LEO Satellite Multi-beam Multicast Precoding and User Grouping Joint Optimization Algorithm
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摘要: 针对多波束低轨卫星(LEO)通信系统中全频率复用引发的波束间干扰，以及现有组播预编码算法计算复杂度高、用户分组公平性不足的挑战，该文提出了一种高效的联合优化方案。首先，设计了一种基于卷积神经网络-长短期记忆网络(CNN-LSTM)混合架构的无监督深度学习预编码模型。该模型能够从信道状态信息(CSI)和信噪比(SNR)中有效提取特征，在满足单天线功率约束(PAC)的前提下最大化系统总速率，其在线计算复杂度仅随天线数量线性增长，显著低于传统方法的立方级复杂度。其次，针对DVB-S2X标准下基于帧的组播预编码对等容量用户分组的硬性要求，该文提出了约束K-means(CK-means)和公平感知MAUG(FA-MAUG)用户分组算法。前者可在保证每组用户数量严格一致的同时维持较高的组内信道相似度；后者通过优先保障边缘弱用户分组质量，有效提升了系统公平性和整体鲁棒性。仿真结果表明，所提深度学习预编码方案在总速率性能上显著优于传统MMSE算法，在不同SNR下平均提升约48%；同时，改进的用户分组算法进一步增强了组内信道一致性并显著提高了系统吞吐量。研究结果展现了所提算法良好的实用价值和工程适用性，为多波束低轨卫星通信系统的资源优化提供了有效技术途径。Abstract:
Objective In 6G LEO communication, multicast precoding is utilized to mitigate the significant inter-beam interference introduced by Full Frequency Reuse (FFR). However, traditional precoding algorithms are hindered by cubic computational complexity, making them unsuitable for massive MIMO. Additionally, existing user grouping strategies often fail to meet the fixed group size requirements of the DVB-S2X standard. Therefore, a joint optimization scheme is developed to integrate a low-complexity unsupervised deep learning model for precoding with improved user grouping algorithms to enhance sum rate and fairness. Methods To address the precoding challenge, an unsupervised deep learning model based on a hybrid CNN-LSTM architecture is proposed ( Fig. 2 ). The Convolutional Neural Network (CNN) is utilized to extract spatial features from the Channel State Information (CSI), while the Long Short-Term Memory (LSTM) network captures their deep feature correlations. Unlike supervised learning, this model is trained by directly maximizing the sum rate as the loss function, subject to the Per-Antenna Constraint (PAC). For user grouping, two algorithms are developed to comply with the DVB-S2X standard. First, the CK-means algorithm is introduced, which modifies the standard K-means to ensure an equal number of users in each group. Second, FA-MAUG algorithm is proposed which prioritizes users with poor channel quality, thereby enhancing the overall robustness and fairness of the grouping result.Results and Discussions The intra-group similarity metric is employed to evaluate user grouping performance, which indicate that the CK-means algorithm achieves a similarity score approximately 0.1 higher than the MAUG algorithm and nearly 0.5 higher than random grouping across various group sizes ( Fig. 3 ). This high similarity translates directly into better beamforming gain. In terms of throughput, the sum rate of the CNN-LSTM precoding combined with CK-means grouping outperforms traditional MMSE across different SNRs and total powers (Fig. 4 ,Fig. 5 ). The sum rate based on the proposed CNN-LSTM precoding scheme is on average 48.59% higher than that of the traditional MMSE algorithm and the gain of the CK-means algorithm compared to random grouping reaches 30.12% under different SNR conditions. Additionally, we analyzed the effects of the