# Optimization Design for Sparse Planar Array in Satellite Communications
## 1 Introduction  
The antenna is a vital device for satellite communication payloads, as shown in Figure 1; until 19 November 2022, the search volume of the keyword \"antenna\" demonstrated a growing search volume on IEEE Xplore's top search. It is currently in third place and also the only device with considerable attention. Antenna technology boasts a rich history spanning over a century; unlike other devices, it enables to effectively transmit RF power signals to the destination and amplify the power density in a certain direction, thereby enhancing the capabilities of wireless systems. In summary, antennas have the characteristics of directionality, spatial directivity, and filtering. Figure 1: IEEE Xplore top searches and matching documents as of 19 November 2022. Antenna arrays are radiation devices consisting of multiple antenna units arranged in a specific manner [1], which have found widespread application in various fields such as satellite communications, satellite Internet of things, radar, and astronomy. Planar arrays use the principle of superposition to form regular or random arrays, thereby facilitating beam scanning, multi-beam, shaped beams, and antenna patterns with high gain, strong directionality, narrow beam width, and low sidelobe in satellite communication scenarios [2]. In light of the development requirements for antenna technology in future B5G and 6G networks, investigating the optimal design of spaceborne antenna arrays is imperative. In the optimal design of planar array antennas, the aperture of the array serves as a key determinant of the upper bounds for system resolution and sensitivity. The actual application range of the antenna array is contingent upon the structure characteristics of the array, as well as the complexity of its software and hardware components. In recent years, array antennas have gained wide usage in satellites due to their narrow beam, which makes them suitable for accurate scanning detection and tracking. Among various antenna types, phased array antennas are the most popular. Unlike common antennas, phased array antennas can use the electric scanning method and the phase difference of the electrical signal sent by the detection unit to control the detection direction. Additionally, they can realize fast scanning by changing the array antenna parameters. Phased array antennas have several characteristics, including long transmission distance, many functions, and good anti-interference performance, making them the most typical planar array antenna in space-borne antennas [3]. At present, mobile satellite communication scenarios predominantly employ intelligent phased array antennas based on digital beamforming technology. These include phased array feeder reflective surface antennas and direct radiation phased antenna arrays. Among them, typical representatives of phased array feeder reflective surface antennas are Inmarsat satellite dishes, Thuraya satellite dishes, Alpha-sat XL satellite dishes, etc. Typical direct radiation phased array antennas include ICO satellite L-band phased array antennas, Harris ADS-B software-defined phased array antennas, Spaceway-3 satellite X-band digital multi-beam phased array antennas, NeLS low-orbit constellation X-band digital multi-beam phased array antennas, SatixFy Ku-band digital multi-beam phased array antennas, and O3b mPower phased array antennas [4]. In phased array antennas, each element has independent amplitude-phase control components and transceiver channels, and the hardware cost is high; moreover, with the expansion of the array aperture, the array requires a considerable number of antenna units and array amplitude-phase control components, making the antenna system very expensive. Additionally, the signal processing complexity of the phased array is high, and an excessive number of receiving channels will make the calculation dimension of the signal processing algorithm too high and reduce the real-time performance of the system.