# Passive Location for 5G OFDM Radiation Sources Based on Virtual Synthetic Aperture
## 5 Simulations and Results  
The parameters of the simulation are shown in Table 4. Since the spectrum of the 5G signal is divided into two regions, 450 MHz to 6 GHz and 24 GHz to 52 GHz, the frequency of the signal is set as 29 GHz. According to the parameters, the virtual aperture time \(T_{s}=kcR_{c}/(vf_{0}D)\approx 0.17\) s (generally, \(k=1\)). The Doppler spectrum with a certain width after range FFT to extract signal at a particular frequency is shown in Figure 4(a). After the phase compensation, the processed signal will be a linear frequency modulation signal in the azimuth domain, as shown in Figure 4(b). Thus, after matched filtering, the location result is shown in Figure 6. The location error is around 10 m. The theoretical value of the azimuth resolution is \(\rho_{a}\approx 5\) m, which is approximately equal to the simulation result. The theoretical value of the range resolution is \(\rho_{r}\approx 16.703\) km, simulation result. Since the center frequency of the simulation signal is high, the virtual aperture is short, which leads to a poor range resolution. To improve the resolution, it is considered to use high-order spectrum instead of amplitude spectrum to analyze the location result. For 4 th-order spectrum, the range resolution is \(\rho_{r}\approx 8.498\)km, and the azimuth is \(\rho_{a}\approx 2.5\) m. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Center frequency \(f_{0}\) & 29 GHz \\ Subcarrier interval \(\Delta f\) & 30 kHz \\ Bandwidth & 50 MHz \\ Sampling frequency \(f_{s}\) & 122.88 MHz \\ Modulation & 16 QAM \\ Antenna aperture \(D\) & 5 m \\ Platform velocity \(v\) & 7313 m/s \\ SNR & 5 dB \\ Radiation source location & (0 km, 600 km) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation parameters. Figure 5: The Doppler spectrum before and after phase compensation. (**a**) The Doppler spectrum before phase compensation. (**b**) The Doppler spectrum before phase compensation. After Monte Carlo simulations, the azimuth and range resolution curves of the amplitude spectrum and 4 th-order spectrum are shown in Figure 7. The result shows that the azimuth and range resolution will be better with the longer virtual aperture. In addition, the simulation result is basically consistent with the theoretical result as Equations (22) and (24). Figure 6: The passive location result. (**a**) The 2-D location result. (**b**) The azimuth location result. (**c**) The range location result. Figure 7: The resolution curves. (**a**) The azimuth resolution. (**b**) The range resolution. Monte Carlo simulations (100 times) under different SNR are carried out, and the location error curve variation with the virtual aperture is shown in Figure 8, which was compared with the traditional DOA and TDOA methods. The DOA method is using phase interferometer for direction finding, the baseline is 5 m, and the phase ambiguity is solved by a shorter baseline with a length of 0.5 m. TDOA method uses Chan to solve the radiation source location with seven satellites. Both methods are simulated at 20 dB SNR. Compared with the DOA method, the accuracy of the virtual aperture passive location method is significantly improved, and Figure 8 shows that the longer virtual aperture leads to higher location accuracy. When SNR = 5 dB and virtual aperture time \(t_{s}\approx 30\)ms, the location error is approximately the same as the DOA method. Under the condition of higher SNR and longer virtual aperture, the location accuracy can reach tens of meters, which is similar to that of the TDOA method, but the system complexity and cost are greatly reduced because only a single satellite and antenna are used. The configuration of satellites is shown in Figure 9. The distance between the satellites is about 100 km. The Monte Carlo simulations of the satellite vibration effect are shown in Figure 10. Since the virtual aperture time is \(T_{s}\approx 0.17\) s, we consider the two cases that the azimuth jitter frequency \(f_{a}<1/T_{s}\) (5 Hz) and \(f_{a}>1/T_{s}\) (10 Hz, 15 Hz).