HPE Transformer: Learning to Optimize Multi-Group Multicast Beamforming Under Nonconvex QoS Constraints

TL;DR

QoS-constrained multi-group multicast beamforming is nonconvex and NP-hard, motivating a real-time solution. The authors introduce an HPE Transformer that leverages the multicast beamforming structure by decomposing the channel-to-beamformer mapping into two permutation-equivariant functions $f(oldsymbol{H})$ and $g(oldsymbol{H},oldsymbol{ heta},oldsymbol{ u})$, implemented via encoding and decoding blocks. The decoding block includes a constraint-augmented gradient-descent pipeline to explicitly reduce QoS constraint violations, while the encoding block preserves intra- and inter-group permutation structure. Empirical results show the HPE Transformer achieves lower transmit power, smaller constraint violations, and far faster inference than optimization-based methods and prior DL approaches, with strong generalization across varying numbers of users, multicast groups, and SINR targets, enabling practical real-time multicast beamforming under QoS constraints.

Abstract

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.

Figures (11)

• Figure 1: The overall architecture of the proposed HPE transformer $g(\cdot,f(\cdot))$, which consists of an encoding block for representing $f(\cdot)$ and a decoding block for representing $g(\cdot,\cdot,\cdot)$.
• Figure 2: The self-attention block in the vanilla transformer.
• Figure 3: The architecture of the proposed encoding block for representing $f(\cdot)$.
• Figure 4: The $\ell$-th hierarchical layer of the proposed encoding block.
• Figure 5: The architecture of the proposed decoding block for representing $g(\cdot,\cdot,\cdot)$.

Theorems & Definitions (5)

• proof
• Theorem 1
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• Theorem 2
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