## 1 Introduction  
Non-terrestrial networks (NTNs) represent a transformative approach in today's communication systems, utilizing satellite constellations, high-altitude platforms (HAPs) and unmanned aerial vehicles (UAVs) or drones. When integrated with terrestrial networks, these technologies constitute the next generation of communication environments [1]. The advancement of NTNs has been driven by an increasing demand for global connectivity, low-latency internet, and secure communications in remote or hostile environments. Within the realm of satellite communications, this paradigm shift has notably highlighted the utilization of Low Earth Orbit (LEO) satellites. Compared to traditional Geostationary Orbit (GEO) systems, LEO satellites provide several significant benefits, including lower propagation delays, reduced signal losses, and access to wider bandwidth. The lower altitudes of LEO satellites not only contribute to better performance but also result in cost savings in each satellite launch. This evolution has fostered a trend towards the establishment of large-scale constellations composed of low-cost satellites utilizing Commercial Off-The-Shelf (COTS) components, since the impact of a single satellite failure becomes less critical. Table 1 presents a summary of the constellation deployed for the Internet of Things (IoT), together with the corresponding operator and the number of satellites. From a technical perspective, the coverage requirements of LEO systems, due to their lower orbital altitude, call for a high number of beams operating at very wide scanning angles to effectively expand the coverage area. In this context, direct radiating arrays are preferred due to their ability to perform electronic scanning, which improves the flexibility and responsiveness of the system in managing coverage. The radiating properties of the array in terms of grating lobes and side-lobe level (SLL), as well as the beamforming architecture adopted, are also critical. Nowadays, there are mainly three architectures for beamforming: analog, digital, and hybrid. In the literature, there are many comparisons between these approaches [2; 3; 4], each with their benefits and drawbacks:  
* Analog beamforming makes use of dedicated ICs to generate each beam by means of variable attenuators and phase shifters. The main drawback of this architecture is the hardware proliferation and complexity scaling with the number of beams, limiting them to a few tens. * Full-digital beamforming feeds each radiating element by up-converting a phase- and amplitude-modulated base-band signal processed in a digital domain. This way it is possible to improve the number of beams with arbitrary directions, with limitations due to processed bandwidth and power consumption. * Hybrid architecture is a combination of analog and digital beamforming: the array is viewed as composed of digitally driven sub-arrays in each of which analog beamforming is implemented. The main drawback is due to the limited instantaneous field-of-view achievable. While analog beamforming is the most consolidated and assessed [5; 6], the request for a growing number of beams for these applications is shifting the attention to digital beamforming. To the authors' knowledge, while some preliminary studies have been conducted [7; 8], an investigation into a practical design on the effect of impairments on the performance of a digital antenna is not present in the literature. In this paper, we firstly consider typical performances of active antennas for LEO telecommunications (see Table 2, [9]) in Ka-band to propose a suitable direct radiating antenna. The satellite size imposes demanding antenna requirements in terms of size, weight, power, and cost; hence, a minimization of the number of elements is desirable, while maintaining high scanning angles and a high side-lobe level, leading to a challenging design. Then, we perform an investigation of a digital chain relying on typical performances