Hierarchical Closed-Loop FP-SGDA Optimization Framework for Beamforming and Task Assignment in ISAC-Enabled Multi-UAV Systems

Abstract

Integrated sensing and communication (ISAC) enabled multi-UAV networks can jointly detect non-cooperative UAVs and serve ground user equipment (UEs) in dense urban environments. However, conventional full-coverage service causes redundant transmissions, power inefficiency, and severe inter-/intra-UAV interference, especially under limited UAV power budgets. This article improves the coverage mode by jointly optimizing UE/target task assignment and ISAC beamforming, which leads to a nonconvex mixed-integer nonlinear programming (MINLP) problem with coupled discrete–continuous variables and complex interference. To address this challenge, we propose a hierarchical closed-loop optimization framework that integrates fractional programming with stochastic gradient descent–ascent (FP-SGDA). The framework decomposes the MINLP into an outer-layer task-assignment problem and an inner-layer beamforming problem, and establishes a bidirectional feedback loop between them. In the inner layer, FP-SGDA efficiently optimizes the nonconvex ISAC beamforming problem and feeds back the optimized beamformers, per-UAV communication rate, sensing Cramér–Rao lower bound (CRLB), signal-to-interference-plus-noise ratio, and actual intra-/inter-UAV interference under the current assignment. Guided by this feedback, the outer layer updates the binary UE/target assignment matrices and reallocates high-interference or high-difficulty tasks among UAVs, thereby reducing coverage overlap and mitigating cochannel ISAC interference at the source. Numerical results demonstrate that the proposed framework outperforms the successive convex approximation and mutual information weighted minimum mean-square error baselines, delivering a higher communication sum rate, a lower sensing CRLB, and enhanced power efficiency in dense urban multi-UAV ISAC networks.