# Analysis and Design of an X-Band Reflectarray Antenna for Remote Sensing Satellite System
###### Abstract  
This paper presents the analysis and design of an X-band reflectarray. The proposed antenna can be used for a medium Earth orbit (MEO) remote sensing satellite system in the 8.5 GHz band. To obtain a nearly constant response along the coverage area of this satellite system, the proposed antenna was designed with a flat-top radiation pattern with a beam width of around 29\({}^{\circ}\) for the required MEO system. In addition, broadside pencil beam and tilted pencil beam reflectarrays were also investigated. The feeding element of the proposed reflectarray antennas is a Yagi-Uda array. The amplitude and phase distribution of the fields due to the feeding element on the aperture of the reflectarray antenna are obtained directly by numerical simulation without introducing any approximation. The required phase distribution along the aperture of the reflectarray to obtain the required flat-top radiation pattern is obtained using the genetic algorithm (GA) optimization method. The reflecting elements of the reflectarray are composed of stacked circular patches. This stacked configuration was found to be appropriate for obtaining a wide range of reflection phase shift, which is required to implement the required phase distribution on the reflectarray aperture. The antenna was fabricated and measured for verification. reflectarray antenna; flat-top radiation pattern; remote sensing satellite system; genetic algorithm 202222211662022222116202  
such as the alternating projections method [15; 16], and evolutionary algorithms, such as GA [17; 18; 19; 20], particle swarm optimization (PSO) [21], and the semidefinite relaxation technique [22]. These different optimization algorithms vary in terms of their computation complexity and final convergence rate. It is shown in [23] that the evolutional optimization algorithms are capable of better performance and providing more flexible solutions than the classical optimization algorithms. Because a reflectarray antenna consists mainly of a large number of reflecting elements, which contribute to the generation of the required radiation pattern, the required optimization algorithm must be computationally efficient to manage a large number of variables. The reflectarray synthesis problem depends only on phase synthesis, which involves only the phase of the reflected field due to each element in the optimization process. The starting point for the optimization process has a significant effect on the convergence rate. As noted in [24], a good initial point is the phase distribution of a broadside pencil beam pattern. In the present work, three different patterns were investigated: a broadside pencil beam, a tilted pencil bean, and a flat-top beam. Conventional pencil beam and tilted pencil beam reflectarray antennas were designed analytically. The flat-top beam reflectarray antenna was designed using GA optimization. This flat-top pattern is important in remote sensing systems and in different communication technologies, such as 2G/3G/LET cellular bands [25; 26; 27; 28]. The reflectarray antenna is usually fed by a horn antenna. However, in this paper, a Yagi-Uda antenna array [29] is used as the feeding antenna for the proposed reflectarray. This Yagi-Uda antenna is characterized by a lower profile and less weight compared to a standard horn antenna [30; 31]. Commonly, the incident field distribution on the surface of a reflectarray is approximately represented by an ideal feed model cos\({}^{q}\theta\)[32]. The value of the power factor \"\(q\)\" is determined by the directivity of the feeding antenna. In the present paper, a more accurate approach is used based on determining the exact field distribution due to the feeding element at the plane of the reflectarray, by separately simulating the feeding element and obtaining its corresponding feed distribution in the required plane. By comparison, the reflecting unit cell of the proposed reflectarray antenna is assumed to consist of two stacked circular patches backed by a ground plane.