# A High-Resolution, Wide-Swath SAR Imaging System Based on Tandem SAR Satellites
## 4 Verification and Analysis
### System Design Example and Imaging Performance  
Table 2 shows the satellite parameters used in this part. Based on the parameters in Table 2, this part designs an example HRWS-SAR system. The azimuth and range resolutions of the system are set to 3 m. The range swath is set to 200 km and divided into six subswaths. Each subswath has the same PRF and different \begin{table}
\begin{tabular}{c c} \hline \hline
**Processing Steps** & **Content** \\ \hline Step one & Obtains \(S_{1}(\eta,\tau)\) by range compression of the original echo. \\ Step two & Extracts the observation vectors \(\{\mathbf{s}_{i}|i=1,\cdots,N_{g}\}\) from \(S_{1}(\eta,\tau)\) \\  & For \(i=1\): \(N_{g}\) \\  & \(\hat{\sigma}_{\text{tem}}=\mathbf{Q}_{s}{}^{-1}\mathbf{S}_{i}\) \\  & \(\mathbf{Q}_{0}=\text{diag}\Big{(}\sigma_{d,i}\cdot\sigma_{d,i}^{*}\Big{)}\) \\ Step three & \(\hat{\sigma}_{i,1}=\mathbf{Q}_{0}\cdot\mathbf{A}^{\text{H}}\hat{\sigma}_{ \text{tem}}\) \\  & \(\mathbf{Q}_{1}=\text{diag}\Big{(}\hat{\sigma}_{i,1}\cdot\hat{\sigma}_{i,1}^{*} \Big{)}\) \\  & \(\hat{\sigma}_{i,2}=\mathbf{Q}_{1}\cdot\mathbf{A}^{\text{H}}\hat{\sigma}_{ \text{tem}}\) \\ Step four & Output: \\  & \(\hat{\sigma}_{\text{sum}}=[\hat{\sigma}_{1,2}\quad\hat{\sigma}_{2,2}\quad \cdots\quad\hat{\sigma}_{N_{g},2}]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Processing steps of the real airborne SAR data. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Carrier frequency (GHz) & 9.6 \\ Range bandwidth (MHz) & 100 \\ Sampling frequency (MHz) & 120 \\ Pulse width (\(\upmu\)s) & 20 \\ Orbital height (km) & 630 \\ Platform velocity (m/s) & 7545 \\ Resolution (m) & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: System parameters for Sat-1 and Sat-2. squint angles. The beam position parameters of the two satellites are the same as in Table 3. The scanning parameters of Sat-1 are listed in Table 4.  
According to the designed SAR imaging system, the received echo of subswath 1 is simulated based on the scene as shown in Figure 9. Then, the BP algorithm, the L1 algorithm, and the proposed algorithm are carried out to image the simulated echo. According to the imaging results in Figure 10, there is obvious ambiguity energy in the imaging result of the BP algorithm, while the L1 algorithm and the proposed algorithm achieve good imaging quality. Figure 11 shows the azimuth profiles of the range gate marked by a red arrow in Figure 10. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Burst Duration(s)** & **3 dB Doppler Bandwidth (MHz)** \\ \hline Subswath 1 & 0.077 & 2446 \\ Subswath 2 & 0.075 & 2428 \\ Subswath 3 & 0.074 & 2323 \\ Subswath 4 & 0.072 & 2231 \\ Subswath 5 & 0.070 & 2148 \\ Subswath 6 & 0.069 & 2032 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Scanning parameters of Sat-1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Look Angle in the** & & & \\  & **Zero Doppler Plane (\({}^{\circ}\))** & & & \\ \hline Subswath 1 & 32.01–34.41\({}^{\circ}\) & 2673 & 0\({}^{\circ}\) & 39.90 \\ Subswath 2 & 29.79–32.19\({}^{\circ}\) & 2673 & 8.70\({}^{\circ}\) & 37.58 \\ Subswath 3 & 27.51–29.91\({}^{\circ}\) & 2673 & 15.30\({}^{\circ}\) & 35.55 \\ Subswath 4 & 25.23–27.63\({}^{\circ}\) & 2673 & 19.40\({}^{\circ}\) & 33.82 \\ Subswath 5 & 22.91–25.31\({}^{\circ}\) & 2673 & 22.50\({}^{\circ}\) & 32.31 \\ Subswath 6 & 20.55–22.95\({}^{\circ}\) & 2673 & 26.80\({}^{\circ}\) & 31.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Beam position parameters of six subswaths. Figure 9: Illustration of the observed scene including 25-point targets. Then, the azimuth resolution, the peak side lobe ratio, the integrated side lobe ratio, and the structure similarity are used to measure the performance of the three algorithms.