## 5 Antenna Model  
The necessity of an antenna model is justified for three major reasons [41; 42; 43; 44]. First, as the number of antenna beams required for the SAR operation increases, an antenna model is needed to effectively shorten the calibration time of the antenna beam. In addition, a precise antenna model is required to satisfy and maintain the radiometric performance of the SAR images. Finally, the antenna model is very helpful in reducing the time of the in-orbit commissioning phase of the satellite and facilitating the calibration/validation (CAL/VAL) activity that occurs regularly. In the case of the S-STEP SAR satellite, hundreds of antenna beams (>40 beams in high-resolution mode) are required to acquire high-quality SAR images in various modes. An antenna model capable of appropriately modeling these beams can accurately determine the numerous antenna patterns required for image acquisition. In most satellite SARs based on active phased-array antennas, such as TerraSAR-X, CosmoSky-Med, and Sentinel-1,  
Figure 16: (**a**) External configuration and (**b**) exploded view of the S-STEP PSU. Figure 15: Functional block diagram of the S-STEP DCU. antenna models have been developed and applied. A satellite SAR based on an active phased-array antenna can flexibly form beams through excellent beam agility. According to the results of the on-ground characterization process, the antenna characteristics can be accurately modeled by applying mathematical models. The antenna--1970 mm in length and 1060 mm in width--contains 192 microstrip patch subarrays arranged in 4 tiles in the azimuth direction (columns), each with 48 subarrays (rows), as depicted in Figure 17, wherein the blue and green squares represent patches and subarray ports connected to the TRMs, respectively. In particular, the nominal antenna pointing was 23.7\({}^{\circ}\) from the nadir. Moreover, the right- and left-looking acquisitions were realized using satellite roll maneuvers. The individual subarrays were connected to a single channel of the TRM, and its amplitude and phase can be adjusted by applying complex excitation coefficients. This enabled the beam steering and formation in the azimuth and elevation directions. The antenna model is primarily used to generate the antenna beam pattern data required for compensating the characteristics of each antenna beam. Specifically, the elevation beam pattern is obtained by measuring the gain variations in the distance direction with a signal measured for an area such as the Amazon Forest. Furthermore, the azimuth beam pattern is acquired by accurately estimating the Doppler spectrum as the azimuth beam pattern appeared therein. In addition, the antenna model can optimize the beam excitation coefficients to enhance the SAR image quality, such as the NESZ and distributed target-to-ambiguity ratio, for full performance at the required level. The antenna model determines the final antenna beam pattern by multiplying the beam excitation coefficients with the weight of the beam pattern of each subarray using geometric information related to the antenna. The drift errors or failure factors occurring in each antenna element can be included in the antenna model as an error matrix. Before testing, the antenna patterns are simulated using a detailed antenna electric model developed based on component test data. Subsequently, the antenna model is used for beam optimization to enhance the SAR performance. During the antenna pattern test phase, the model is verified and amended by comparing the tested and simulated patterns. The antenna model mathematically evaluates the radiation patterns based on the superposition of the four inputs: subarray radiation patterns, beam excitation coefficients of each TRM, exact array geometry, and the actual state of the SAR antenna, including the  
Figure 17: Array geometry of the S-STEP SAR antenna model. drifting or failure of the TRMs. The following equation for a phased array provides the model for the antenna radiation pattern \(G_{a}(\theta,\phi)\)[41; 42]:  
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