## 1 Introduction  
Synthetic aperture radar (SAR) interferometry and other satellite remote sensing instruments are pivotal for studying changes in Earth's surface topography or deformation. These tools are highly effective for mapping the topography of Earth's land, ice, and even sea surfaces. Leveraging deformation measurements is essential for the management of global natural resources and mitigation of hazards, providing crucial information for scientists to understand the impacts and rate of climate change [1]. The Arctic is rapidly exhibiting signs of global climate change [2]. The transition from thick perennial sea ice to a seasonally ice-free Arctic Ocean has major consequences for sustainable development, transportation, and communities in Arctic regions [3, 4]. Designing a small satellite for such a mission is essential for studying changes in sea ice extent, type, and coverage in the Arctic. Currently, there is a growing trend in utilizing small spacecraft and their constellations to address pressing issues concerning Earth observation from space [5]. A CubeSat is a standardized small spacecraft concept introduced at the end of the previous century [6]. Within CubeSats, the antenna plays a pivotal role as part of the radio frequency (RF) front end, facilitating the transmission of RF waves between space and Earth. Satellite antennas are required to facilitate communication across various frequency bands, including high-speed links like S-band, X-band, and Ku-band for data downlink, as well as low data rate links such as Very High Frequency (VHF) and Ultra High Frequency (UHF) for telemetry and control data [7, 8]. Compact antennas must align with spacecraft speces and meet mission requirements. Proposed space mission antennas include the monopole, dipole, slot,patch, helical, reflectarray, and reflector types [9; 10; 11; 12]. The first four are often chosen due to their light weight, compact size, and ease of fabrication. Nevertheless, their performance in terms of gain tends to be moderate, a crucial aspect in the antenna design process for space missions. Helix antennas offer moderate gain along with inherent circular polarization and broad bandwidth. Nevertheless, their deployment mechanism presents significant design hurdles, particularly when the antenna length surpasses the satellite's dimensions. Reflectarray antennas offer the advantages of being lightweight, relatively inexpensive, and foldable into panels for efficient stowage. However, they are limited by narrow bandwidths (<10%), and the maximum gain is constrained by the number of panels feasible for folding into a CubeSat [13; 14]. Reflector antennas, like the parabolic and cylindrical types, offer high gain, but their large structures pose a challenge for fitting them into SmallSats. Deployable systems offer a solution to this dilemma by allowing the large antenna size to be stowed in a compact space. These systems allow antennas to be stowed inside the CubeSats during launch and then deployed once they are in orbit. Antenna systems, as in [15; 16], based on reflectors for high-frequency bands, were achieved with meshed or inflatable antennas. Although these deployable systems can make optimum use of the footprint in CubeSats, the complexity of deployable mechanisms may limit their commercial viability. Cylindrical parabolic reflectors are widely employed in various applications, especially in satellite communication systems, where high-gain antennas are essential. They necessitate focus from a line source rather than a single point source. Various feed lines have been suggested to illuminate the cylindrical reflector, such as arrays of horns and patch antenna arrays [17; 18]. The former is larger in mass and profile compared to the planar array structure, which provides a lightweight and low-profile design, essential factors in CubeSats design. The use of patch antenna arrays to feed cylindrical reflectors is advantageous in radar applications [19].