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Non-uniform coverage is a central challenge in UAV-assisted wireless networks, yet most existing methods either assume uniform demand or depend on precise user locations. This letter proposes a distribution-centric trajectory design that uses only statistical demand maps to generate ergodic UAV paths, guaranteeing that time-averaged presence converges to the prescribed spatial distribution. The scheme modulates UAV speed via a time-warping function for smooth transitions between high- and low-density regions, uses continuous angular adjustments, and provides rigorous convergence and complexity analyses. Simulations demonstrate that our method improves coverage fairness and distribution matching by 4.7× and 5.8×, respectively, relative to a deep-reinforcement-learning baseline, while also achieving 1.1× and 1.5× gains over an optimaltransport approach. It reduces outage probability by up to 65 % compared with uniform coverage. Experiments with the Telecom Italia Milano dataset show that the resulting coverage closely matches real urban demand patterns under wind and sensor disturbances. 

The surge in demand for e!cient radio resource management has necessitated the development of sophisticated yet compact neural network architectures. In this paper, we introduce a novel approach to Graph Neural Networks (GNNs) tailored for radio resource management by presenting a new architecture: the Low Rank Message Passing Graph Neural Network (LR-MPGNN). The cornerstone of LR-MPGNN is the implementation of a low-rank approximation technique that substitutes the conventional linear layers with their low-rank counterparts. This innovative design signi"cantly reduces the model size and the number of parameters. We evaluate the performance of the proposed LR-MPGNN model based on several key metrics: model size, number of parameters, weighted sum rate of the communication system, and the distribution of eigenvalues of weight matrices. Our extensive evaluations demonstrate that the LR-MPGNN model achieves a sixtyfold decrease in model size, and the number of model parameters can be reduced by up to 98%. Performance-wise, the LR-MPGNN demonstrates robustness with a marginal 2% reduction in the best-case scenario in the normalized weighted sum rate compared to the original MPGNN model. Additionally, the distribution of eigenvalues of the weight matrices in the LR-MPGNN model is more uniform and spans a wider range, suggesting a strategic redistribution of weights.