This work develops a physics-driven self-supervised graph learning framework that directly optimizes the distortion-aware precoder under nonlinear correlated power amplifier (PA) distortion, without relying on expensive optimizer-generated labels for a user-centric satellite system. We minimize nonlinear PA consumption subject to user quality-of-service (QoS) constraints under PA nonlinearity for a downlink multi-input-single-output (MISO) satellite system. Our pipeline jointly designs the precoder and admission control that minimize nonlinear PA consumed power. In particular, a graph neural network (GNN) for the design of a distortion-aware precoder is optimized end-to-end in a self-supervised manner using a differentiable Itô-Hermite model of the true modified Rapp amplifier model. The precoder output by the GNN is used to initialize a low-complexity distortion-aware signal-to-interference-distortion (SINDR) tracking algorithm that jointly optimizes for power and admission control. Our proposed physics-based pipeline closely tracks a successive convex approximation (SCA) based solution in consumed power performance with the advantage of faster runtime and a wide operating range covered during training.

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