This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Flor Ortiz, University of Luxembour; (2) Juan A. Vasquez-Peralvo, University of Luxembour; (3) Jorge Querol, University of Luxembour; (4) Eva Lagunas, University of Luxembour; (5) Jorge L. Gonzalez Rios, University of Luxembour; (6) Marcele O. K. Mendonc¸a, University of Luxembour; (7) Luis Garces, University of Luxembour; (8) Victor Monzon Baeza, University of Luxembour; (9) Symeon Chatzinotas, University of Luxembou. Table of Links Abstract & Introduction System Model and Problem Statement Antenna Design and Training Data Generation Supervised Learning for Adaptive Beamforming Numerical Results Conclusions, Acknowledgment, and References III. ANTENNA DESIGN AND TRAINING DATA GENERATION A. Antenna Design For GEO missions, efficient antenna design is crucial due to substantial free space losses and stringent constraints on permissible losses. To address these challenges, we have developed an open-ended waveguide antenna as the unit cell antenna for this scenario, as explained in [8]. This antenna design offers significantly lower losses than alternative solutions like patch antennas or dielectric-based antennas. The antenna consists of three main components: the open-ended waveguide itself, the groove polarizer responsible for circular polarization, and the rectangular-to-circular transition for connecting to the distribution network. Simulation results, confirm that the antenna meets the requirements. It radiates within the required frequency band, emitting Left-Hand Circular Polarized (LHCP) waves with minimal cross-polarization. This is evident from the S11 parameter, below -10 dB, and the axial ratio measuring less than 3 dB within the intended frequency range [8] We consider the coverage area over the Earth’s surface to determine the number of elements required for the array antenna. In the context of Very High Throughput satellite missions, where small areas need to be covered to avoid channel link saturation, we set a minimum beam diameter of 260 km or a coverage area Ac = 53093 km2 when the satellite is at nadir. It’s worth noting that the coverage area can be adjusted based on specific beam requirements We then calculate the 3 dB antenna beamwidth θ−3dB required to illuminate this area. Using geometric relations and the satellite’s location, we estimate θ−3dB, which in this case is found to be 0.41◦ . However, this number of elements is impractical regarding space, cost, and power requirements, as each element requires an RF chain. To address this, subarrays are introduced. The number of subarray elements is determined to avoid grating lobes intersecting the antenna’s Field of View (FoV) over the Earth’s surface resulting in an element spacing of d = 3.5λ0. With this spacing, subarrays of 4×4 elements are employed, resulting in 36×36 RF chains B. Training Data Generation The approach chosen in this study is array thinning, which consists of selectively activating and deactivating elements to form the desired antenna beam, as illustrated in Figure 1. Array thinning allows precise control of the beamwidth, uniform power distribution among the elements in multi-beam scenarios and orientation of the radiation pattern in the desired direction by progressive phase shifting. To create the training data for this antenna array, a Genetic Algorithm (GA) was employed. The goal of the GA was to find the optimal set of active antenna elements while respecting specific constraints, such as beamwidth, SLL and EIRP. The GA optimization process iteratively refines the antenna element configurations, starting from an initial configuration and continuing until convergence or until a predefined maximum iteration limit is reached. It considers several performance parameters simultaneously, such as beamwidth, SLL and EIRP, making it particularly suitable for optimizing complex antenna systems such as the distributed reflector antenna. The resulting training dataset consists of 174,203 samples, each representing different antenna element configurations that meet the defined constraints. This dataset serves as a reference for evaluating antenna performance and training machine learning models in the later sections of this paper. The main purpose of this database is to establish correlations between beamforming array weights and critical system parameters, including beamwidth, SLL, and EIRP. For more detailed information on the generated database, including access to the dataset itself, see [9], where it is openly available.

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