# High-Temporal-Resolution High-Spatial-Resolution Spaceborne SAR Based on Continuously Varying PRF
## 2 CVPRF Concept
We consider a design example with the parameters listed in Table 2, and the simulation results are shown in Figure 8. Here, the dark solid line represents the slant range of a 5 km ground swath width with a squint angle of 17.3\({}^{\circ}\), and the red solid line represents the slant range of a 5 km ground swath width with a squint angle of 23.5\({}^{\circ}\). For the uniform PRF system, as apparent from the left of Figure 8, the acquisition would be invalid due to the conflict between the echo data and the blind ranges, and the maximum of \(\Delta R_{squit}\) is also limited to 18.6 km. However, this limitation would be overcome with the CVPRF system, where the PRF varies with the slant range. As shown on the right of Figure 8, the maximum of \(\Delta R_{squit}\) increases to 31.6 km, and the corresponding squint illumination angle can increase up to 23.5\({}^{\circ}\). During the acquisition of echo data, the slant range between the SAR sensor and the target varies with the squint angle, which causes a variation in the travel time for different pulses. As we know, for spaceborne SAR systems, the echo of a certain transmitted pulse will be received after several pulses. Without loss of generality, we assume a case in which the reflected pulse is received at the fifth PRI after being transmitted. As shown in Figure 9, the duration between transmitting and receiving can be defined as \(\Delta T_{i}=\frac{4}{PRF}+\tau+t_{prot}+\Delta t_{i}\). Here, \(\Delta t_{i}\) represents the location of the echo data in the receive window. Given the above-mentioned considerations, the slant range varies with the squint angle, which means that the duration \(\Delta T_{i}\) cannot remain fixed, resulting in a changing \(\Delta t_{i}\). For certain pulses, the echo data would overlap with the transmitted pulse, called blind ranges (Figure 9c). If, instead of a constant PRF, a sequence of continuously varying pulse intervals, which change according to the slant range, is employed, the interval \(\Delta t_{i}\) would be unchanged and would keep the echo away from the blind ranges (Figure 9d). Simulation result has validated the efficiency of the CVPRF technique, allowing echo data to remain in the receive window instead of conflicting with the transmitted pulse or nadir echo. Figure 6.0 Timing diagrams (slant range versus PRF) of the uniform PRF (**left**) and the CVPRF (**right**). The dark solid line represents the slant range of a 5 km ground swath width with a squint angle of 17.3\({}^{\circ}\), and the red solid line represents the slant range of a 5 km ground swath width with a squint angle of 23.5\({}^{\circ}\). The slant range of the acceptable squint angle is represented by the blue line, where the maximum of \(\Delta R_{squit}\) is limited to 18.6 km. The comparisons in the timing diagram and in the diagram of the transmitted and received pulses have demonstrated the strengthened acquisition capability of the CVPRF system. Based on the aforementioned analysis, one minute repeat-observation interval images with a 0.25 m resolution and 5 km swath in both the azimuth and range would be practical with parameters similar to those of TerraSAR-X. The following section will analyze and propose an elaborate sequence of PRFs that leads to an efficient echo acquisition for the CVPRF system.