## 4 SAR System Requirements Effect on Satellite Design
### SAR System Optimization by Using ModeFRONTIER
Other parameters including PRF were taken from the defined limits shown in Table 4. The optimization algorithm will iteratively refine the design space to find optimal solutions. Monitoring and analyzing the results involves real-time monitoring and post-optimization analysis, respectively. Real-time monitoring involves tracking the optimization progress using modeFRONTIER's monitoring tools. Post-optimization analysis is an evaluation to understand the trade-offs between transmitting power, antenna area, and NESZ. Table 4 shows the optimized parameters and their limits needed to obtain reasonable results. These values are taken from real SAR satellite missions, especially from micro-size ones which are already given in Table 1 of this paper. Figure 11 shows the workflow of modeFRONTIER. The constants and input parameters are given in accordance with the values discussed in this paper and limits given in Table 4. The objective function is the NESZ equation. To trade-off parameters and optimize it to see the requirements for a micro-size satellite, the desired system performance needs to be obtained. Furthermore, the limits of the desired NESZ values are realistic and sensible. NESZ should be the lowest but within these limits to obtain all results within the range of acceptable values. The PRF bounds and other conditions are the same as in the system design flow in Figure 1. The goal is to minimize the antenna area and minimize the resolution, as well. Therefore, all parameters can be optimized and the optimized transmitting power values corresponding the antenna dimensions, resolutions, and NESZs can be obtained. Figure 10: ModeFRONTIER optimization flow. Figure 12 shows the modeFRONTIER optimization graphs for transmitting power. The graph displayed on the left for effective antenna area vs. transmitting power requirement shows the optimized results. Given the feasible results for a reasonable and minimized antenna area of around 10-15 m\({}^{2}\), the optimized and corresponding transmitting power values are 2 to 2.5 kW. This can be confirmed from the NESZ versus transmitting power graph on the right. The same transmitting power values can be read for around \(-\)30 dB NESZ which can be assumed as a good system performance. Figure 13 shows graphs for the bandwidth on the left and system losses on the right vs. NESZ values. After optimization the application, acceptable values are obtained. The bandwidth values differ between 150 MHz and 500 Mhz for an NESZ value of \(-\)30 dB. In this case, one can select 150 MHz in accordance with real-world applications. Furthermore, the system losses depend on variable factors. Therefore, for the desired NESZ the system loss may be 6 dB to 10 dB. Even though this might be engineered to a smaller value, this range is selected as an optimized one. \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Value Limits** \\ \hline Operating Frequency & 9.65 GHz \\ \hline System Temperature & 290 K \\ \hline Incidence Angle & \(15^{\circ}\) to \(45^{\circ}\) \\ \hline Pulse Width (\(\mathbf{\tau_{p}}\)) & 1 \(\mu\)s to 10 \(\mu\)s \\ \hline Band Width (\(\mathbf{B_{r}}\)) & 100 MHz to 150 MHz \\ \hline System Loss (\(\mathbf{L_{s}}\)) & 3 dB to 12 dB \\ \hline Duty Cycle \% & \%10 to \%50 \\ \hline Azimuth Resolution (\(\mathbf{\delta_{x}}\)) & 1 m to 20 m \\ \hline Range Resolution (\(\mathbf{\delta_{R}}\)) & 1 m to 20 m \\ \hline Antenna Length (\(\mathbf{L_{a}}\)) & 5 m to 15 m \\ \hline Athena Width (\(\mathbf{W_{a}}\)) & 1 m to 3 m \\ \hline Transmitting Power (\(\mathbf{P_{t}}\)) & 1000 W to 2500 W \\ \hline Altitude (h) & 500 km to 800 km \\ \hline NESZ & \(-\)50 dB to 50 dB \\ \hline \end{tabular}
\end{table} 
Table 4: Limits of design parameters. Figure 11: ModeFRONTIER workflow. The antenna dimensions are the focus of Figure 14. Even though the antenna area is illustrated in Figure 12, the details of the dimensions are separately important and fundamental for SAR systems and imaging.