## 3 Azimuth Deramping Pre-Processing for GTLR-BiSAR  
During the data acquisition of GTLR-BiSAR operating in SS or TOPS mode, the azimuth Doppler bandwidth of the echo data increase with the steering of the LEO receiver antenna's main beam. Under this circumstance, the azimuth Doppler bandwidth is much larger than the pulse repetition frequency (PRF), which results in the azimuth signal aliasing in the Doppler domain. In other words, the supporting area of the signal azimuth frequency spectrum for GTLR-BiSAR SS or TOPS modes is folded because of spatial undersampling. In order to process the echo data of GTLR-BiSAR SS or TOPS modes efficiently in the frequency domain, we should remove the azimuth aliasing first. As shown in Figure 2, the coordinate frame \(O\)-\(XYZ\) is consistent with the previous definition in Figure 1. The black dashed lines \(L_{1}\) and \(L_{2}\) indicate the edges of the illuminated scene. The black dotted line \(L_{c}\) stands for the center line of the illuminated scene. These lines are parallel to the flight direction of LEO receiver. The LEO receiver moves with an effective radar velocity \(V_{eff}\), and the closest range from the virtual rotation center to the LEO receiver's trajectory is \(R_{ref}\). The range between \(L_{c}\) and the LEO receiver's trajectory is \(R_{r0}\). According to Figure 2, the equivalent projecting velocity of the scene center line is \(V_{c}=V_{eff}/\alpha\) geometrically. For the GTLR-BiSAR SS mode (Figure 1(a)), \(\alpha=R_{ref}/(R_{ref}-R_{r0})\), and for the GTLR-BiSAR TOPS mode (Figure 1(b)), \(\alpha=R_{ref}/(R_{ref}+R_{r0})\). We define \(\alpha\) as the sliding factor, which is a critical parameter to determine the azimuth resolution and scene width for the SS and TOPS modes. To remove the azimuth aliasing, [PERSON] et al. [19], [PERSON] et al. [20], and [PERSON] [21] have proposed the azimuth pre-processing methods for the SS or TOPS mode in monostatic SAR system. In this section, we further propose two kinds of uniform pre-processing methods, mathematically and geometrically, for the SS and TOPS modes in the GTLR-BiSAR system. The two methods are essentially the same. They are both utilized to calculate the azimuth frequency modulation rate \(K_{rot}\) caused by the rotation of the LEO receiver main beam. 1. The geometrical method to obtain \(K_{rot}\) Using Figure 2, we can calculate the Doppler history \(f_{d\_rot}\) of the virtual rotation center according to the LEO receiver orbit track data, i.e., the position and velocity data of the LEO satellite. Assume that the azimuth duration of the LEO receiver orbit track data are \(t_{track}\), \(K_{rot}\) is calculated as follows: \[K_{rot}=[Max(f_{d\_rot})-Min(f_{d\_rot})]/t_{track}\] (22) where \(Max(\cdot)\) and \(Min(\cdot)\) indicate the maximal Doppler value and the minimal Doppler value, respectively. Figure 2: Data Acquisition of the GTLR-BiSAR System (not scaled). (**a**) Data Acquisition of the SS mode. (**b**) Data Acquisition of the TOPS mode. 2. The mathematical method to obtain \(K_{rot}\) According to the conventional monostatic SAR deramping operation in SS or TOPS modes, \(K_{rot}\) is usually calculated by using the parameters \(R_{ref}\), \(\lambda\) and \(V_{eff}\), as follows: \[K_{rot}=\frac{V_{eff}^{2}}{\lambda R_{ref}}\] (23) For the GTLR-BiSAR system operating in SS or TOPS modes, it is worth noting that only the moving station, i.e., the LEO receiver, provides the azimuth Doppler contribution, so the constant coefficient 2 is absent in Equation (23) compared with the monostatic case. Once we obtain \(K_{rot}\) by either of the above mentioned methods, the reference function can be expressed as: \[S_{ref}(t_{a})=exp(\xi j\pi K_{rot}t_{a}^{2})=exp(\xi j\pi\frac{V_{eff}^{2}}{ \lambda R_{ref}}t_{a}^{2})\] (24) Furthermore, the azimuth deramping pre-processing to remove the azimuth Doppler aliasing is achieved through a convolution operation with the above reference function: \[