## 3 Performance Evaluation of the Proposed SAR Processor
### Precision Comparison of the Proposed SAR Processor and MATLAB-Based SAR Processor  
The proposed SAR processor, as in Figure 4, was synthesised and implemented into the FPGA device, Altera Stratix IV GX series EP4 SGX230 KF40C2, located within the embedded SAR processor, a DE4 development board. Captured raw SAR data is loaded into the proposed SAR processor for the RDA processing operations. The intermediate results of \begin{table}
\begin{tabular}{l l l} \hline \hline
**Name of Parameters** & **Symbols** & **Value (Units)** \\ \hline Slant-range centre & \(R(\eta_{c})\) & 30 km \\ Transmitted pulse duration & \(T\) & 2.5 \(\mu\)s \\ Chirp-signal bandwidth & \(B\) & 50 MHz \\ Range-chirp signal sweep rate & \(\beta\) & 20 MHz/\(\mu\)s \\ Range resolution & \(\delta_{R}\) & 3-m \\ Range-sampling frequency & \(f_{s}\) & 100 MHz \\ Carrier-signal frequency & \(f_{0}\) & 5.3 GHz \\ Azimuth-sampling frequency (PRF) & \(f_{a}\) & 350 Hz \\ Radar-platform velocity & \(V_{r}\) & 150 ms\({}^{-1}\) \\ Real antenna-aperture length & \(L_{a}\) & 1 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters of C-band airborne SAR. Figure 4: Block-diagram architecture-partitioning of SAR processor. the SAR processor were observed and compared with the results of RDA in MATLAB in terms of precision and accuracy. The evaluation was conducted starting from the range compression by comparing the SAR raw data that transformed into the frequency domain by MATLAB and that of the proposed SAR processor. In the SAR image, brighter colours represent lower reflection from the targets, and darker colour indicates stronger reflection from the targets. Figure 5 shows the magnitude plot of the SAR raw data that is transformed into the frequency domain by using the built-in FFT function in MATLAB, while Figure 6 shows the magnitude plot of the SAR raw data that is transformed into the frequency domain by the proposed SAR processor. It can be observed that there are very significant similarities in the patterns of the two images. In order to clearly evaluate the differences between the two images, the range-profile differences between the two results were computed, and the MATLAB result was treated as reference for the calculation of the differences. MATLAB was used as the reference of comparison, as the range-profile generation. SAR image formation via MATLAB is  
Figure 5: Raw Data Transformed by MATLAB 1024-FFT into Frequency Domain. Figure 6: SAR raw data transformed by the proposed processor into the frequency domain. already well established, and its built-in functions, such as FFT and IFFT, have proven to be correctly implemented. For quantitative comparison, the differences between the results of FPGA and MATLAB were calculated based on the equation below. \[\Delta\left(\%\right)=\frac{\text{Range Profile of FPGA -- Range Profile of MATLAB}}{\text{Range Profile of MATLAB}}\times 100\% \tag{1}\]  
Since SAR image is formed by multiple range lines, the most positive and the most negative differences throughout all the range lines were calculated. Figure 7 illustrates these differences in the SAR raw data range profile in the frequency domain. The figure shows that the majority of differences in the results are in the range of \(\pm 0.5\%\), with a maximum error of no more than 3%. This error is mainly due to the quantisation error from the ADC. From the difference error, it can be concluded that the range profile is around 1% of the quantisation noise floor. This noise floor exists in the raw data even when there is no point target. After the data were transformed into the frequency domain by FFT, they were then passed through the matched-filtering process by multiplying the data with the precomputed range reference function using the designed complex multiplier. The output of the matched filter is transformed into time domain, and the data appear as range-compressed data.