  This paper investigates the optimization of the long-standing
probabilistically robust transmit beamforming problem with channel
uncertainties in the multiuser multiple-input single-output (MISO) downlink
transmission. This problem poses significant analytical and computational
challenges. Currently, the state-of-the-art optimization method relies on
convex restrictions as tractable approximations to ensure robustness against
Gaussian channel uncertainties. However, this method not only exhibits high
computational complexity and suffers from the rank relaxation issue but also
yields conservative solutions. In this paper, we propose an unsupervised deep
learning-based approach that incorporates the sampling of channel uncertainties
in the training process to optimize the probabilistic system performance. We
introduce a model-driven learning approach that defines a new beamforming
structure with trainable parameters to account for channel uncertainties.
Additionally, we employ a graph neural network to efficiently infer the key
beamforming parameters. We successfully apply this approach to the minimum rate
quantile maximization problem subject to outage and total power constraints.
Furthermore, we propose a bisection search method to address the more
challenging power minimization problem with probabilistic rate constraints by
leveraging the aforementioned approach. Numerical results confirm that our
approach achieves non-conservative robust performance, higher data rates,
greater power efficiency, and faster execution compared to state-of-the-art
optimization methods.
