## 3 SAR Payload Design
### System Parameter Design  
The SAR payload can be designed using two major approaches: performance- and constraint-driven. Because small satellites pose tight restrictions on size, weight, power, and cost (SWaP-C), the SAR payload should be designed using a constraint-driven method. To reduce the size of the SAR satellite to fit the microsatellite, the size of the SAR antenna should be reduced foremost. Alternatively, the power consumption, thermal control, and data rate should be decreased. Fundamentally, the constraints impacting the design of the SAR systems for small satellites include the size, mass, power, and cost. Moreover, the mass and size limit the area of the antenna and, consequently, limit the gain of the antenna. This, in turn, affects the sensitivity of the SAR image, as well as the azimuth resolution and swath width. Furthermore, the maximum transmission power is limited by the available DC power, and the sensitivity of the SAR image is expressed in the NESZ as follows:  
\[\sigma_{NE}=\frac{4(4\pi)^{3}R_{s}^{3}L_{s}kT_{s}B_{t}\sin\theta_{i}\tau_{s}}{c \cdot G_{t}(\theta_{e})\cdot G_{r}(\theta_{e})\lambda^{3}P_{t}\tau_{p}f_{p}}\, \tag{1}\]  
where \(L_{s}\) denotes the system loss, \(B_{t}\) represents the transmitted bandwidth, \(\tau_{p}\) denotes the pulse width, \(T_{s}\) represents the system noise temperature, \(G_{t}\) and \(G_{r}\) represent the transmit and receive (Rx) antenna patterns, respectively, \(P_{t}\) denotes the peak transmitted power, \(f_{p}\) represents the PRF, \(R_{s}\) denotes the slant range to the scene center, \(\lambda\) denotes the wavelength, \(\theta_{i}\) represents the incidence angle, \(k\) denotes the Boltzmann constant, \(c\) denotes the propagation velocity, and \(v_{s}\) represents the satellite velocity. As observed from this equation, the sensitivity of the SAR image can be improved by increasing the transmission output or the transmission pulse width. Alternatively, the slant range of the target can be reduced as well. Therefore, in small satellites, the incidence angle is typically set in the range of 15-35\({}^{\circ}\) with a small slant range owing to the limitations of the transmission power and antenna size. In another approach, the physical size of the antenna can be increased (in this case, the azimuth resolution decreases) or the antenna gain is increased. As the transmission bandwidth increases, the system complexity increases as well. Thus, the required resolution is reduced to diminish the transmission bandwidth. Moreover, the noise level can be decreased by reducing the receiver or quantization noise, which consequently minimizes the system losses. After designing the SAR system based on the stripmap mode, other modes such as the ScanSAR mode were designed based on the obtained results. The azimuth resolution can be evaluated as follows:  
\[\rho_{a}=\frac{\lambda}{2\theta_{int}}, \tag{2}\]  
where \(\theta_{int}\) denotes the integration angle, which is more advantageous than the L-band and C-band for selecting the X-band and obtaining high-resolution SAR images. Because the antenna gain is inversely proportional to the square of the wavelength, the X-band selection (9.65 GHz) is extremely advantageous for small and lightweight antennas. In addition, the X-band SAR payload can facilely achieve a high resolution with a smaller satellite mass. Moreover, the X-band is suitable for recognizing the ground surface objects, and the frequency bands located higher than the Ku-band are subject to large rain attenuation. Furthermore, the technology of GaN devices such as high-power amplifiers did not mature well in higher frequency bands. Therefore, the X-band was selected for the S-STEP mission. The antenna size (antenna length) was determined using the azimuth resolution because the azimuth resolution of the stripmap mode was determined to be 1/2 of the antenna length.