Robust Beamforming for Space–Air–Ground Integrated Network (SAGIN) With CSI Uncertainty Using Multiple Kernel Learning

This paper focuses on the robust beamforming for space-air-ground integrated networks (SAGIN) under uncertain channel state information (CSI). In SAGIN, uncertain CSI undermines the precise adjustment of beamforming, posing a major challenge to meeting users’ quality of service (QoS) requirements. To address this challenge, we first formulate the optimization problem as a quadratic program, which ensures a specified outage probability to maintain QoS. We then propose a multiple kernel-based machine learning method to model the uncertain CSI as an asymmetric convex polyhedron set. Leveraging semidefinite relaxation, the quadratic objective function is transformed into a linear function composed of beamforming matrix traces. Under the constructed CSI uncertainty set, a general robust transformation method is developed to linearly approximate the original probability constraints. Finally, we reformulate the joint optimization problem as a standard semidefinite program (SDP) and design an adaptive robust strategy to find its optimal solution. Simulation results show that our proposed method outperforms traditional robust and non-robust methods, effectively addressing limitations in existing SAGIN-related research.