# Passive Location for 5G OFDM Radiation Sources Based on Virtual Synthetic Aperture
## 3 The Signal Model and Principle of Virtual Synthetic Aperture Radiation Source Location Method  
### The Signal Model  
Different from synthetic aperture radar (SAR), the moving platform (satellite) is only equipped with a receiver to obtain the signal transmitted by radiation sources. A geometric model of the virtual synthetic aperture radiation source location method is shown in Figure 1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Advantages** & **Disadvantages** \\ \hline DOA & \begin{tabular}{c} Performance is independent of source \\ form, which can be applied to \\ narrowband and wideband signals. \\ \end{tabular} & \begin{tabular}{c} High antenna complexity. Limited by the moving platform. \\ Location accuracy is relatively poor. \\ \end{tabular} \\ Doppler Frequency & \begin{tabular}{c} The principle and system are simple. \\ \end{tabular} & \begin{tabular}{c} Requires relative motion between the source and base \\ station. Accuracy is limited by location time. Accurate \\ instantaneous Doppler change rate measurement is difficult. \\ \end{tabular} \\ TDOA & \begin{tabular}{c} Provides more accurate localization. The \\ principle is relatively simple. Suitable for \\ wideband signal. \\ \end{tabular} & \begin{tabular}{c} High requirement for time synchronization. Performance \\ depends on signal bandwidth. \\ \end{tabular} \\ FDOA & \
\begin{tabular}{c} More suitable for narrowband signal. \\ \end{tabular} &
\begin{tabular}{c} High requirement for time and frequency synchronization. \\ The principle is more complex. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Overview of the source localization methods. Figure 1: Geometric model of the virtual synthetic aperture radiation source location method. The y-axis is parallel to the flight track of the receiver, the z-axis is the direction from the center of the earth to the receiver, and the x-axis direction is determined by the right-hand rule. The receiver flies over the source radiation at speed \(v\) and the flight time of the satellite is \(t\). \(R_{0}\) and \(X_{0}\) denote the range and azimuth distance of the radiation source, respectively. The range direction is perpendicular to the flight track and the azimuth direction is parallel to the flight track. The receiver can receive a signal from the radiation source for the first time at starting point A and can just miss the signal at point B. Thus, the slant distance from the satellite to the radiation source \(R(t)\) is  
\[R(t)=\sqrt{R_{0}^{2}+(vt-X_{0})^{2}}\approx R_{0}+\frac{(vt-X_{0})^{2}}{2R_{0}} \tag{4}\]  
The radiation source of this research is the 5G base station, and the signal form of the 5G radiation source is the OFDM signal. The principle of generating the OFDM signal is shown in Figure 2. After PSK/QAM modulation, the input data stream is loaded onto the single frequency subcarriers and then the modulated subcarriers are added with fixed spacing frequencies together. This process is equivalent to reconstruction of the time domain signal from the frequency domain, so the OFDM signal is generated by inverse fast Fourier transform (IFFT). Unlike LTE/4G, 5G has a more flexible frame structure. According to 3 GPP, the downlink transmission is organized into frames with \(T_{f}=10\)ms duration, each consisting of ten subframes of 1 ms duration. The subframe is divided into slots, which is the minimum unit of data scheduling and the slot duration is decided by the subcarrier spacing (SCS) \(\Delta f\). In addition, to remove the influence of the multipath effect, the OFDM system adopts the cyclic prefix (CP). There are two modes of 5G cyclic prefix, \"Normal\" and \"Extended\". However, the \"Extended\" mode is only applicable to a specific subcarrier spacing 60 kHz, which is not considered in this paper. The subcarrier spacing available for 5G and its corresponding parameters are shown in Table 3. The parameter \(\mu\) is the subcarrier spacing configuration, \(\Delta f=2^{\mu}\cdot 15\)kHz.