Adversarial Water-Filling: Minimax Resource Allocation Optimization with Proximal Decomposition in Open RAN

With the rapid rise of Open RAN, adversarial interference and dynamic spectrum sharing present new challenges to classical water-filling-based resource allocation. In particular, NTN integration and satellite mobility introduce highly dynamic interference that goes beyond the assumptions of traditional models. To address scenarios in which an adversary can dynamically allocate interference power, this paper introduces an adversarial water-filling framework grounded in min-max optimization and strongly convex-concave game. This framework is motivated by 6G scenarios where spectrum coexistence and real-time threats require robust, adaptive solutions. We propose an Adversarial Water-Filling (AWF) algorithm, which solves the problem in a finite number of steps. We also highlight the close connection between water-filling, proximal operators, and the classical first-order optimization method PDHG. Numerical experiments on large-scale problems demonstrate that Algorithm AWF retains robust allocation performance, significantly reduces computational overhead, and offers a promising approach for future network optimization.