无线先验对多用户多天线预编码学习计算与能耗开销的影响

丛鹏宇; 韩圣千; 邓鸣宇; 刘胜杰; 杨晨阳; 沈嵩辉

doi:10.11999/JEIT260388

无线先验对多用户多天线预编码学习计算与能耗开销的影响

doi: 10.11999/JEIT260388 cstr: 32379.14.JEIT260388

1.
北京航空航天大学电子信息工程学院北京 100191
2.
中国移动通信有限公司研究院北京 100053

详细信息

作者简介:
丛鹏宇：男，博士生，研究方向为智能通信

韩圣千：男，副教授，研究方向为智能通信、移动通信等

邓鸣宇：男，博士生，研究方向为智能通信

刘胜杰：男，博士生，研究方向为智能通信

杨晨阳：女，教授，研究方向为智能通信、移动通信等

沈嵩辉：男，工程师，研究方向为移动通信物理层技术

计量
- 文章访问数: 35
- HTML全文浏览量: 17
- PDF下载量: 1
- 被引次数: 0
出版历程
- 修回日期: 2026-07-15
- 录用日期: 2026-07-15
- 网络出版日期: 2026-07-25

Impact of Wireless Priors on the Computation and Energy Cost of MU-MIMO Precoding Learning

1.
School of Electronic Information Engineering, Beihang University, Beijing 100191, China
2.
China Mobile Research Institute, Beijing 100053, China

摘要

摘要: 随着移动通信系统中天线阵列规模的持续增大，多用户多输入多输出(Multiuser Multi-Input Multi-Output, MU-MIMO)预编码在显著提高系统性能的同时，也带来了高计算复杂度与高能耗等挑战。本文针对MU-MIMO预编码策略学习问题，研究在神经网络结构设计中引入无线策略数学先验(简称“无线先验”)知识对深度学习计算和能耗的影响。为此，首先分析MU-MIMO预编码策略的多维联合置换等变性和不变性，在此基础上构建一种注意力图神经网络(Attention-based Graph Neural Network, AGNN)；然后，基于3GPP标准信道数据集开展仿真与硬件实测，对AGNN与传统数值算法和Transformer模型进行比较。研究结果表明，AGNN在频谱效率、计算复杂度和推理能耗方面均优于仅满足一维置换等变性的Transformer模型，表明充分利用无线先验对高效学习的重要影响。同时，随着天线规模与带宽的扩大，传统数值算法的计算复杂度和能耗增长速度明显高于性能增益；而AGNN能够在提高系统性能的同时，显著降低推理时间与推理能耗，表明融入无线先验的学习方法是未来6G预编码优化的有效技术路径。
- 6G /
- 预编码 /
- 无线先验 /
- 图神经网络 /
- 计算能耗
Abstract: Objective This paper studies the learning of downlink MU-MIMO (Multiuser Multi-Input Multi-Output) precoding policy from the perspective of computational complexity and energy consumption. Traditional numerical optimization achieves strong performance but incurs rapidly growing computational complexity with the number of base-station’s antennas and served users, leading to high inference latency and inference energy consumption. In recent years, deep learning has been widely used to reduce online computational cost, yet existing evaluations typically rely on training/inference time or FLOPs and lack direct energy/power measurements. More importantly, the computational cost of a deep model is tightly coupled with the network architecture, which should be designed to effectively exploit the prior knowledge of the precoding policy. The objective of this paper is thus to develop a network architecture that matches the multi-dimensional permutational properties of the policy, and to analyze how policy priors influence the complexity and energy through comprehensive hardware-based energy/power measurements and simulations. Methods We formulate the MU-MIMO precoding policy as a mapping from multi-user channel information to the optimal precoding matrix under a transmit power constraint. The optimal policy exhibits multi-dimensional joint permutation equivariance and invariance with respect to user indices, receive-antenna indices, and base-station antenna indices. To exploit this prior, we propose an Attention-based Graph Neural Network (AGNN) built on a hypergraph structure, whose update and aggregation procedures are designed to satisfy the required equivariance/invariance properties. An attention mechanism modeling inter-user interference is introduced to improve generalization to varying number of users. For broadband precoding, the input layer aggregates multi-subcarrier channel information into an expanded input representation. To quantify energy cost, we build a mixed CPU/GPU measurement framework that collects energy and power for GPU, CPU, and DRAM during training and inference. Simulations use 3GPP TR 38.901 UMa channel data with different antenna array sizes and bandwidth settings. We compare the proposed AGNN against numerical baselines (ZFBD+Greedy pairing) and two Transformer-based architectures, where only one-dimensional permutation properties are satisfied. Results and Discussions : The paper reveals two main findings. First, partial exploitation of policy priors leads to poor performance and high cost. In the MU-MISO scenario, the Transformer variants with one-dimensional permutation equivariance yield lower spectral efficiencies than the numerical baseline ZFBD+Greedy and much larger model sizes and inference FLOPs than AGNN. In contrast, AGNN, designed to match the multi-dimensional permutation properties, achieves higher spectral efficiency while reducing inference FLOPs by about one order of magnitude. Hardware measurements further show that AGNN reduces inference energy and power on both CPU and GPU. Second, in the MU-MIMO scenario with small- and large-scale settings, ZFBD+Greedy increases the system sum rate to 10.9 times, but raise inference FLOPs to 436.4 times, inference time to 20.8 times, and inference energy to 40.8 times. Conversely, AGNN increases the sum rate to 11.5 times while inference FLOPs rise to only 5.3 times; inference time and inference energy become dramatically smaller (0.03 times and 0.22 times, respectively). These results suggest that matching the precoding policy’s multi-dimensional permutation priors is an effective way to reduce the computational cost, including FLOPs, latency, and energy consumption, in large-scale 6G MU-MIMO systems. Conclusions This paper investigated how policy priors affect computational complexity and energy consumption in MU-MIMO precoding learning. By analyzing the multi-dimensional joint permutation equivariance/invariance properties of the optimal precoding policy, we designed an attention-based GNN (AGNN) that matches these properties. A hardware-aware measurement platform was built to obtain direct energy/power measurements for training and inference on CPU, GPU, and DRAM components. Simulations on 3GPP TR 38.901 channel datasets showed that Transformer architectures satisfying only one-dimensional permutation properties can lead to both inferior spectral efficiency and significantly higher computational/energy overhead. In contrast, AGNN achieves higher spectral efficiency while substantially reducing inference FLOPs, inference time, inference energy, and training complexity. As system size increases, traditional numerical methods incur rapidly growing energy costs relative to rate gains, whereas the proposed policy-prior learning method maintains low inference time and energy consumption. Overall, exploiting the prior knowledge of MU-MIMO precoding policy for network architecture design is a key enabler for energy- and complexity-efficient high-dimensional precoding optimization in future 6G networks.
- 6G /
- Precoding /
- Policy priors /
- Graph neural networks /
- Computational energy consumption

