# High-Temporal-Resolution High-Spatial-Resolution Spaceborne SAR Based on Continuously Varying PRF
## 1 Introduction
Without loss of generality, we take one minute repeat-observation interval as an example to clarify the proposed technique, and the following simulations are based on parameters in Table 2.  
For SAR systems, high squint angle would cause an increased range cell migration (RCM), which leads to a contradiction between the receive window and 'blind ranges' (e.g., nadir echo blockage and transmit pulse blockage). Compared with the conventional stripmap SAR, the RCM of the sliding spotlight and staring spotlight modes at high squint angles takes a substantially greater percentage of the receive window (Figure 3), thereby resulting in a narrow imagery swath. Figure 3: Illustration of the receive window. The PRI (\(1/\mathrm{PRF}\)) includes a transmitted pulse duration \(\tau\), two guard intervals \(t_{\mathit{prot}}\), and the receive window. \(t_{\mathit{ERS}}\) is the echo time of the effective range swath, \(t_{\tau}=\tau\) is the received pulse duration for each point, ensuring that the targets to be imaged are with full range resolution, and \(t_{\mathit{RCM}}\) is the duration caused by the RCM. The duration \(t_{\Delta R_{\mathit{limit}}}\), related to the span of the slant range, consists of \(t_{\mathit{ERS}}\) and \(t_{\mathit{RCM}}\). Figure 2: Squint angle as a function of illumination time for different orbit height. Black line represents the synthetic aperture process for images. The look angles of different simulations are chosen as 35\({}^{\circ}\). The required squint angle decreases along with an increasing orbit height. For systems with an orbit height of 1000 km, images with repeat-observation intervals varying from tens of seconds to 4 min will be available when the squint angle is higher than 32.1\({}^{\circ}\). The concept of continuously varying PRF (CVPRF) is proposed to overcome this limitation, as shown in Figure 4. With this technique, the RCM can be efficiently reduced by varying the PRF according to the changing slant range (defined as the range between SAR sensor and target) of each transmitted pulse. As apparent from the right of Figure 4, the slant range decreases along with the decreasing squint angle during the acquisition of the first image. For example, to avoid transmitted pulse blockage and nadir echo blockage, we choose 4030 Hz for the red pulse, according to the timing diagram on the left. For the green pulse, the slant range decreases along with the decreasing squint angle. Under this condition, we need to change the PRF for the green pulse, because 4030 Hz is not suitable any more. Similarly, the suitable PRFs should also be changed for pulses with the other colors. For the second image, the suitable PRFs would vary inversely along with the increasing squint angle. Using this technique, echo data of all pulses can be received by SAR sensor and high-squint-angle SAR images can be achieved. Several other continuous PRF variation concepts have been suggested for different purposes. To overcome the limitation of multibeam SAR systems, EADS Astrium and DLR both have proposed Staggered-SAR to image a large continuous swath, as illustrated in Figure 5. According to [17], the strategy of Staggered-SAR attempts to avoid transmitted pulse blockage at the expense of missing pulses for each target, which would lead to a degradation of imaging quality. However, for higher resolution, the missing pulses would increase exponentially, bringing more challenge to recover the missing samples by means of interpolation. The CVPRF technique proposed in this paper, varies the PRF according to the changing slant range, and every transmitted pulse is received efficiently. This technique is effective for high-spatial-resolution and high-squint-angle SAR systems. This paper is organized as follows: In Section 2, the CVPRF concept is presented in detail, therein showing how the limitation of the RCM is overcome. Moreover, a comparison concerning the data acquisition ability is presented. In Sections 3 and 4, the design method of the sequence of the PRF is proposed, and range ambiguities are discussed.