relative Jammer Screening Algorithm Based on Mixed-Strategy Game
### Multidimensional Utility Function Construction
The value of D, as a jammer performance parameter, should be a fixed value. In engineering realisation, when the number of main interference sources is \(\leq\)5, the value of D is taken as 20. The engineering empirical values of weights A, B, and C, with respect to the signal-to-noise ratio (SNR) and the ratio of the velocity of the target to be jammed to the magnitude of the jammer's velocity (VR), are given in Table 1. We subsequently consider a large number of experimental data to fit the appropriate coefficients for different scenarios, in order to achieve adaptive adjustment. The Nash equilibrium of a mixed-strategy set for the N-player non-cooperative game is \(\boldsymbol{S}^{*}=\left(X_{1}^{*},X_{2}^{*},\ldots,X_{N}^{*}\right)\), i.e., let \(P_{ip}\left(\boldsymbol{S}^{*}\middle|\middle|x_{ig}^{ip}\right)\leq P_{ip}( \boldsymbol{S}_{i})\) hold. For any primary jammer, an arbitrary change in its decision variables cannot lead to an increase in its effectiveness, i.e., the game reaches the Nash equilibrium point, provided that the strategies of the other sources of interference remain unchanged. 1. Forwarding interference time loss model  
The time-delay principle of the distributed jamming system is that the relative jammer receives all currently available satellite signals, time-delays them separately, and then broadcasts the combined spoofed signals to the target to be jammed. When the correlation peak of the spoofed signal is higher than the true signal, the tracking loop of the target receiver can be made to lock on to the spoofed signal and produce an erroneous position solution. The signal from the LEOs is transmitted to the primary jamming source to receive, process, and forward to the secondary jamming source, which receives the jamming information from the primary jamming source and forwards the kth LEO satellite signal to the mth user as the target to be jammed. The calculated pseudo-range of the interfering signal, when it reaches the target receiver, is shown in Equation (5). \[\rho_{1}=\left|\boldsymbol{J}_{ip}-\boldsymbol{S}_{k}\right|+\left|\boldsymbol{ J}_{i_{M}}-\boldsymbol{J}_{i_{k}}\right|+\left|\boldsymbol{U}_{m}-\boldsymbol{J}_{i_{ k}}\right|+c\cdot\left(\tau_{MV}+\delta_{m}+\Delta\tau_{km}\right) \tag{5}\]  
where \(\boldsymbol{J}_{ip}\) is the position of the \(i_{p}\)th primary jammer, \(\boldsymbol{S}_{k}\) is the position of the kth LEO satellite, \(\boldsymbol{J}_{i_{R}}\) is the position of the \(i_{R}\)th relative, \(\boldsymbol{U}_{m}\) is the desired spoofing position of the mth user, \(\tau_{MV}\) is the processing delay of the jammer, \(c\) is the speed of light, \(\delta_{m}\) denotes the reception clock difference of the mth user, and \(\Delta\tau_{km}\) is the mth user's signal processing of the kth LEO satellite delay. The actual signal arrives at the user's calculated pseudo-distance, as shown in Equation (6). \[\rho_{2}=\left|\boldsymbol{U}_{m}-\boldsymbol{S}_{k}\right|+\delta_{m}\cdot c \tag{6}\]  
The time loss is shown in Equation (7). \[\tau_{LOSS}=\frac{\rho_{1}-\rho_{2}}{c} \tag{7}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**SNR/dB** & **VR** & **A** & **B** & **C** \\ \hline
3 & 1 & 1.22 & 1.80 & 1.31 \\
5 & 1 & 1.13 & 1.61 & 1.31 \\
7 & 1 & 1.05 & 1.37 & 1.31 \\
6 & 0.7 & 1.18 & 1.54 & 1.53 \\
6 & 1.5 & 1.25 & 1.54 & 1.66 \\
6 & 2 & 1.83 & 1.54 & 1.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The engineering empirical values of weights A, B, and C.  
Interference power loss model  
The power loss is mainly caused by the path attenuation, and the power loss will be compensated to some extent due to the antenna gain, as shown in Equation (8). \[\left\{ \begin{aligned} & W_{Loss}=10\dot{[}(P_{t}-L_{M,V}+G_{t/r} \ )/10]-10\dot{(}P_{t}/10)\\ & L_{M/V}=32.44+20 lg(f_{M,V})+20 lg(d_{M,V})\\ & G_{t/r}=10 lg\left[4.5*\left(\frac{D}{\lambda}\right)^{2}\right] \end{aligned} \right.