HTML全文

图 1 大规模MU-MIMO场景下的总计算能耗

下载: 全尺寸图片幻灯片

表 1 测试平台硬件设置

硬件组件	型号名称 × 数量	存储容量	TGP 或TDP	闲置功耗
GPU	NVIDIA GeForce RTX 4090 D GPU×1	24 GB (显存)	425 W	6.76 W
CPU	Intel Xeon Gold 5515+ CPU×1	—	165 W	34.11 W
DRAM	Samsung DDR5 R-ECC 32 GB 内存×2 SK Hynix DDR5 R-ECC 32 GB 内存×2	128 GB	30.5 W	5.31 W
注：全文各表中“—”表示该指标不适用。

下载: 导出CSV

表 2 GPU、CPU和DRAM能耗测试流程

1) 测试准备阶段
正式测量前终止所有非必需后台进程，独立启动两个命令行终端，分别运行NVSMI和Intel PCM，采样间隔100ms并保持连续采样。工具　开启后，服务器空闲运行10 分钟，使各硬件组件进入稳定的空闲水平(GPU和CPU均进入深度休眠)。此阶段数据不参与后续能耗计算。
2) 测量服务器闲置功耗
服务器继续保持空闲状态运行10分钟。该阶段内由NVSMI与Intel PCM采集的数据用于计算GPU、CPU和DRAM 的闲置功耗，计算结果　为10分钟内平均值。
3) 测量算法运行的能耗与功耗
启动PyCharm等待加载完毕，运行目标程序。为确保测量期间CPU和GPU稳定，先对所有样本执行一轮预热推理(数据不参与最终统　计)。程序记录算法起止时间戳，以划定功耗/能耗采样数据的统计区间。不同类型算法的测量方式如下：
● 传统数值算法：先把所有测试数据加载至DRAM，再记录预编码计算过程的起止时间戳。
● AI算法：先把数据加载至DRAM并构建网络模型；若在GPU上进行计算，则需再把数据和模型参数从DRAM迁移至显存。之后记录时　间戳，具体方式如下：
–训练阶段：记录模型整个训练周期的起止时间戳；
–推理阶段：测试样本需逐个输入网络，记录完成所有测试样本推理的起止时间戳。

