## 1 Introduction  
Small satellites are becoming more and more attractive for low-earth orbit (LEO) missions due to their low cost, relatively fast development, and satellite network application capabilities. To increase the data transmission speed, a high gain antenna of low mass and low profile is the fundamental requirement. Matching of polarization of the transmitter and receiver antennas is one of the important factors to increase the gain. To accomplish this, the transmitter and the receiver antennas should have the same axial ratio (AR), spatial orientation, and the same sense of polarization. Practically, it is difficult to emulate the orientation of the antennas on a continuous basis. Circularly polarized (CP) antennas have been widely applied to satellite communication and radar [1] owing to their ability to allow flexible orientations of the transmitter and receiver antennas. LEO satellite antennas need high gain with effective circular polarization in the angular range of \(\pm\)10\({}^{\circ}\) to establish a good communication path. Along with the high gain, the size of the design is the key parameter. Many studies have been proposed for such applications, such as integration of meta-surface with antenna [2, 3, 4, 5], insertion of air gap between the antenna and metasurface layer [6], electromagnetic bandgap (EBG) structure [7], frequency selective surface (FSS) [8], artificial magnetic conductor (AMC) [9], and parasitic patches [10]. In [11], the main radiation part composed of two orthogonal bowtie dipole that are printed on both sides of the substrate, and are suspended at a distance of 62.5 mm above metallic reflector. A similar idea is implemented in [12, 13]. In [12] the radiator composed of meander line with the crossed scythe-shaped dipoles, whereas in [13] the radiator is consisting of meander line with arrow-shaped dipoles. Inboth cases, the crossed dipoles are suspended at the center of the cavity at a height of 40 mm and 30 mm. All of the above techniques increase the gain and AR performance, but either the design becomes bulky or increases the footprint. Thus, a compact single-layer and high gain antenna is preferred. Feeding networks also play a vital role in CP antennas. Different kinds of feeding networks are utilized. Corporate microstrip feed lines are used due to simplicity, but result in more resistive losses [14]. To achieve good radiation performance, it has been suggested that sequentially rotated (SR) phase feeding structures should be used. The SR phase feed network is an effective feeding technique that is widely used in CP microstrip antennas and has been widely applied by many researchers to antenna arrays. As a result, the array will increase the main beam cross-polarization rejection, voltage standing wave ratio (VSWR), and axial ratio bandwidth (ARBW) that result in the purity of polarization [15; 16]. The SR feed is used in a variety of designs. In [17], a 2 \(\times\) 2 array with center-to-center (C-to-C) distance of 0.77\(\lambda_{0}\), a 3 dB ARBW of 15.5%, and peak gain of 8.25 dBic is presented. Another study [18] proposed a 2 \(\times\) 2 array that is designed at 5.87 GHz with the separation of the elements of 0.99\(\lambda_{0}\). The design achieved a peak gain and ARBW of 10.04 dBic and 7.71%, respectively. However, the parasitic rectangular patches are used to increase the bandwidth performance, but increase the footprint. Reference [19] presented a Ka-band 2 \(\times\) 2 array based on a simple rectangular microstrip patch with truncated corners fed by SR feed. The element's centers are kept at a distance of 1.72\(\lambda_{0}\), resulting ARBW of 28.45 to over 30 GHz. A maximum gain of 13.59 dBi is due to the increased array size. In [20], an SR fed 2 \(\times\) 2 slot antenna array that obtains a wide ARBW of 58% and a maximum gain of 8.9 dBic is presented. An approximate distance of 0.72\(\lambda_{0}\) is kept between the element's centers.