number of users per group, the number of groups, and the number of antennas on the system rate(Fig. 6 ,Fig. 7 ,Fig. 8 ), verifying the performance of the model in systems of different scales. Additionally, the complexity analysis confirms that the proposed precoding approach reduces the online overhead from the cubic level of traditional MMSE to a linear level relative to the number of antennas, which is critical for real-time deployment in massive MIMO satellite systems.Conclusions This paper presents a joint optimization framework for LEO satellite multicast systems, addressing the dual challenges of high computational complexity in precoding and lack of fairness in user grouping. Simulation results demonstrate that the proposed solution significantly enhances the system sum rate—by over 48.59% in typical SNR scenarios—compared to traditional methods. The approach provides a robust and scalable solution for the coordinated management of multi-beam interference in future 6G satellite communications. Future work will further explore the impact of hardware impairments and highly dynamic channel conditions on the generalization capabilities of the proposed model. -
表 1 CNN-LSTM模型参数
模型层名称 输出维度 激活函数 参数量 输入层 64×36×1 \ 0 卷积层 32×64 ReLU 4672 LSTM层 64×1 \ 33024 全连接层1 512×1 ReLU 33280 全连接层2 256×1 ReLU 131328 全连接层3 128×1 sigmoid 32896 
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表 2 代表深度学习预编码算法在线计算复杂度
论文 模型 在线复杂度 Lin 2020[14] 端到端神经网络 $ O(({2N}_{I}-1){N}_{O}) $ Luo 2022[17] CNN+迭代优化算法 $ O({N}_{o}{N}_{i}+2{N}_{t}\text{S)} $ Li 2025[13] 多智能体强化学习 $ O({N}_{a}TB{N}_{p}) $ 本文 端到端CNN+LSTM $ \text{O}\left({N}_{o}{N}_{i}+4{N}_{\text{L}}\left({N}_{\text{L}}+{N}_{\text{X}}\right)+\left(2{N}_{\text{I}}-1\right){N}_{\text{O}}\right) $ *$ {N}_{o} $：卷积层输出维度；$ {N}_{i} $：卷积层输入维度；$ S $：卷积层特征大小；$ {N}_{O} $：全连接层输出维度；$ {N}_{I} $：全连接层输入维度； $ {N}_{\text{X}} $：LSTM层输入维度；$ {N}_{L} $：LSTM层隐藏层维度；$ {N}_{a} $：智能体个数；$ T $：状态更新步数；$ B $:缓冲采样数；$ {N}_{p} $：前向传播数量
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1 约束K-means用户分组算法(CK-means)
输入：用户位置集合$ \mathcal{X}=\{{\boldsymbol{x}}_{1},{\boldsymbol{x}}_{2},\cdots ,{\boldsymbol{x}}_{{{N}_{\text{u}}}}\} $，组数$ K $，每个组
用户数$ M $输出：最优聚类集合$ \mathcal{G}=\{{\mathcal{G}}_{1},{\mathcal{G}}_{2},\cdots ,{\mathcal{G}}_{K}\} $ 1: 初始化$ K $个质心位置$ C= {\boldsymbol{c}}_{1},{\boldsymbol{c}}_{2},\cdots,{\boldsymbol{c}}_{K}\} $ 2: Repeat 3: 计算距离矩阵$ \boldsymbol{D}={\left|\left|{\boldsymbol{x}}_{i}-{\boldsymbol{c}}_{k}\right|\right|}^{2}\in {\mathbb{C}}^{{{N}_{\text{u}}}\times K},i\in \left\{1{,}2,\cdots ,{N}_{\text{u}}\right\} $,
$ k\in \{1{,}2,\cdots ,K\} $4: 将$ \boldsymbol{D} $中元素值按照升序重新排列 5: for $ \boldsymbol{D}\text{中元素}{\boldsymbol{d}}_{i,k},i\in \left\{1{,}2,\cdots ,{N}_{\text{u}}\right\},k\in \{1{,}2,\cdots ,K\} $ do 6: if用户$ {\boldsymbol{x}}_{i} $ 尚未被分配 and $ \left| {\mathcal{G}}_{k}\right| \lt M $ then
$ {\mathcal{G}}_{k}\leftarrow {\mathcal{G}}_{k}\cup \{{\boldsymbol{x}}_{i}\} $7: end if 8: end for 9: 更新质心：$ {\boldsymbol{c}}_{k}\leftarrow \dfrac{1}{\left| {\mathcal{G}}_{k}\right| }{\sum}_{\boldsymbol{x}\in {{\mathcal{G}}_{K}}}\boldsymbol{x},\;\forall k\in \{1{,}2,\cdots ,K\} $ 10: until质心集合$ C $不再发生变化 11: return最优聚类集合$ G $
