# Analysis of Electromagnetic Interference Effects of 5G Signals on Radio Altimeters
## 2 Analysis of Interference Mechanisms
### Analysis of RA Receiver Interference Mechanisms
When the input signal is large, nonlinear characteristics manifest in the circuit response, and the first four terms of the power series are typically employed for approximation. Since the 5G signal is an OFDM signal consisting of multiple subcarriers, directly substituting it into the power-series model is not conducive to calculation and organization. We began our derivations with the simpler case of a single subcarrier signal. When N = 1, it becomes a single subcarrier signal. By substituting Equation (5) into Equation (6), we obtain Equation (7):  
\[ \begin{split} uo(t)=& A_{0}+A_{1}[B_{s}U_{s}cos2 \pi(f_{s}t+\mathrm{F_{B}}t^{2}/2\mathrm{T_{M}})+B_{1}U_{1}cos(2\pi f_{1}t+ \theta_{n})]\\ &+A_{2}[B_{s}U_{s}cos2\pi(f_{s}t+\mathrm{F_{B}}t^{2}/2\mathrm{T_ {M}})+B_{1}U_{1}cos(2\pi f_{1}t+\theta_{n})]^{2}\\ &+A_{3}[B_{s}U_{s}cos2\pi(f_{s}t+\mathrm{F_{B}}t^{2}/2\mathrm{T_ {M}})+B_{1}U_{1}cos(2\pi f_{1}t+\theta_{n})]^{3}+\cdots\end{split}  \tag{7}\]  
Figure 2: Principle of FMCW signal ranging. The power-series expansion of Equation (7) can be derived and organized, resulting in the determination of the DC component. \[A_{0}+\frac{A_{2}}{2}\left({B_{s}}^{2}{U_{s}}^{2}+{B_{1}}^{2}{U_{1}}^{2}\right) \tag{8}\]  
The fundamental component is  
\[\left[A_{1}+\frac{3}{4}A_{3}\big{(}{B_{s}}^{2}{U_{s}}^{2}+2{B_{1}}^{2}{U_{1}}^{ 2}\big{)}\right]B_{s}U_{s}cos(f_{s}t+F_{B}t^{2}/2{\rm T}_{M}) \tag{9}\]  
\[\left[A_{1}+\frac{3}{4}A_{3}\Big{(}{B_{s}}^{2}{U_{s}}^{2}+2{B_{1}}^{2}{U_{1}}^ {2}\Big{)}\right]B_{1}U_{1}cos(2\pi f_{1}t+\theta_{n}) \tag{10}\]  
In general, the third-order component of the signal is minimal and can therefore be neglected [22]. In the context of nonlinear response output, the useful signal corresponds to the fundamental component of the echo signal. After processing through a mixer for frequency conversion, the IF signal \(u_{IF}(t)\) is  
\[u_{IF}(t)=\left[A_{1}+\frac{3}{4}A_{3}\Big{(}B_{s}^{2}U_{s}^{2}+2B_{1}^{2}U_{1 }^{2}\Big{)}\right]B_{s}U_{s}cos[2\pi f_{IF}t] \tag{11}\]  
In Equation (11), it is established that under the condition of single subcarrier interference from a 5G signal, the gain of the IF useful signal, denoted as \(K_{1}\), is defined as follows:  
\[K_{1}=A_{1}+\frac{3}{4}A_{3}\big{(}{B_{s}}^{2}{U_{s}}^{2}+2{B_{1}}^{2}{U_{1}} ^{2}\big{)} \tag{12}\]  
In a similar manner, when the useful signal remains unchanged, the gain of the useful signal, denoted as \(K_{2}\), under dual-frequency subcarrier interference is as follows:  
\[K_{2}=A_{1}+\frac{3}{4}A_{3}\Big{(}{B_{s}}^{2}{U_{s}}^{2}+2{B_{1}}^{2}{U_{1}} ^{2}+2{B_{2}}^{2}{U_{2}}^{2}\Big{)} \tag{13}\]  
According to Equation (13), it is evident that under the OFDM interference of the 5G signal, the gain of the useful signal at the RA receiver, denoted as \(K_{n}\), is given by  
\[K_{n}=A_{1}+\frac{3}{4}A_{3}\Bigg{(}{B_{s}}^{2}{U_{s}}^{2}+2\sum_{n=1}^{N}{B_ {n}}^{2}{U_{n}}^{2}\Bigg{)} \tag{14}\]  
Since \(P=\frac{V^{2}}{2R}\), Equation (14) can be reformulated into power form. Here, \(R\) represents the input impedance of the receiver, which is conventionally 50 \(\Omega\). The subcarriers of the 5G signal can be regarded as having equal power distribution. The power of each subcarrier is denoted as a constant \(P_{n}\), while the gain of the IF signal is expressed as follows:  
\[K_{n}=A_{1}+\frac{3}{2}A_{3}{R{B_{s}}}^{2}P_{s}+3A_{3}{R{B_{n}}}^{2}NP_{n} \tag{15}\]  
In Equation (15), in the presence of 5G interference signals, the effect of the 5G interference signal on the RA receiver is reflected in the third term of the equation. Since \(A_{3}<0\), the 5G interfering signal causes the IF signal gain to be reduced. \(B_{s}\) is the frequency selection coefficient of the RF front-end bandpass filter for the 5G signal subcarrier, which is dependent on the frequency of the 5G signal. \(NP_{n}\) denotes the power of the 5G signal. Consequently, the interference effects are influenced by both the power and frequency of the 5G signal.