## 3 Near-Space Passive Radar Remote Sensing
### Technical Challenges  
Near-space passive radar shows much promise for remote sensing applications, but several challenges must be overcome. The most important one, besides synchronization compensation (including phase [61, 62], spatial [63, 64] and time [65] synchronization) is image formation algorithm. In near-space passive bistatic SAR system, the illuminator (take also GPS satellite as an example) follows a rectilinear trajectory, while the receiver follows also a rectilinear trajectory but with a different velocity.  
Consider the geometry depicted in Figure 6, the instantaneous slant range of a given point target is  
\[R(\tau)=\sqrt{R_{T0}^{2}+(v_{T}\tau)^{2}}+\sqrt{R_{R0}^{2}+(v_{R}\tau)^{2}} \tag{6}\]  
where \(R_{T0}\) is the closest slant range to the transmitter, \(R_{R0}\) is the closest slant range to the receiver, \(v_{T}\) is the transmitter velocity, \(v_{R}\) is the receiver velocity, \(\tau\) is the slow time in azimuth, respectively. It is noticed that the range history of a given point target does not depend any more only on the zero-Doppler distance and the relative distance from the target to the transmitter, but also on the absolute distance to the receiver. The instantaneous Doppler frequency is  
\[f_{d}(\tau)=-\frac{1}{\lambda}\frac{\mathrm{d}R(\tau)}{\mathrm{d}\tau}=-\frac {1}{\lambda}(\frac{v_{T}^{2}\tau}{\sqrt{R_{T0}^{2}+(v_{T}\tau)^{2}}}+\frac{v_ {R}^{2}\tau}{\sqrt{R_{R0}^{2}+(v_{R}\tau)^{2}}}) \tag{7}\]  
The corresponding Doppler chirp rate can be derived as  
\[k_{d}(\tau)=-\frac{1}{\lambda}\frac{\mathrm{d}^{2}R(\tau)}{\mathrm{d}^{2}\tau }\approx-\frac{1}{\lambda}[\frac{v_{T}^{2}}{R_{T0}}\cos(\frac{v_{T}\tau}{R_{T0 }})+\frac{v_{R}^{2}}{R_{R0}}\cos(\frac{v_{R}\tau}{R_{R0}})] \tag{8}\]As near-space passive SAR is an azimuth-variable bistatic SAR, from Figure 7 we find that there is a range ambiguity that does not exist in monostatic or azimuth-invariable bistatic cases. Two or more point targets located at different positions can have the same range delay at zero-Doppler but will have different range histories. Further analysis shows that its Doppler chirp rate will be azimuth variable, as shown in Figure 8. Note that the simulation parameters used in this plot are: transmitter velocity and altitude are 3,870 m/s and 20,183 km, near-space receiver velocity and altitude are 5 m/s and 20 km, respectively. The results show that there is a technical challenge towards developing efficient focusing algorithms. This situation will get more complicated for unflat digital earth model (DEM) topography. In monostatic or azimuth-invariable bistatic SAR systems, scene topography is ignored in image formation processing because the measured range delay is related with the double target distance and the observed range curvature; Hence, topography is only used to project the compressed image, which is in slant range to the ground range. However, for near-space passive SAR, because of its azimuth-variant configuration, it is a mandatory to know both transmitter-to-target distance and target-to-receiver distance to properly focus its raw data.  
In this case, efficient monostatic SAR algorithms such as Chirp scaling [66] and \(\omega\)-K [67], may be unsuitable to accurately focus the collected data due to topography dependence of the impulse response. Therefore, some new efficient image formation algorithm should be found for this near-space SAR configuration. Possible solutions are back-projection algorithm [68] and nonlinear chirp scaling algorithm [69].