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2 公平感知MAUG用户分组算法(FA-MAUG)
输入：卫星天线数$ {N}_{\text{t}} $，用户数$ {N}_{\text{u}} $，组数$ K $，每组用户数$ M $，
用户信道向量$ {\tilde{\boldsymbol{h}}}_{i}\in {\mathbb{C}}^{{{N}_{\text{t}}}\times 1},i\in \{1{,}2,\ldots ,{N}_{\text{u}}\} $输出：最优分组集合 $ \mathcal{G}=\{{\mathcal{G}}_{1},{\mathcal{G}}_{2},\cdots ,{\mathcal{G}}_{K}\} $ 1: 初始化代表用户集合 $ \mathcal{I}=\mathit{\varnothing } $，剩余用户集合
$ U=\left\{1{,}2,\cdots ,{N}_{\text{u}}\right\} $2: 步骤1：选择代表用户 3: for $ i=1 $ to $ K $ do 4: for $ j\in U $ do 5: $ {\boldsymbol{g}}_{j}={\tilde{\boldsymbol{h}}}_{j}-\displaystyle\sum\limits_{q=1}^{i-1}\frac{\tilde{\boldsymbol{h}}_{j}^{\text{H}}{\boldsymbol{g}}_{q}}{\parallel {\boldsymbol{g}}_{q}{\parallel }^{2}}{\boldsymbol{g}}_{q} $ 6: end for 7: 选择代表用户：$ {j}^{*}=\arg \max \parallel {\boldsymbol{g}}_{j}\parallel $ 8: $ \mathcal{I}\leftarrow \mathcal{I}\cup \left\{{j}^{*}\right\},U\leftarrow U\smallsetminus \left\{{j}^{*}\right\},{\mathcal{G}}_{i}\leftarrow {\mathcal{G}}_{i}\cup \left\{{j}^{*}\right\},{\boldsymbol{g}}_{i}={\boldsymbol{g}}_{{{j}^{*}}} $ 9: end for 10: 步骤2：剩余用户分配 11： 将 $ U $ 中剩余用户按照信道范数降序重新排列 12： for $ i\in U $ do 13： for$ j=1 $ to $ K $ do 14: if $ |{\mathcal{G}}_{j}|\leq M $ then计算用户$ i $与代表用户$ \mathcal{I}\{j\} $的相似度
$ {u}_{i,j}=\dfrac{\tilde{\boldsymbol{h}}_{\mathcal{I}\{j\}}^{\text{H}}{\tilde{\boldsymbol{h}}}_{i}}{\parallel {\tilde{\boldsymbol{h}}}_{i}{\parallel }^{2}}{\tilde{\boldsymbol{h}}}_{i} $15: end if 16: end for 17: 查找相似度最高的组并进行分配：
$ {j}^{*}=\arg \max {u}_{i,j},{\mathcal{G}}_{{{j}^{*}}}\leftarrow {\mathcal{G}}_{{{j}^{*}}}\cup \{i\} $18: end for 19: return最优聚类集合 $ G $
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表 3 用户分组算法计算复杂度
用户分组算法 计算复杂度 CK-means $ O\left({N}_{\text{t}}{N}_{\text{u}}K+{N}_{\text{u}}K\log \left({N}_{\text{u}}K\right)\right) $ FA-MAUG $ O\left({N}_{\text{t}}{N}_{\text{u}}{K}^{2}+{N}_{\text{t}}{N}_{\text{u}}K+{N}_{\text{u}}\log \left({N}_{\text{u}}\right)\right) $ MAUG $ O\left({N}_{\text{t}}{N}_{\text{u}}{K}^{2}+{N}_{\text{t}}{N}_{\text{u}}K\right) $
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[1] KUMARI S and HOSSAIN A. Comprehensive review on performance analysis for satellite communication MIMO over terrestrial communication MIMO[J]. International Journal of Satellite Communications and Networking, 2026, 44(4): 445–463. doi: 10.1002/sat.70035. [2] 郑斌, 曾令昕, 黄辉, 等. 密集低轨卫星网络辅助地面通信的鲁棒波束赋形方法[J]. 电子与信息学报, 2025, 47(3): 623–632. doi: 10.11999/JEIT240732.ZHENG Bin, ZENG Lingxin, HUANG Hui, et al. Robust beamforming method for dense LEO satellite network assisted terrestrial communication[J]. Journal of Electronics & Information Technology, 2025, 47(3): 623–632. doi: 10.11999/JEIT240732. [3] European Telecommunications Standards Institute. ETSI EN 302 307-1 V1.4. 