## 3 Materials and Methods  
### Interference Theory Analysis  
Power series expansion [10] is mainly employed for the analysis of non-linear systems. The influence of jamming signals on tested equipment could be analyzed by useful signal gain. Generally, the relationship between the input and output of tested equipment under the electromagnetic radiation can be expressed by the first four terms of the power series expansion, namely Equation (1):  
\[u_{o}=b_{0}+b_{1}u_{i}(t)+b_{2}u_{i}^{2}(t)+b_{3}u_{i}^{3}(t) \tag{1}\]  
where, \(u_{o}\) is the output signal of the receiver, \(b_{i}(i=1,2,3)\) is the non-linear coefficient, and \(u_{i}(t)\) is the input signal of the receiver.  
When it is under single electromagnetic radiation, the input signal \(u_{i}(t)\) of the receiver can be denoted as Equation (2):  
\[u_{i}(t)=A_{s}E_{s}\cos w_{s}t+A_{i}E_{i}\cos w_{i}t \tag{2}\]  
where, \(A_{s}\) and \(A_{i}\) is the selective coefficient of useful signal and the interference signal of the receiver, respectively, including the antenna coefficient and amplitude-frequency coefficient of the filter in radio frequency (RF) front-end; \(E_{s}\) and \(E_{i}\) is the field intensity of the useful signal and interference signal, separately; \(\omega_{s}\) and \(\omega_{i}\) is the radian frequency of the useful signal and interference signal, respectively.  
By substituting Equation (2) into Equation (1), the fundamental component of the useful working signal and interference signal can be obtained as Equations (3) and (4), separately:  
\[x_{s}=(b_{1}A_{s}E_{s}+\frac{3}{4}b_{3}A_{s}^{3}E_{s}^{3}+\frac{3}{2}b_{3}A_{ s}E_{s}A_{i}^{2}E_{i}^{2})\cos\omega_{s}t \tag{3}\]  
\[x_{i}=(b_{1}A_{i}E_{i}+\frac{3}{4}b_{3}A_{i}^{3}E_{i}^{3}+\frac{3}{2}b_{3}A_{ i}E_{i}A_{s}^{2}E_{s}^{2})\cos\omega_{i}t \tag{4}\]  
Hence, the useful signal gain under the single-frequency electromagnetic radiation could be obtained from Equation (3). It can be expressed as Equation (5):  
\[K_{s}=b_{1}+\frac{3}{4}b_{3}A_{s}^{2}E_{s}^{2}+\frac{3}{2}b_{3}A_{i}^{2}E_{i}^ {2} \tag{5}\]when the input signal is small, the system works in a linear region, then \(K=b_{1}\). When the input signal is gradually increased to non-linear region that the system works in, the useful signal gain decreases with the increase of the input signal. When \(A_{s}^{2}E_{s}^{2}+2A_{i}^{2}E_{i}^{2}=-\frac{4}{3}\frac{b_{1}}{b_{s}}\), then \(K=0\). In this case, the useful signal completely disappears, and the system is interfered by electromagnetic radiation. This is caused by the blocking interference of the RF front-end of the receiver, which could result in the interruption of data transmission. It also shows that the coefficient \(b_{3}\) is a negative number.  
Whether the useful signal or the interference signal is too large, the blocking interference of the RF front-end will be generated. However, the contribution of the interference signal to the useful signal gain reduction is obviously greater than that of the useful signal. The working signal of the navigation system is weak, and this feature is more apparent.  
The useful signal gain of multi-frequency interference can be analogized, but there may be a blunt effect [25]. In this case, the fifth order term or even higher order term of power series expansion needs to be taken into account, and its effect phenomenon on navigation receivers deserves careful further study. However, the effect phenomenon must be the reflection of the useful signal gain.