# Study on Electromagnetic Radiation Interference Caused by Rocket Fuel
## 3 Electromagnetic Radiation Analysis and Modelling
### Analysis and Modelling of the Frequency-Domain Characteristics of Electromagnetic Radiation  
The frequency-domain characteristics represent the overall state of the spectrum occupied by the spacecraft's electromagnetic environment, usually expressed by parameters such as frequency occupancy. Frequency occupancy is the ratio of the frequency band occupied by the signal power density spectrum of the electromagnetic environment in a certain space and time interval that exceeds the specified environmental level threshold of the frequency range of Device A, which reflects the amount of the electromagnetic spectrum's resources that are occupied by the space's electromagnetic radiation [24; 25]. According to Equation (4), in a certain space of V\({}_{\Omega}\) and time range of [\(t_{1}\),\(t_{2}\)], the average power spectrum of the signal at different frequencies can be expressed using Equation (10), where double integration is used to integrate over time and space. \[S(f)=\frac{1}{V_{\Omega}(t_{2}-t_{1})}\int_{\Omega}\int_{t_{1}}^{t_{2}}S( \boldsymbol{r},t,f)dtd\Omega. \tag{10}\]  
According to the calculation method of the spectrum range, the spectrum range occupied by the electromagnetic radiation signal in a certain time and space can be calculated from the average power spectrum function of the signal strength represented by Equation (10), which is abbreviated as \(\Delta\)B. For the electronic equipment of spacecraft, it is assumed that there are different radiation frequencies of \(f_{k}\) (\(k\) = 1\(\sim\)\(n\)) due to the joint action of n radiation sources, and each radiation source has a different spectrum range of \(\Delta\)B\({}_{\text{k}}\) (\(k\) = 1\(\sim\)\(m\)). If there is no overlapping part of the spectrum, that is, there is no self-interference or mutual interference, as shown in the first coordinate axis of Figure 4c, then the spectrum occupancy is defined as 0, which is \(\Delta\)B = \(\sum_{k=1\sim n}\Delta\)B\({}_{k}\). However, in actual situations, there will be interference from other signals in the range of \(\Delta\)B, and frequency overlap will occur; then, S(\(f\)) must exceed the allowable threshold \(S_{0}\). As shown in the second and third coordinate axes of Figure 4c, the spectrum occupancy will not be 0; if the spectrum width exceeding the threshold is \(\Delta\), the spectrum occupancy is \(\text{FO}=\frac{\Delta}{\Delta\text{B}}\), and the electromagnetic environment becomes more complicated with the spectrum occupancy being greater. This quantitatively describes the relevant conditions and calculates the degree of correlation in the frequency domain: assuming that the bandwidth of the linear part of Device A is \(\Delta f_{r}\), the central frequency of Device A is \(f_{r}\), the signal bandwidth of the radiation source is \(\Delta f_{j}\), and the central frequency of the signal is \(f_{j}\), it is clear that when the power and bandwidth of the signal or receiver are determined, the signal power of a jamming device is related to the frequency aiming error of \(\delta_{f}\) and \(\frac{\Delta f_{j}}{\Delta f_{r}}\). Due to the frequency aiming error of \(\delta_{f}\), the central frequency of the radiation source cannot be completely aligned with the central frequency of Device A, and the bandwidth of the radiation source cannot completely cover the working bandwidth of Device A, so the degree of coincidence between the signal bandwidth of the radiating source and of the receiver is used to determine the frequency-domain correlation, as shown in the second coordinate axis in Figure 4d. The frequency-domain-correlated calculation model is as follows:  
\[\left\{ \begin{array}{c}\text{FR}=\frac{f_{max}-f_{min}}{\Delta f_{r}}U(f_{max}- f_{min})\\ \Delta f_{r}=f_{max}-f_{min}\\ f_{max}=\min\big{[}f_{max},f_{jmax}\big{]},f_{min}=max\big{[}f_{min},f_{jmin} \big{]}\end{array} \right.