Adversarial Water-Filling: Theory, Algorithms and Foundation Model

A new mathematical framework called Adversarial Water-Filling (AWF) has been proposed to manage real-time spectrum sharing among competing low Earth orbit satellite constellations, according to a paper submitted to arXiv in May 2026 [1]. The approach models competitive resource allocation as a minimax interaction between transmit power and worst-case interference, a formulation that arises naturally when multiple operators' LEO satellites interfere with one another [1][2]. Under Gaussian channel conditions, the AWF problem is strongly convex-concave on nondegenerate active channels, providing a tractable structure for optimization [2]. However, when discrete signal constellations are used, the problem shifts to generally nonconvex mercury/water-filling formulations, which are more difficult to solve [2]. To address these computational challenges, the researchers developed a wireless foundation model designed to learn the AWF search dynamics [1]. The architecture incorporates permutation-invariant channel representations and a constraint-aware graph neural network with sparse message passing [2]. Global latent variables capture the low-dimensional water level implied by the AWF optimality conditions [2]. The model uses learned projected extragradient iterations to approximate stationary solutions of the constrained minimax problem that emerges under mercury/water-filling [2]. The paper also provides theoretical convergence guarantees. Under local regularity and contractivity conditions, the learned AWF dynamics converge locally linearly around regular stationary points [2]. In experiments, the model generalized across unseen problem sizes, different constraints, and multiple discrete constellations while achieving more than one-order-of-magnitude runtime improvements over iterative baselines [1][2]. The related code has been released on GitHub [2]. Spectrum sharing among LEO constellations has become a pressing regulatory and engineering issue as thousands of new satellites are deployed. The AWF framework offers a structured way to analyze these interactions, though the paper does not address broader risk assessment processes that regulators might apply when evaluating interference hazards and their potential consequences [3].