Joint Beam Selection and Power Allocation for Cell-Free Integrated Sensing and Communication Networks: An Optimal Transport Theory Approach

Low-altitude cell-free integrated sensing and communication (ISAC) networks represent a promising paradigm for next-generation wireless systems, enabling distributed deployment for unmanned aerial vehicle (UAV) communications and sensing. However, these networks encounter critical resource management challenges: spatially heterogeneous user distributions, severe inter-beam interference, dynamic topologies and complex resource coupling. This paper proposes a novel joint beam direction selection and power allocation algorithm based on optimal transport theory to tackle the computationally intractable mixed-integer NP-hard optimization problem. The key innovation lies in transforming discrete allocation problems into optimal mapping between continuous probability distributions, leveraging Kantorovich duality theory and the Sinkhorn algorithm for efficient global optimization. Unlike conventional approaches that suffer from exponential complexity and local optima convergence, our method achieves polynomial-time complexity with theoretical convergence guarantees. Results demonstrate substantial long-term sum rate improvements of 43% and 18.8% compared to baseline methods, while achieving remarkable sensing accuracy enhancements of 72.8% and 69.9%, respectively.