## 1 Introduction  
The successful implementation of highly automated driving, connected cars (5G/6G), and efficient fleet management demands real-time wireless connectivity architectures with functional redundancy [1]. This is considered a pre-requisite to enable fail-operational automated driving functionality within the operational design domain. Redundant connectivity links are mandatory for such safety-relevant applications, according to current traffic regulations. LEO satellite systems offer non-terrestrial network (NTN) connectivity and can serve as supplements or back-ups for terrestrial networks (TNs) and thus help meet regulatory requirements. The 5G Automotive Association (5 GAA) pushes the need for seamless interactions between TNs and NTNs by 2030 [2]. This will be critical for the future car industry so as to ensure continuity of service for mobile users anywhere and at any time. NTNs using suitable LEO satellite constellations promise broadband internet access with latencies below 50 ms and data rates up to hundreds of Mbps, allowing for high-quality multimedia, connectivity, and broadcasting. Moreover, this wireless functionality enables global coverage, especially in remote areas where terrestrial networks are sparse [3]. However, the required link budget of an NTN system, including the transmit power, antenna gain, and frequency bandwidth, in combination with the potentially large size of the antenna, poses challenges for its integration into a car. As state-of-the-art examples, the Starlink antenna terminal from Space-X [4], Amazon's Ka-band antenna for Kuiper satellites [5], the beam-steering antennas from ALCAN Systems [6], the SOTM terminals from Requtech [7], and Kymeta [8], each have a diameter between 30 and 60 cm, i.e., 10 \(\lambda\) and 20 \(\lambda\) at 10 GHz. The integration of such large antennas into cars is not feasible for mass applications. A trade-off between size and performance needs to be found and thoroughly studied in terms of the link budget required for given use cases and the antenna's radiation characteristics, as well as regulatory aspects and a design for manufacturability. There are Ku-band antenna arrays for LEO connectivity available on the market. But the approach to the miniaturization of such an antenna by designing a single antenna element with high gain per unit area is novel. This miniaturization is critical for an automotive application in which space and aesthetics are major constraints. In this regard, this paper proposes a low-profile, dual-band, dual-polarized, vertically stacked patch antenna with a superstrate with a focus on two main aspects:  
* The calculation of the LEO satellite link budget, which establishes a general relationship between any desired data rate in downlink and the corresponding antenna gain necessary for achieving the same. Several other authors [9; 10; 11] discuss Ku-band antennas (with frequency range of 12 to 18 GHz and wavelengths of 1.7 to 2.5 cm) and the corresponding link budgets. In this paper, the link budget for broadband internet data rates \(DR\) >25 Mbps are consolidated for LEO connectivity in Section 2.
* The simulation and measurement results for the proposed single antenna element with and without superstrate loading are presented and discussed. With the superstrate, the single-element gain was enhanced by more than 3 dB, which has significant consequences for the potential miniaturization of the Ku-band array antenna in that theoretically, the array size could be halved compared to an array without superstrate loading. These results are elucidated in Section 3. Section 4 presents the conclusion and the future work.