# Optimization Design for Sparse Planar Array in Satellite Communications
## 1 Introduction
Furthermore, the small element spacing of phased arrays makes it challenging to process T/R components, and there is considerable coupling between elements, especially in the millimeter wave band. Lastly, phased array antennas are heavy and struggle to dissipate heat, which is not conducive for their installation on aircraft and space carriers. However, phased array antennas exhibit certain limitations, including complex calculations, high costs, and large size and weight, that render them unsuitable for use in satellite transceivers. To address the issue of onboard loading, sparse array antenna technology has emerged as a potential solution. Under specific conditions, sparse planar arrays can achieve the same performance as uniformly spaced full arrays while utilizing a smaller number of elements. Sparse arrays can reduce the complexity and cost of satellite antennas by minimizing the number of elements and mitigating mutual coupling between array elements without significantly altering beam width or aperture size [5]. As shown in Figure 2a, the American PAVE PAWS radar system operates within the frequency range of 420-450 MHz and employs a large double circular array design [6]. Each circular array comprises 2677 elements, with approximately 67% of the elements remaining active during operation, resulting in a detection distance of approximately 4800 km. This system represents the first engineering-level application of sparse planar arrays. In recent years,the research on sparse planar arrays has gained traction, with increasing focus on the optimization design of such arrays, extending from theoretical research to engineering implementation. For instance, the German ARTINO radar system [7] applies sparse plane arrays to drone imaging. Figure 2b (provided by the SKA Program Development Office, [[https://www.skao.int/](https://www.skao.int/)]([https://www.skao.int/](https://www.skao.int/)), accessed on 30 March 2023) shows the Square Kilometer Array (SKA) project [8] involving 20 countries around the world, which constitutes the largest astronomical telescope array under construction worldwide. At present, the research of sparse arrays on a satellite has become the famous topic. In this paper, the optimization design for sparse arrays we discuss is also based on the general context of satellite communication [9]. Sparse planar arrays possess the necessary attributes of small cost, low software and hardware intricacy, and robust anti-interference capabilities in large-scale array designs. By means of an optimized design, these arrays can attain superior performance metrics, rendering them a vital component for transmitting and receiving electromagnetic waves in emerging antenna systems. The present research topic has garnered significant attention in recent years and encompasses a multitude of investigative directions. Within this context, the current article focuses on the optimization design of sparse planar arrays in satellite communication scenarios. After over five decades of development, theoretical research on the optimal design of sparse planar arrays has attained a relatively advanced level and yielded numerous research findings. As shown in Figure 3, the optimization design of the sparse plane array can be likened to a large tree. wherein the root represents the array arrangement, geometry, mathematics, and physics, while the trunk denotes the material support and production technology levels. The branches and leaves of the tree represent various optimization design methods. Figure 3: Optimal design of sparse planar arrays. Figure 2: Applications of sparse planar array: (a) PAVE PAWS [10]; (b) SKA.