# Design of an Integrated System for Spaceborne SAR Imaging and Data Transmission
### Design Concept  
We propose a method that independently modulates radar and data transmission signals on different subcarriers within the same frequency band. By adjusting the power of each subcarrier separately, we can optimize the performance of both radar and data transmission systems simultaneously. Figure 1 illustrates an application scenario involving integrated spaceborne SAR and data transmission for single-target imaging. X, Y, and Z represent the range, azimuth, and elevation directions, respectively, with the system operating in a single-transmit-single-receive mode. The figure shows that the SAR satellite continuously transmits pulse signals and receives pulse echoes during the reception window. In stripmap and scan modes, the synthetic aperture time of SAR is relatively short, limiting the amount of data transmission and image resolution for mobile terminals. By using the spotlight mode, which continuously adjusts the antenna's direction toward the target, the synthetic aperture time can be extended. This method enhances radar echo quality and supports large data transmission requirements. During its flight, the SAR platform transmits a signal to the ground that combines SAR and data transmission functions. The platform can use the same antenna to receive echoes from ground targets for SAR imaging. It then sends the echo images as communication data to mobile terminals within the coverage area. This process uses spotlight mode to acquire echo information continuously and enable data transmission. The SAR system's signal, modulated by FBMC-OQAM, can be expressed as [25]:  
\[x_{\mathrm{r}}(t)=\sum_{k=1}^{K}\sqrt{p_{\mathrm{r},k}}q_{\mathrm{r}}(t)e^{2 \pi(f_{\mathrm{c}}+k\Delta f_{\mathrm{r}})t+\phi(t)}=\sum_{k=1}^{K}\sqrt{p_{ \mathrm{r},k}}\Phi_{\mathrm{r},k}(t) \tag{1}\]  
where \(x_{\mathrm{r}}(t)\) represents the transmitted SAR signal; \(K\) denotes the number of subcarriers; \(\mathbf{p_{\mathrm{r}}}=[p_{\mathrm{r},1},\dots,p_{\mathrm{r},k}]^{\mathrm{T}}\) indicates the power allocated to each subcarrier in the SAR system; \(\Delta f_{\mathrm{r}}\) is the subcarrier bandwidth spacing; \(\phi(t)\) refers to the phase shift in the spotlight mode; \(q_{\mathrm{r}}\) refers to the prototype pulse modulation signal of FBMC-OQAM; and \(\Phi_{\mathrm{r},k}(t)\) represents the modulated radar waveform. Using non-random sequence signals from data transmission systems for SAR imaging can compromise range ambiguity suppression in SAR imaging. Therefore, data transmission signals should not be used for SAR imaging in FBMC-OQAM systems. Figure 1: Schematic diagram showing the application scenario for the integrated spaceborne SAR and data transmission system. The transmitted signal in an FBMC-OQAM data transmission system can be expressed as [26]:  
\[x_{\text{c}}(t)=\sum_{k=1}^{K}\sqrt{p_{c,k}}d_{k}q_{\text{c}}(t)e^{\text{j}2\pi(f _{\text{c}}+k\Delta f_{\text{c}})t+\phi(t)}=\sum_{k=1}^{K}\sqrt{p_{c,k}}d_{k} \Phi_{c,k}(t) \tag{2}\]  
where \(x_{\text{c}}(t)\) represents the transmitted data signal; \(\mathbf{p}_{\text{c}}=[p_{\text{c},1},\dots,p_{\text{c},K}]^{\text{T}}\) denotes the power allocated to each subcarrier in the data transmission system; and \(d_{k}\) is the signal carrier symbol on the \(k\)-th subcarrier. To ensure consistent modulation, we use 4 QAM modulation, which meets the condition \(|d_{k}|_{2}=1\); \(q_{\text{c}}\) refers to the prototype pulse modulation signal of FBMC-OQAM; \(B_{\text{w}}\) indicates the signal bandwidth; \(\Delta f_{\text{c}}\) represents the subcarrier bandwidth spacing; and \(\Phi_{c,k}(t)\) represents the modulated waveform of the data transmission signal. The SAR signal reflects off the ground and is returned to the SAR satellite.