1 Second generation framing structure, channel coding and modulation systems for broadcasting, interactive services, news gathering and other broadband satellite applications; Part 1 (DVB-S2)[S]. Cedex: ETSI, 2014. [4] European Telecommunications Standards Institute. ETSI EN 302 307-2 V1.4. 1 Second generation framing structure, channel coding and modulation systems for broadcasting, interactive services, news gathering and other broadband satellite applications; Part 2: DVB-S2 Extensions (DVB-S2X)[S]. Cedex: ETSI, 2024. [5] CHRISTOPOULOS D, CHATZINOTAS S, and OTTERSTEN B. Multicast multigroup precoding and user scheduling for frame-based satellite communications[J]. IEEE Transactions on Wireless Communications, 2015, 14(9): 4695–4707. doi: 10.1109/TWC.2015.2424961. [6] SIDIROPOULOS N D, DAVIDSON T N, and LUO Zhiquan. Transmit beamforming for physical-layer multicasting[J]. IEEE Transactions on Signal Processing, 2006, 54(6): 2239–2251. doi: 10.1109/TSP.2006.872578. [7] YIN Shiqi and DONG Min. Computation-and-communication efficient coordinated multicast beamforming in massive MIMO networks[J]. IEEE Transactions on Communications, 2025, 73(9): 7811–7827. doi: 10.1109/TCOMM.2025.3541031. [8] CHRISTOPOULOS D, CHATZINOTAS S, ZHENG Gan, et al. Linear and nonlinear techniques for multibeam joint processing in satellite communications[J]. EURASIP Journal on Wireless Communications and Networking, 2012, 2012(1): 162. doi: 10.1186/1687-1499-2012-162. [9] WU S X, MA W K, and SO A M C. Physical-layer multicasting by stochastic transmit beamforming and Alamouti space-time coding[J]. IEEE Transactions on Signal Processing, 2013, 61(17): 4230–4245. doi: 10.1109/TSP.2013.2263500. [10] KARIPIDIS E, SIDIROPOULOS N D, and LUO Zhiquan. Quality of service and max-min fair transmit beamforming to multiple Cochannel multicast groups[J]. IEEE Transactions on Signal Processing, 2008, 56(3): 1268–1279. doi: 10.1109/TSP.2007.909010. [11] LUO Zhiquan, MA W, SO A M C, et al. Semidefinite relaxation of quadratic optimization problems[J]. IEEE Signal Processing Magazine, 2010, 27(3): 20–34. doi: 10.1109/MSP.2010.936019. [12] 李振东, 巴建乐, 苏洲, 等. 可移动天线赋能的ISAC系统中波束赋形与天线位置联合优化[J]. 电子与信息学报, 2025, 47(10): 3482–3491. doi: 10.11999/JEIT250146.LI Zhendong, BA Jianle, SU Zhou, et al. Joint beamforming and antenna position optimization in movable antenna empowered ISAC systems[J]. Journal of Electronics & Information Technology, 2025, 47(10): 3482–3491. doi: 10.11999/JEIT250146. [13] DONG Min and WANG Qiqi. Multi-group multicast beamforming: Optimal structure and efficient algorithms[J]. IEEE Transactions on Signal Processing, 2020, 68: 3738–3753. doi: 10.1109/TSP.2020.2994753. [14] LI Huiting, JIANG Yanxiang, HUANG Yige, et al. A multi-agent DRL method for distributed energy-efficient association and hybrid precoding in mmWave cell-free massive MIMO systems[J]. IEEE Communications Letters, 2025, 29(1): 70–74. doi: 10.1109/LCOMM.2024.3494537. [15] LIN Tian and ZHU Yu. Beamforming design for large-scale antenna arrays using deep learning[J]. IEEE Wireless Communications Letters, 2020, 9(1): 103–107. doi: 10.1109/LWC.2019.2943466. [16] SOHRABI F, ATTIAH K M, and YU Wei. Deep