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.

翻译：本文研究服务质量（QoS）约束下的多组多播波束成形设计问题，其中每个多播组由若干需要相同内容的用户组成。由于非凸的QoS约束，该问题具有非凸性和NP难特性。尽管现有基于优化的迭代算法能获得次优解，但其迭代特性导致计算复杂度高、延迟大。为促进实时部署，本文提出一种基于深度学习的方法，包括波束成形结构辅助的问题转换和名为层次置换等变性（HPE）Transformer的定制化神经网络架构。理论证明，所提HPE Transformer对每个多播组内用户具有置换等变性，且对不同多播组也具有置换等变性。仿真结果表明，在总发射功率、约束违反度和计算时间方面，所提HPE Transformer优于最先进的基于优化和深度学习的多组多播波束成形设计方法。此外，所提HPE Transformer在不同用户数量、不同多播组数量及不同信干噪比目标下均展现出良好的泛化性能。