# Small-Satellite Synthetic Aperture Radar for Continuous Global Biospheric Monitoring: A Review
## 2 Design Principles of Synthetic Aperture Radar  
The underlying physics is identical between large-satellite SAR and small-satellite SAR in their design process, but the optimization goals might be different. Design principles of Smallsat SAR are unconventional in that minimizing the antenna sizes and the number of observation modes has priority over improving the ground resolution, whose trend is prominent under the launch mass of 200 kg [45]. In general, the best possible ground resolution for stripmap SAR in the along-track (azimuthal) dimension is given by:  
\[\delta_{x}\geq L_{a}/2 \tag{1}\]  
where \(L_{a}\) is the along-track (azimuthal) physical length of the SAR antenna, which is illustrated in Figure 3 (left). To avoid ambiguity and maximize the swath, the minimum antenna area that is the product of \(L_{a}\) and the across-track (cross-track) width \(W_{a}\) should be:  
\[A_{a}=W_{a}L_{a}>\frac{4V\lambda R_{m}}{c}\tan\eta \tag{2}\]  
where \(V\) is the satellite speed (\(\sim\)7 km/s), \(\lambda\) is the radar wavelength, \(c\) is the speed of light, \(R_{m}\) is the range to the middle of the swath, and \(\eta\) is the look angle. The corresponding swath is  
\[W_{g,max}=\frac{c}{2 PRF_{min}\cdot\sin\eta}=\frac{cL_{a}}{4V\sin\eta} \tag{3}\]  
under the condition that the ground swath must be wider than the antenna footprint on the ground at the minimum pulse repetition frequency (PRF) equal to 2\(V\)/\(L\) or the Doppler bandwidth [46]. From the linear relation between the ground swath and the antenna size, it is possible to reduce the antenna length without sacrificing the ground resolution by accepting a smaller swath, or vice versa. The antenna width may also be reduced with a smaller noise bandwidth. The following expression shows, however, that reducing the antenna width (\(W_{a}\)) has squaring impacts that must be absorbed by the noise bandwidth (\(B_{n}\)), the transmit pulse duration (\(\tau_{p}\)), the peak transmission power (\(P_{t}\)), or the antenna length in order to keep the signal-to-noise ratio (SNR) constant:  
\[SNR_{max}\propto\frac{P_{t}L_{a}W_{a}^{2}\tau_{p}}{B_{n}} \tag{4}\]  
The ground-range resolution is dependent on the chirp bandwidth as well as the incidence angle:  
\[\delta_{gr}=\frac{c}{2B\sin\eta} \tag{5}\]  
Figure 3: Basics of spaceborne SAR: (**left**) Nomenclature of design parameters. (**right**) Ground-range resolution as a function of look angle (ground swath) and bandwidth. Source: JPL, Capella Space.  
where by better ground-range resolution would increase the bandwidth and thus require a higher transmitter power per Equation (4). Unlike 2-D optical images, this altimetry capability of SAR leads to numerous 3-D applications, which is why the ground-range resolution is an important performance metric; the design specifications of an optical satellite only mention ground sample distance (GSD) whereas SAR satellites are usually specified by both azimuthal resolution and ground-range resolution as listed in Table 1. Figure 3 (right) describes the multi-parametric dependence of ground-range resolution on look angle and bandwidth.  
The data rate should also be carefully chosen to maximize on-time of SAR and the transferrable data volume, under the ground station constraints, in addition to the relationship among the antenna size, the orbit geometry, the SNR, and the power requirement. Small satellites usually minimize the number of observation modes and the number of channels to cope with their inherent design constraints. While smaller and more efficient commercial-off-the-shelf (COTS) parts are becoming available with respect to communications and power electronics, even more innovative technologies such as inter-satellite links (e.g., optical laser communications) or wireless power transfers may be envisioned.