learning for distributed channel feedback and multiuser precoding in FDD massive MIMO[J]. IEEE Transactions on Wireless Communications, 2021, 20(7): 4044–4057. doi: 10.1109/TWC.2021.3055202. [17] ZHOU Huibin, GONG Xinrui, TSINOS C G, et al. GNN-enabled precoding for massive MIMO LEO satellite communications[J]. IEEE Transactions on Communications, 2025, 73(10): 9028–9042. doi: 10.1109/TCOMM.2025.3568216. [18] LUO Jie, FAN Jiancun, and ZHANG Jinbo. MDL-AltMin: A hybrid precoding scheme for mmWave systems with deep learning and alternate optimization[J]. IEEE Wireless Communications Letters, 2022, 11(9): 1925–1929. doi: 10.1109/LWC.2022.3188167. [19] YING Ming, CHEN Xiaoming, QI Qiao, et al. Deep learning-based joint channel prediction and multibeam precoding for LEO satellite internet of things[J]. IEEE Transactions on Wireless Communications, 2024, 23(10): 13946–13960. doi: 10.1109/TWC.2024.3406952. [20] ZHANG Yuxin, WANG Xingwei, LUO Xuewen, et al. A survey on AI-empowered task-oriented sensing, communication, and computation in 6G networks[J]. Computer Science Review, 2026, 60: 100899. doi: 10.1016/j.cosrev.2026.100899. [21] 李国权, 程涛, 郭永存, 等. 基于深度强化学习的IRS辅助认知无线电系统波束成形算法[J]. 电子与信息学报, 2025, 47(3): 657–665. doi: 10.11999/JEIT240447.LI Guoquan, CHENG Tao, GUO Yongcun, et al. Deep reinforcement learning based beamforming algorithm for IRS assisted cognitive radio system[J]. Journal of Electronics & Information Technology, 2025, 47(3): 657–665. doi: 10.11999/JEIT240447. [22] 薛青, 来东, 徐勇军, 等. 基于分布式联邦学习的毫米波通信系统波束配置方法[J]. 电子与信息学报, 2024, 46(1): 138–145. doi: 10.11999/JEIT221536.XUE Qing, LAI Dong, XU Yongjun, et al. Beam configuration for millimeter wave communication systems based on distributed federated learning[J]. Journal of Electronics & Information Technology, 2024, 46(1): 138–145. doi: 10.11999/JEIT221536. [23] DONG Hao, HUA Cunqing, LIU Lingya, et al. Intelligent reflecting surface-aided integrated terrestrial-satellite networks[J]. IEEE Transactions on Wireless Communications, 2023, 22(4): 2507–2522. doi: 10.1109/TWC.2022.3212049. [24] GUIDOTTI A and VANELLI‐CORALLI A. Clustering strategies for multicast precoding in multibeam satellite systems[J]. International Journal of Satellite Communications and Networking, 2020, 38(2): 85–104. doi: 10.1002/sat.1312. [25] SU Delong, LIU Lingya, XU Jing, et al. Multicast-aware user grouping for frame-based precoding in multibeam satellite systems[C]. ICC 2024 - IEEE International Conference on Communications, Denver, USA, 2024: 1855–1860. doi: 10.1109/ICC51166.2024.10622393. [26] YOO T and GOLDSMITH A. On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming[J]. IEEE Journal on Selected Areas in Communications, 2006, 24(3): 528–541. doi: 10.1109/JSAC.2005.862421. [27] ZHANG Shuo, JIA Min, WEI Yuming, et al. User scheduling for multicast transmission in high throughput satellite systems[J]. EURASIP Journal on Wireless Communications and Networking, 2020, 2020(1): 133. doi: 10.1186/s13638-020-01749-7. -
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