GNN-driven Beamforming and Resource Allocation for RIS-assisted MISO-OFDMA Multi-group Multicasting System
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摘要: 针对可重构智能表面(Reconfigurable Intelligent Surface, RIS)辅助的多输入单输出-正交频分多址(Multiple-Input Single-Output-MISO Orthogonal Frequency Division Multiple Access, MISO-OFDMA)系统，围绕提升频谱效率这一核心需求，开展子载波分配、基站主动波束赋形与RIS被动波束赋形的联合优化研究。为解决传统优化方法在多变量耦合场景下计算复杂、易陷入局部最优的问题，提出了一种模型驱动的图神经网络(Graph Neural Network, GNN)方案。该方案将通信物理模型嵌入网络架构设计，实现从信道特征到多优化变量的端到端映射，无需依赖复杂迭代求解。仿真结果表明：与传统基准算法相比，所提方案不仅提高了系统的频谱效率，还显著降低了系统的计算复杂度。同时，在用户组数动态变化和基站传输功率调整等场景下仍保持良好鲁棒性，具备实际部署潜力。Abstract:
Objective Reconfigurable intelligent surfaces (RISs) have shown strong potential for enhancing coverage and spectral efficiency (SE) in future wireless networks. However, when they are applied to wideband multiple-input single-output (MISO)-orthogonal frequency division multiple access (OFDMA) systems, their practical benefits are limited by two key challenges: the frequency-selective mismatch of RIS reflection coefficients across subcarriers, and the strong coupling among subcarrier allocation, base station (BS) active beamforming, and RIS passive beamforming. These issues become even more critical in multi-group multicast scenarios, where shared data streams intensify inter-group interference. Therefore, this article proposes a graph neural network (GNN)-driven optimization framework that maximizes the system SE by jointly designing active and passive beamforming together with resource allocation. Methods To overcome the optimization difficulties caused by the tight coupling among subcarrier allocation, BS active beamforming, and RIS passive beamforming in RIS-assisted multi-user MISO-OFDMA systems, this work develops a model-driven GNN-based joint optimization framework with the objective of maximizing the system SE.First, a complete system model involving the BS, RIS, and multi-group multicast users is established ( Figure 1 ). The formulation explicitly incorporates practical constraints, including the BS transmit power limit, the unit-modulus constraint of RIS elements, and the binary nature of subcarrier assignment. To reflect the multicast requirement, the SE of each group is defined as the minimum SE among its users, which further increases the non-convexity of the optimization problem.The first component of GNN, GNN1 (Figure 3 ), consists of an initialization layer followed by a message-update layer. For each subcarrier $ n\in \mathcal{N} $, every user is modeled as a node, and the input to GNN1 is the set of channel matrices $ \left\{{\mathbf{H}}_{k,n},k\in \mathcal{K}\right\} $. Since standard GNNs operate on real-valued features, each complex channel vector is decomposed into its real and imaginary parts and used as the node feature representation. The group-level (Figure 4 ) and RIS-level (Figure 5 ) aggregations are subsequently performed.GNN2 (Figure 6 ) takes as input the set of subcarrier-wise embeddings generated by GNN1 and constructs an expanded graph that explicitly incorporates group nodes (Figure 7 ) and RIS nodes (Figure 8 ). By aggregating messages among subcarrier nodes, group nodes, and the RIS node, GNN2 performs cross-subcarrier information fusion and captures the global coupling structure across all system components. Based on the integrated representation, GNN2 outputs the BS active beamforming vectors and RIS passive phase shifts, while ensuring satisfaction of all physical constraints through output-layer normalization.Finally, given the beamforming parameters, subcarrier assignment is performed using a greedy max-SE rule. The overall learning objective is defined as maximizing the total SE.Results and Discussions The proposed GNN algorithm consistently outperforms all random allocation schemes, including APG-randAllocate, APG-randActive, and APG-randPassive, across the entire transmit power range from 0 to 20 dBm. This clear superiority indicates that the proposed method is effective in dynamically handling subcarrier assignment and joint active–passive beamforming optimization, and can maintain stable and superior performance even when the transmit power varies significantly. From the overall trend, the system spectral efficiency (SE) of all schemes increases monotonically with the BS transmit power, since higher transmit power improves the received signal-to-noise ratio and thus increases the achievable rate. Compared with the benchmark methods, GNN can adaptively