Learning-Based Beamforming for Energy Efficiency of Continuous Aperture Array Systems

This paper jointly optimizes the base-station (BS) continuous aperture array (CAPA) dimensions and beamforming functions to maximize energy efficiency (EE) of the downlink multiuser multi-CAPA system, where both the BS and the users are equipped with CAPAs. Since the beamforming functions are continuous current distribution over the BS CAPA, the resulting EE maximization problem is a nontrivial functional optimization problem that couples aperture sizing and beamforming design. To address this challenge, we propose a cascaded network architecture consisting of a graph neural network (GNN) and a functional-gradient based implicit neural representation (FGB-INR) to learn the BS CAPA dimensions and beamforming functions, respectively. Both networks exploit the permutation equivariance of the optimal optimization policy, and the update equations of FGB-INR are designed according to the functional-gradient structure of the EE objective. Simulation results show that the proposed method approaches the EE of the numerical method while substantially reducing inference latency. They also demonstrates that the functional-gradient structure in FGB-INR improves EE while reducing sample complexity and training time.