# Passive Bistatic Ground-Based Synthetic Aperture Radar: Concept, System, and Experiment Results
## 2 System Overview
### Link Budget Analysis  
Considering the power of the satellite digital TV signal on the Earth surface is low, this subsection analyzes the link budget of PB-GB-SAR to provide the necessary fundamentals for system parameter selection and signal processing. As shown in Figure 4, the power budget of the reference channel is similar to a communication link budget. Assuming the one-way distance between the satellite and the reference antenna is \(R_{1,1}\), the power of the received reference signal from a single TV channel can be expressed as [38]  
\[P_{ref}=\frac{EIRP\cdot G_{ref}\lambda^{2}}{(4\pi)^{2}R_{1,1}^{2}} \tag{1}\]  
where the typical value of EIRP is from 50 to 59 dBW, as shown in Figure 3, and \(G_{ref}\) denotes the gain of the reference antenna; \(\lambda\) = _c/f\({}_{c}\)_ is the wavelength with \(c\) as the speed of light and _f\({}_{c}\)_ as the carrier frequency. For the surveillance channel, the signal power is given by [39]  
\[P_{surv}=\frac{EIRP\cdot G_{surv}\lambda^{2}\sigma}{(4\pi)^{3}R_{1,2}^{2}R_{2} ^{2}} \tag{2}\]  
where \(R_{1,2}\) is the distance between the TV satellite and the target, \(R_{2}\) is the distance between the target and the surveillance antenna, \(G_{surv}\) is the gain of the surveillance antenna (we note that, since only the feed-horn of the parabolic antenna without the reflector is used for the surveillance channel, as shown on the right of Figure 8, \(G_{surv}\) is much smaller than \(G_{ref}\)), and \(\sigma\) denotes the Radar Cross Section (RCS) of the target. Given the system noise temperature \(T_{0}\) and the system noise bandwidth \(B_{0}\), the noise power can be written as [39]  
\[P_{n}=k_{0}T_{0}B_{0} \tag{3}\]  
where \(k_{0}\) is the Boltzmann constant. According to Equations (1)-(3), and using the parameters in Table 1, the SNR of the reference and surveillance channels can be obtained by  
\[SNR_{ref}=P_{ref}/P_{n}=\frac{EIRP\cdot G_{ref}\lambda^{2}}{(4\pi)^{2}R_{1,1}^ {2}k_{0}T_{0}B_{0}L_{r}}=10.1\;dB \tag{4}\]  
and  
\[SNR_{surv}=P_{surv}/P_{n}=\frac{EIRP\cdot G_{surv}\lambda^{2}\sigma}{(4\pi)^{ 3}R_{1,2}^{2}R_{2}^{2}k_{0}T_{0}B_{0}L_{r}}=-49.9\;dB \tag{5}\]  
It can be seen from Equations (4) and (5) that the SNR of the reference signal is more than 10 dB and can be used to form a near-optimal matched filter for range compression [43] (the small integration gain loss caused by the noise can be ignored), while the SNR of the surveillance signal is quite low and thus the TV spectrum cannot be explicitly observed. In Table 1, the antenna moving step is selected as 5 mm, which is smaller than a quarter of the wavelength. The synthetic aperture length and the coherent integration time are to be determined (TBD) by the following simulations. Firstly, based on the matched filtering theory and by using multiple TV channels, the SNR after range compression obtained by cross-correlating the surveillance signal with the reference signal is given by [44]  
\[SNR=\frac{EIRP\cdot G_{surv}\lambda^{2}\sigma}{\left(4\pi\right)^{3}R_{1,2}^{2 }R_{2}^{2}k_{0}T_{0}L_{r}}NT_{\text{int}} \tag{6}\]  
where \(N\) is the number of used TV channels. With the parameters in Table 1, the SNR of the range compression result versus the integration time \(T_{int}\) is shown on the left of Figure 6. Due to the memorylimitation of the used oscilloscope (only 1 Mpts deep memory is available for a data sampling rate of 10 GSamples/s); an integration time of 100 us is used in this study. As we can see, to get an SNR higher than 0 dB after range compression, the minimal integration time should be \(\sim\)236 us, which cannot be obtained by the used oscilloscope in a single measurement (summing multiple measurements together is however possible). With a 100 us coherent integration time, the SNR is still lower than 0 dB (\(-\)3.74 dB) and the target cannot be detected. Therefore, azimuth compression is further conducted.