## 1 Introduction
A compact 2 \(\times\) 2 array is described in [21], which consists of square radiating patches that are fed by the SR feed with a truncated ground plane having the C-to-C distance of 0.4\(\lambda_{0}\). However, the design has ARBW from 1.5-2.5 GHz and peak gain of 7.8 dBi. In [22], an aperture coupled 2 \(\times\) 2 CP array is constructed at 5.8 GHz that has the inter-element distance of 0.74\(\lambda_{0}\). There is an air gap between the radiating element's PCB and the PCB on which the aperture has been etched, as a result of which a high gain of 14.25 dBi is achieved. The total impedance bandwidth (IBW) is 22.8% and ARBW of 17.5%. A very compact 2 \(\times\) 2 CP array is proposed in [23] at 10.4 GHz that has C-to-C distance of 0.4\(\lambda_{0}\) between the elements. The measured 10 dB IBW and 3 dB ARBW are 13.6% and 11.2%, respectively. The design achieved a peak gain of 9.8 dBi. A compact 4 \(\times\) 4 CP array antenna is developed using the SR feeding network at 922.5 MHz in [24]. The ARBW of 2.7% with the peak gain of 12.5 dBic is achieved by keeping the C-to-C distance of 0.48\(\lambda_{0}\) among the elements. An SR feed is applied to a compact 4 \(\times\) 4 CP antenna array in [25] that has the element's C-to-C distance of 0.45\(\lambda_{0}\) at 6.7 GHz. The array has a wide IBW of 53% (4.5-7.75) GHz. A gain of 12 dBic and 12.6 dBic is achieved within the 3 dB ARBW of 5.25-6.2 GHz and 6.4-7.1 GHz, respectively. Another work in [26] presented a 4 \(\times\) 4 CP array fed by a multistage SR feeding network. The design notifies the IBW of 14.7% (5.38-6.23) GHz and overlapping ARBW of 12.4% (5.44-6.16) GHz. An edge-to-edge (E-to-E) distance of 0.74\(\lambda_{0}\) is maintained among the elements. Moreover, a peak gain of 18 dBi is obtained. The performance of SR feed to 4 \(\times\) 4 CP array is evaluated in [27]. The simulated IBW and ARBW of 245 MHz and 125 MHz are achieved. The E-to-E distance is 0.74\(\lambda_{0}\). The studies above significantly improve the IBW and 3 dB ARBW of the array antennas. However, there is always a trade-off between the gain and size of the antenna. For the efficient communication of the next-generation small satellite application, the compact antennas should have an adequate level of gain that is greater than 12 dBic and the AR less than 1.5 dB. All the previous research has focused on the gain and bandwidth enhancement, but these studies have not given full attention to the application requirements. Table 1 shows the detail of the antenna array specifications. Considering the need of communication satellites, the first section of this article presents a single layer 2 \(\times\) 2 CP array antenna fed by SR phase feeding structure of compact size and acceptable level of gain. In the second section, a 4 \(\times\) 4 CP microstrip antenna array is designed which satisfy the requirements of next-generation small satellite application. The C-to-C element distance is 0.535\(\lambda_{0}\). A commercially available tool, Computer Simulation Technology (CST) is used for simulation purposes. The array is constructed on PCB Roger RT6006 (\(\epsilon_{r}\) = 6.15, tand = 0.0027, thickness = 1.27 mm). To realize the design we constructed a 2-stage SR phase feeding structure. The IBW, as well as the a ARBW of the array covers the total X-band. The left-handed circularly polarized (LHCP) gain varies from 15 to 15.5 dBic in the band of interest. The measured results show that the gain and AR values satisfy that criteria in angular width for LEO satellites.