# Spatial Baseline Optimization for Spaceborne Multistatic SAR Tomography Systems
## 5 Experimental Verification
### Analysis of Imaging Intensity Results  
The experiment set the step size \(\Delta q=0.05\), and then simulated the satellite image data in \(q=0.05:2.0\), thereby focusing the image through three imaging algorithms: DFT, NDFT, and CS. Given the main image height and baseline span, the Rayleigh resolution of the three imaging algorithms satisfies  
\[\textit{rows\_DFT}=\textit{rows\_NDFT}=\textit{rows\_CS}=15.9\ \text{m}. \tag{12}\]  
Table 2 shows the actual imaging height and phase of three imaging algorithms under nine different \(q\) values. The experiment set the target height \(S_{0}=8\) and the target phase \(\varphi_{0}=45^{\circ}\). It can be seen from Table 2 that all three imaging algorithms could accurately obtain the target height and phase information. Figure 4 shows the PSLR, ISLR, and broadening coefficient (actual imaging resolution/Rayleigh resolution) of DFT, NDFT, and CS imaging algorithms under different intensity data. It can be seen from the above results that both the NDFT imaging algorithm and the CS imaging algorithm could achieve and exceed the imaging performance along the height direction of the DFT imaging algorithm when \(q=1\). For the NDFT imaging algorithm, the values of PSLR and ISLR at \(q=0.86\sim 1.16\) were close to the imaging results of the DFT imaging algorithm, where the actual imaging resolution became gradually worse as \(q\) increased. The PSLR and ISLR of the CS imaging algorithm at \(q=1\sim 1.22\) also achieved and exceeded the imaging results of the DFT imaging algorithm, but with increasing \(q\), the actual imaging resolution gradually became worse. And as \(\left|q-1\right|\) increased (i.e., the baseline position gradually moved away from or close to the track of the main image), PSLR and ISLR generally increased gradually. In order to ensure a weak target is not obscured by an adjacent strong target, the system requires that the PSLR must be less than 13 dB. It can be seen from Figures 4 and 5 that the imaging algorithm had better imaging performance when the baseline distribution had \(\left|q-1\right|\) close to 0 (i.e., the baseline tended to be uniformly distributed). \begin{table}
\begin{tabular}{c c c} \hline  & **DFT** & **NDFT** & **CS** \\ \hline \(q=0.2\) & 0.42 m/45.0\({}^{\circ}\) & 0.42 m/45.0\({}^{\circ}\) \\ \(q=0.4\) & 0.42 m/45.0\({}^{\circ}\) & 0.33 m/45.0\({}^{\circ}\) \\ \(q=0.6\) & 0.42 m/45.0\({}^{\circ}\) & 0.29 m/45.0\({}^{\circ}\) \\ \(q=0.8\) & 0.42 m/45.0\({}^{\circ}\) & 0.42 m/45.0\({}^{\circ}\) \\ \(q=1.0\) & 0.42 m/45.0\({}^{\circ}\) & 0.42 m/45.0\({}^{\circ}\) \\ \(q=1.2\) & 0.42 m/45.0\({}^{\circ}\) & 0.42 m/45.0\({}^{\circ}\) \\ \(q=1.4\) & 0.42 m/45.0\({}^{\circ}\) & 0.42 m/45.0\({}^{\circ}\) \\ \(q=1.6\) & 0.42 m/45.0\({}^{\circ}\) & 0.11 m/45.0\({}^{\circ}\) \\ \(q=1.8\) & 0.42 m/45.0\({}^{\circ}\) & 0.42 m/45.0\({}^{\circ}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Actual imaging height error and phase. CS: compressive sensing; DFT: discrete Fourier transform; NDFT: non-uniform discrete Fourier transform. In order to further verify the above conclusion, the experiment evaluated the imaging results where PSLR \(<-10\) dB, i.e., \(q=0.86\sim 1.16\), and took the step size \(\Delta q=0.01\). The experimental results are shown in Figure 6.  
The imaging performance in the height direction of the NDFT and CS imaging algorithms changed gradually. The PSLR of the NDFT imaging algorithm increased at \(q<0.86\), and the imaging performance along the height direction declined sharply when the PSLR of the CS imaging algorithm was greater than \(-11\) dB at \(q<0.86\). Notably, the actual imaging accuracy decreased significantly at \(q>1.16\).