## 1 Introduction  
Ku-band satellite communication (SATCOM), with the superiority of high throughput and comprehensive coverage, is drawing more and more attention to dynamic inter-satellite and satellite-to-earth communications [1, 2]. Phased array antennas have been utilized in the SATCOM system due to their flexible beam controlling and high communication capacity. Taking into account the capability requirement and launch cost of satellite carrier platforms,a spaceborne phased array antenna should be characterized by high-gain, lightweight, and low-profile performances. Phased array antennas have the potential to provide flexible beam reconfigurability, such as coverage area [3; 4; 5], sidelobe level [6; 7], and beam scanning [8; 9]. Research on the interconnection between antennas and phase-shifter circuits has been discussed. Multilayer package substrates made of high-temperature co-fired ceramic (HTCC), low-temperature co-fired ceramic (LTCC), printed circuit board (PCB), thin film, or organic high-density interconnect (HDI) have been demonstrated for phased array antennas. In [8], a phased array antenna embedded in a flip-chip ball grid array (BGA) package with 11 layers of LTCC substrates is proposed. However, poor thermal conductivity and uncontrollability during the firing process of an LTCC are inevitable. Furthermore, massive adoption of transmitter/receiver (T/R) modules is challenging for process cost and complexity. As a new generation to reduce T/R modules, the subarray scheme is proposed as an effective alternative [10; 11]. In [10], subarrays are utilized in a 2D phased array scheme with up to 60% reduction in the number of phase shifts while keeping sidelobes lower than \(-15\,\mathrm{dB}\). In addition, various researchers have sought for high-gain antennas in recent years: their methods have included waveguide [12; 13; 14], metasurface [15; 16], and microstrip patch [17; 18; 19] antennas. In [13], an air-filled waveguide-fed magneto-electric (ME) antenna array is investigated and fabricated with 3D printing technology. The measured gain results are up to 28.5 dBi, but the complicated process, heavy weight, and low integration with the back-end RF circuit are disadvantages for the SATCOM application. The quad-band reflectarray antenna (RA) in [15] is proposed for the Ku- and Ka-bands. However, the aperture efficiency at the Ku-band is decreased by the overlapping radiation elements and frequency-selective surface (FSS). In addition, the multiple complex feeding system imposes some challenges to the overall profile and fixed installation. As a proven and effective generation for antenna array design, the patch antenna is an alternative to the above two types of antennas with a low profile and ease of integration. It should be noted that the maximum gain is restricted by the feed network [20]. In terms of the typical microstrip line (MS), high loss and leakage radiation are unavoidable [21; 22]. Although the insertion loss of the substrate integrated waveguide (SIW) is reduced, the bandwidth is limited by the cut-off frequency of the dominant mode [23]. A substrate integrated coaxial line (SICL) is better than the above two structures and has better transmission features. The transmitted intrinsic TEM mode of SICL has the advantages of wideband single-mode operation, low loss, and interference-free performance. In addition, differential-fed schemes have been widely proposed in the antenna array design due to their features of low cross-polarization level, symmetric radiation patterns, and leakage wave suppression. In [24], two types of 2 \(\times\) 2 antenna array are proposed. One is fed with dual out-of-phase feeding probes, and the other is constructed with differential pairs of single-end antennas. The measured results of cross-polarization are about \(-17\,\mathrm{dB}\) at the boresight for the two proposed antennas. Compared with the latter antenna, the former has worse gain performance due to massive losses caused by the bulky feed network.