The latest satellite communication (SatCom) missions are characterized by a fully reconfigurable on-board software-defined payload, capable of adapting radio resources to the temporal and spatial variations of the system traffic. As pure optimization-based solutions have shown to be computationally tedious and to lack flexibility, machine learning (ML)-based methods have emerged as promising alternatives. We investigate the application of energy-efficient brain-inspired ML models for on-board radio resource management. Apart from software simulation, we report extensive experimental results leveraging the recently released Intel Loihi 2 chip. To benchmark the performance of the proposed model, we implement conventional convolutional neural networks (CNN) on a Xilinx Versal VCK5000, and provide a detailed comparison of accuracy, precision, recall, and energy efficiency for different traffic demands. Most notably, for relevant workloads, spiking neural networks (SNNs) implemented on Loihi 2 yield higher accuracy, while reducing power consumption by more than 100$\times$ as compared to the CNN-based reference platform. Our findings point to the significant potential of neuromorphic computing and SNNs in supporting on-board SatCom operations, paving the way for enhanced efficiency and sustainability in future SatCom systems.

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