## 2 Fundamentals of SAR for Antenna Sizing and Transmitting Power Consideration
### PRF Bounds  
In a spaceborne SAR system, the PRF (pulse repetition frequency) bounds are important for various reasons. The PRF refers to the rate at which pulses are transmitted by the radar system. The effect of PRF is detailed in the relevant scientific publications [33; 37; 38; 45; 52; 53; 54; 55; 56; 57]. All the parameters are related to each other for the satellite in question. The relation of PRF to all others is explained in detail. The minimum and maximum PRF values determine the range of possible pulse repetition rates. The range resolution in SAR is determined by the pulse length and is inversely proportional to the bandwidth. A lower PRF allows for a longer pulse length, resulting in improved range resolution. The minimum PRF determines the pulse length limit for achieving the desired range resolution. The maximum PRF determines the unambiguous range, which is the maximum distance that can be accurately measured without range ambiguities. Higher PRF values lead to a larger unambiguous range, allowing for the detection of targets at greater distances. The antenna area is inversely proportional to the maximum PRF. A higher maximum PRF requires a smaller antenna area to achieve the desired range resolution. Conversely, a lower maximum PRF necessitates a larger antenna area to maintain the range resolution. The PRF bounds also affect the swath coverage, which refers to the ground area covered by the radar beam. The minimum PRF determines the maximum azimuth resolution, while the maximum PRF influences the minimum azimuth coverage. A larger PRF range allows for a wider swath coverage, enabling the imaging of a larger ground area. The PRF bounds impact the signal processing requirements of the SAR system. A wider PRF range requires more complex processing algorithms to handle variations in pulse repetition rates, while a narrower PRF range simplifies the processing requirements. The PRF bounds and antenna area are related to spaceborne SAR systems because they impact each other and are important for optimizing the system's performance. They affect the system's ability to avoid range ambiguities and Doppler effects, especially in spaceborne SAR systems that are in motion. The lowerbound of PRF is determined by the desired range resolution to avoid range ambiguities. Doppler shifts occur because the radar platform (e.g., a satellite) is in motion relative to the Earth's surface. These shifts result in a change in the frequency of the radar signals reflected from moving scatterers on the ground. Doppler shifts can be positive (for targets moving toward the radar) or negative (for targets moving away from the radar). The upper bound of PRF should be set to accommodate the maximum Doppler frequency shift expected in the imaging scenario. If the PRF is too low compared to the maximum Doppler shift, it can lead to Doppler ambiguities, where the radar signals from moving targets are misinterpreted. Setting an appropriate PRF is essential to avoid Doppler ambiguities and ensure accurate imaging, especially in spaceborne SAR systems where the satellite's motion can introduce significant Doppler shifts. To effectively image moving objects or account for the Doppler effects in spaceborne SAR, the choice of PRF bounds should be considered together with the satellite's velocity, the incidence angle, and the expected range of Doppler shifts due to the relative motion between the satellite and the Earth's surface. In summary, the max-min PRF bounds in a spaceborne SAR system play an important role in determining the range resolution, unambiguous range, antenna area, swath coverage, and signal processing requirements. Finding an optimal balance between these parameters is essential for designing an effective SAR system that meets specific imaging and operational requirements. In SAR systems, the PRF must be carefully chosen within certain bounds to optimize performance and avoid ambiguities.