coordinate BS active beamforming and RIS passive beamforming at different power levels and better exploit the reflection gain provided by the RIS. As a result, GNN maintains a consistent performance advantage over the entire power range. In addition, even in the high-power region, GNN still outperforms APG and LAO, which further demonstrates its robustness ( Figure 10 ).When the number of RIS elements varies, GNN maintains a clear performance advantage over both APG and LAO. In general, the system SE increases with the number of RIS elements, since a larger RIS provides higher array gain and improves the equivalent channel conditions. According to the numerical results, the proposed GNN achieves a spectral efficiency of2.0665 bps/Hz, outperforming LAO and APG by approximately 6.94% and 3.65%, respectively. Meanwhile, the average computational time of GNN is only about0.0075 s, which is approximately 4% of that required by the benchmark methods. These results demonstrate that the proposed GNN can effectively utilize the performance gains brought by RIS scaling, while achieving a good balance between performance and computational complexity (Figure 11 and Table II).The system SE versus the number of user groups under given settings of the number of transmit antennas and users is then examined. It can be observed that the overall SE decreases as the number of user groups increases, mainly because more multicast groups lead to stronger inter-group interference and the limited subcarrier resources have to be shared among more groups. Under all considered scenarios, the proposed GNN consistently outperforms LAO. Although its SE is slightly lower than that of APG, GNN still achieves about 98% of APG’s performance while requiring only about 4% of the computational time. This indicates that the proposed method can significantly reduce computational overhead while maintaining near-optimal system performance, which is particularly desirable for real-time or large-scale deployment (Figure 12 ).The generalization capability of the proposed GNN is further evaluated by training the model at a fixed transmit power level and testing it over a wide transmit power range from 0 to 20 dBm. The training and testing curves almost overlap, which indicates that the proposed GNN generalizes well to unseen transmit power levels. Over the entire power range, GNN consistently outperforms the LAO and APG benchmarks, further confirming its robustness and adaptability under different transmission conditions (Figure 13 ).Conclusions For the RIS-assisted MISO-OFDMA system, this paper formulates a joint optimization of subcarrier allocation, BS active beamforming, and RIS passive beamforming to maximize system SE. To this end, a model-driven GNN is proposed. To validate the effectiveness of the proposed method, comparative experiments were conducted against benchmark algorithms. The results demonstrate that the proposed GNN algorithm consistently outperforms LAO and APG in overall performance. Moreover, it exhibits strong robustness under different number of groups and transmit power settings, further highlighting its potential for practical deployment in complex engineering scenarios. -
表 1 GNN网络参数
函数 参数量 函数 参数量 $ {f}_{\text{tl}} $ $ 6{N}_{t}\times 2M+2M $ $ {f}_{\text{tl}} $ $ 2M{N}_{t}\times 6{N}_{t}+6{N}_{t} $ $ {f}_{\text{t2}} $ $ 2M\times 2{N}_{t}+2{N}_{t} $ $ {f}_{\text{w2}} $ $ 6{N}_{t}\times 2{N}_{t}+2{N}_{t} $ $ {f}_{\text{t3}} $ $ (2M+2{N}_{t})\times M+M $ $ {f}_{\text{w3}} $ $ 10{N}_{t}\times 4{N}_{t}+4{N}_{t} $ $ {f}_{\text{t4}} $ $ M\times M+M $ $ {f}_{\text{w4}} $ $ 4{N}_{t}\times 4{N}_{t}+4{N}_{t} $ $ {f}_{\text{t5}} $ $ M\times 2{N}_{t}+M $ $ {f}_{\text{w5}} $ $ 4{N}_{t}\times 2{N}_{t}+2{N}_{t} $ $ {f}_{\text{t6}} $ $ (M+2{N}_{t})\times 2M+2M $ 
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表 1 GNN网络参数
函数 参数量 函数 参数量 $ {f}_{\text{tl}} $ $ 6{N}_{t}\times 2M+2M $ $ {f}_{\text{tl}} $ $ 2M{N}_{t}\times 6{N}_{t}+6{N}_{t} $ $ {f}_{\text{t2}} $ $ 2M\times 2{N}_{t}+2{N}_{t} $ $ {f}_{\text{w2}} $ $ 6{N}_{t}\times 2{N}_{t}+2{N}_{t} $ $ {f}_{\text{t3}} $ $ (2M+2{N}_{t})\times M+M $ $ {f}_{\text{w3}} $ $ 10{N}_{t}\times 4{N}_{t}+4{N}_{t} $ $ {f}_{\text{t4}} $ $ M\times M+M $ $ {f}_{\text{w4}} $ $ 4{N}_{t}\times 4{N}_{t}+4{N}_{t} $ $ {f}_{\text{t5}} $ $ M\times 2{N}_{t}+M $ $ {f}_{\text{w5}} $ $ 4{N}_{t}\times 2{N}_{t}+2{N}_{t} $ $ {f}_{\text{t6}} $ $ (M+2{N}_{t})\times 2M+2M $
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