# Robust Space Time Adaptive Processing Methods for Synthetic Aperture Radar
## 5 Simulation Result  
A multi-channel SAR simulation was implemented using the parameters given in Table 1. The synthetic aperture time is about 4.4 s, and the number of received pulses is 1024. The range bin number used in simulation is less than that used in practice but sufficient to demonstrate the adaptive algorithm. At 40 km, the width of the SAR receiving beam is about 7\({}^{\circ}\) and the azimuth range of the SAR receiving beam is 5000 m.  
The distribution maps of simulation points are given in Figure 4. The \(3\times 3\) individual scatters are distributed in this area, and the space between each scatter is 30 m. The jammer with noise interference was set to near the mainlobe direction of the antenna, 10 km away from the radar platform. The DOA of interference varied about 2\({}^{\circ}\) in the synthetic aperture time. The images were formed using a typical Range-Doppler algorithm for stripmap SAR.  
Figure 4: Simulation point targets.  
The simulation results are illustrated in Figure 5. Figure 5a is the ideal image without any interference and Figure 5b is the image affected by interference, which clearly shows the large amount of degradation. Figure 5c,e,g show the image suppressed by conventional piecewise STAP processing where the numbers of sub-apertures are 16, 32 and 64, respectively.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Carrier frequency (\(f_{c}\)) & \(10\,\mathrm{GHz}\) \\ \hline Bandwidth (\(B\)) & \(200\,\mathrm{MHz}\) \\ \hline Number of pulses (\(M\)) & \(1024\,/\,512\) \\ \hline Range bins (\(M_{r}\)) & \(2048\) \\ \hline Number of receive channel (\(N\)) & \(16\) \\ \hline Element spacing & \(0.5\,\lambda\) \\ \hline Range resolution & \(1\,\mathrm{m}\) \\ \hline Azimuth resolution & \(1\,\mathrm{m}\) \\ \hline Velocity (\(v_{c}\)) & \(150\,\mathrm{m/s}\) \\ \hline Height of platform (\(H_{c}\)) & \(3000\,\mathrm{m}\) \\ \hline SAR Squint angle (\(\theta_{0}\)) & \(15^{\circ}\) \\ \hline Range center & \(40\,\mathrm{km}\) \\ \hline Jammer offset/ Direction of jammer(\(\theta_{j}\)) & \(35\,\mathrm{km}/\,10^{\circ}\) \\ \hline Jam noise ratio/Signal noise ratio & \(20\,\mathrm{dB}/\,15\,\mathrm{dB}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters.  
Figure 5: _Cont._  
It can be seen that the interference is effectively suppressed, but the azimuth focusing of the image is reduced to a certain extent compared with the original image, as the variation of adaptive weight vectors modulates the SAR waveform resulting in the image defocus. Figure 5d,f,h show the images suppressed by the piecewise constrained STAP method proposed in this paper. While effectively suppressing interference, the focusing performance is greatly improved. The processing result based on the piecewise constrained GSC algorithm is almost the same as the piecewise constrained STAP, which are not presented here. The target response characteristics are shown in Figure 6.  
Figure 5: Imaging simulation result. (**a**) Image with no interference; (**b**) Before interference cancellation; (**c**) Result of conventional STAP (M = 16); (**d**) Result of PC-STAP (M = 16); (**e**) Result of conventional STAP (M = 32); (**f**) Result of PC-STAP (M = 32); (**g**) Result of conventional STAP (M = 64); (**h**) Result of PC-STAP (M = 64).  
Figure 6: Comparison of point target profile (M = 16): (**a**) Range profile; (**b**) Azimuth profile.  
A Hamming window is used in the SAR process in order to reduce the sidelobe levels. It can be seen that the azimuth focusing performance of the conventional piecewise STAP processing is obviously degraded due to the destruction of the echo phase continuity between sub-apertures, and the sidelobes also increase to a certain extent. The result where the numbers of sub-apertures are 32 and 64 is similar to that in Figure 6. The specific quantitative analysis including peak side lobe ratio (PSLR), integral side lobe ratio (ISLR), and spatial resolution (3 dB width) of point targets are shown in Table 2.