  This paper studies the quality-of-service (QoS) constrained multi-group
multicast beamforming design problem, where each multicast group is composed of
a number of users requiring the same content. Due to the nonconvex QoS
constraints, this problem is nonconvex and NP-hard. While existing
optimization-based iterative algorithms can obtain a suboptimal solution, their
iterative nature results in large computational complexity and delay. To
facilitate real-time implementations, this paper proposes a deep learning-based
approach, which consists of a beamforming structure assisted problem
transformation and a customized neural network architecture named hierarchical
permutation equivariance (HPE) transformer. The proposed HPE transformer is
proved to be permutation equivariant with respect to the users within each
multicast group, and also permutation equivariant with respect to different
multicast groups. Simulation results demonstrate that the proposed HPE
transformer outperforms state-of-the-art optimization-based and deep
learning-based approaches for multi-group multicast beamforming design in terms
of the total transmit power, the constraint violation, and the computational
time. In addition, the proposed HPE transformer achieves pretty good
generalization performance on different numbers of users, different numbers of
multicast groups, and different signal-to-interference-plus-noise ratio
targets.
