## 1 Mission Objectives and Constraints  
Specify detailed mission objectives, including the target resolution, swath width, and imaging modes. Define constraints related to the satellite platform, such as size, weight, satellite electric power budget, and orbital parameters. Radar System Parameters  
Confirm the use of the X-band frequency, detailing the specific frequency range for optimal performance. Detail the antenna specifications: phased array antenna type, number of elements, individual element characteristics, and overall antenna dimensions. Set specific requirements for incidence angle range and resolution, both range and azimuth. Satellite Platform  
Include details about the satellite bus, such as stabilization (3-axis or spin-stabilized), available electric power, and data handling capabilities. Specify orbit parameters like altitude, inclination, and expected lifespan. Antenna Design  
In-depth design of the phased array antenna, focusing on array configuration, element design, and materials. Considerations for beamforming, beam steering, and polarization capabilities. Simulate antenna performance for gain, beamwidth, and sidelobe characteristics. PRF and Ambiguity Considerations  
Develop a more detailed approach to setting the PRF, including trade-offs between swath width, range ambiguity, and ground moving target indication (GMTI) capabilities. Include considerations for minimizing azimuth ambiguities. System Losses  
Expand to include losses due to the entire signal path, including transmit/receive modules, waveguide losses, and any digital processing losses. Doppler Frequency Calculation  
Enhance the Doppler calculation by considering beam steering effects and the satellite's orbital decay over time. Effective Antenna Area  
Calculate considering not just physical dimensions but also the efficiency of the antenna elements and the impact of the array design. NESZ Calculation  
Detailed calculation incorporating all relevant parameters, including system noise figure, antenna gain, and pulse width. Iterate and Optimize  
Include a feedback loop for continual refinement based on test results and simulations. Consider the use of machine-learning or optimization algorithms to fine-tune the design parameters. In this paper, the design for a micro-X-band SAR satellite placed in a circular orbit is focused on finding the ideal antenna area. This involves trading off between resolution, payload power, range, and antenna area and examining their interplay with other SAR parameters. A system loss of 5 dB and a system temperature of 290 K were assumed to start the design. The other input parameters and desired resolutions were selected to provide a system performance NESZ of \(-\)5 dB. Although the most existing SAR missions have around \(-\)20 dB, this value is taken as optimal to keep the system power as optimal for a small SAR satellite to start off the trade-off. Table 2 presents the optimal parameters for desired resolutions at a 500 km altitude. The optimal values are selected from the examples given in Table 1. The aim is to analyze the effect of parameters as input and outputs. Therefore, frequency allocation by International Telecommunication Union (ITU) or other regulations are neglected. However, the nearest values that fall within the allowed ranges can be selected for usage. Table 2 above is generated from the NESZ equation, and the parameters are taken as optimal. To minimize the satellite, the transmitting power and antenna size are the paramount constraints. Based on the selected NESZ and altitude, the transmitting power requirement vs. antenna area graphs are shown Figure 2, Figure 3, and Figure 4, respectively. The figures show the same parameters and inputs as in Table 2, but the altitudes are 500 km, 600 km, and 700 km, respectively. It can be observed that altitude has a direct impact on both the antenna area and transmitting power requirements. As the altitude increases, the required transmitting power and antenna area also increase.