## 4 Simulation Results
### Point Target Simulation
A simulation with multiple synthetic point targets is used to verify the improvements in the frame rate and the image size achieved by the proposed MIMO ViSAR system, by suppressing azimuth ambiguities using MCRA. The five targets are located within a maximum of 30 m from the scene center, as shown in Figure 17.  
As shown in Figure 5, the maximum scene size of the PFA, which, according to Equation (6), is limited by wave front curvature, is 126.7 m, when \(R_{a}=1000\) m and \(f_{c}=94\) GHz. As shown in Figure 4, the Doppler bandwidth is proportional to the image size. The Doppler bandwidths for \(2^{\circ}\)-wide azimuth beamwidths are 437 Hz, and 1750 Hz for \(v=20\) m/s, and 80 m/s, respectively. The Doppler bandwidths for \(4^{\circ}\)-wide azimuth beamwidths are 874 Hz, and 1750 Hz for \(v=20\) m/s, and 40 m/s, respectively. Therefore, a wider image size requires a wider Doppler bandwidth, which results in the need for a higher PRF in the FMCW SAR system. According to Equation (5), when the frame rate and the image size are increased by a factor of two, the Doppler bandwidth is four times wider. Thus, a four-times-higher PRF is required, which is 4 kHz for the system under investigation. In this case, increases to both the frame rate and image size can be achieved through the suppression of Doppler ambiguities in the azimuth spectrum, with the application of the MCRA, while maintaining the same PRF, which is 1 kHz. The dechirped azimuth signal, gotten after BFD FMCW demodulation is performed in this multiple point target simulation, is shown in Figure 18. The SAR signal on the circular path is azimuth dechirped as described in Section 3.2. Scatterers farther from the scene center have a higher Doppler frequency, which is proportional to the scene size, according to Equation (27). We observe three azimuth ambiguities for each target in Figure 18 (\(l=1,\ 2,\ 3\)). Due to these azimuth ambiguities, the ambiguous azimuth frequency of Scatterer E is measured as 248.3 Hz, as shown in Figure 18c. As a result of these errors, the image size of the single channel ViSAR system is limited to 40 m.  
After applying the MCRA, azimuth ambiguities are suppressed, as shown in Figure 11:0 The unambiguous azimuth frequency of Scatterer E, which is measured as 751.3 Hz, is reconstructed correctly by the MCRA, as shown in Figure 19c. The other peaks in Figure 19c include the sidelobe of scatterer A, the sidelobe of scatterer C, and residual azimuth ambiguities due to mismatch of the azimuth reconstruction model. No windows are applied for sidelobe reduction for clear visualization the sidelobes. Figure 11:1 Impulse response analysis (**a**) in down-range; (**b**) in cross-range. PSLR: peak sidelobe ratio  
Figure 11:2 Collection geometry and scene geometry. Figure 11:3 Simulation results before MCRA: (**a**) three-dimensional plot; (**b**) two-dimensional plot; (**c**) azimuth frequency cut at Scatterer E.  
The SAR video frame is shown in Figure 11:4 The video frame is 80 m in the down-range and cross-range, which is two times wider than the single channel system. As both the frame rate and image size are doubled, the azimuth frequency bandwidth is four times bigger than in the single channel case, as suggested by Equation (5). Figures 21 and 22 show the SAR video frames before and after image rotation from \(20^{\circ}\) to \(70^{\circ}\), with a \(10^{\circ}\) step in aspect angle, in order to recognize the difference between the SAR video frames. Only the values above \(-60\) dB from the peak level are plotted. As shown in Figure 21, stationary targets appear to rotate, since the aspect angle changes continuously while the radar moves on a circular path. Image rotation is implemented using Equation (55). As shown in Figure 22, when viewed successively, stationary targets appear fixed after image rotation to CDU, even though the aspect angle changes continuously.