下载: 导出CSV

表 3 不同场景下各神经网络的超参数

系统配置	$ N=32, 带宽51\mathrm{RB} $				$ N=128, 带宽273\mathrm{RB} $
MIMO技术	MU-MISO			MU-MIMO	MU-MIMO
学习算法	Transformer适配一/二	AGNN	MDGNN	AGNN	AGNN
网络规模	2*[2560]	5*[32]	5*[32]	4*[32]	6*[16]
批大小	256	256	256	64	64
学习率	0.0001	0.0001	0.0001	0.001	0.001
注1：网络规模m*[n]表示隐藏层数为m，隐藏表示数为n。注2：表中各模型超参数均基于不同场景下的实际训练收敛性能调优确定。

下载: 导出CSV

1 计算第$ k $个用户的子带等效信道

输入：第$ k $个用户在子带内$ C $个子载波上的信道矩阵$ {\mathbf{H}}_{k,c} $。
输出：第$ k $个用户的子带等效信道$ {\widetilde{\mathbf{H}}}_{k} $。
1. 计算子带信道相关矩阵　$ {\mathbf{R}}_{k}=1/C\displaystyle\sum \nolimits_{c=1}^{C}\mathbf{H}_{k,c}^{\text{H}}{\mathbf{H}}_{k,c}\in {\mathbb{C}}^{{{N}_{\text{T}}}\times {{N}_{\text{T}}}} $；
2. 对$ {\mathbf{R}}_{k} $进行特征分解$ {\mathbf{R}}_{k}={\mathbf{U}}_{k}{\mathbf{\Sigma }}_{k}\mathbf{U}_{k}^{\text{H}} $，得到特征值和特征　向量；
3. 从$ {\mathbf{\Sigma }}_{k} $中选取最大的$ {N}_{\text{R}} $个特征值$ {\sigma }_{i} $及对应的特征向量；
4. 计算等效信道矩阵$ {\widetilde{\mathbf{H}}}_{k}={\left[\begin{array}{ccc}\sqrt{{\sigma }_{1}}{\mathbf{u}}_{1} & \cdots & \sqrt{{\sigma }_{{{N}_{\text{R}}}}}{\mathbf{u}}_{{{N}_{\text{R}}}}\end{array}\right]}^{\text{H}} $

下载: 导出CSV

表 4 小规模MU-MISO场景下的频谱效率、训练和推理复杂度比较

预编码算法	ZFBD+Greedy	Transformer适配一	Transformer适配二	AGNN	MDGNN
频谱效率(bps/Hz)	24.6	17.0	18.2	25.8	17.6
推理FLOPs	6.7×10⁸	7.5×10⁹	5.6×10⁹	1.3×10⁷	2.6×10⁶
CPU推理时间 (ms)	320	21.3	14.5	4.02	2.61
GPU推理时间 (ms)	—	2.07	2.45	5.22	3.94
训练时间 (s)	—	2,715	1,186	970	839
模型参数量	—	1.1×10⁸	7.0×10⁷	2.5×10⁴	1.5×10⁴

下载: 导出CSV

表 5 小规模MU-MISO场景下训练与推理阶段的能耗与功耗比较

预编码算法	硬件组件	训练阶段		推理阶段(CPU)		推理阶段(GPU)
预编码算法	硬件组件	能耗 (J)	功耗 (W)	能耗 (mJ)	功耗 (W)	能耗 (mJ)	功耗 (W)
ZFBD+ Greedy	CPU	—	—	1.2×10⁴	36.4	—	—
	DRAM	—	—	1,750	5.46	—	—
	合计	—	—	1.3×10⁴	41.9	—	—
Transformer适配一	GPU	9.1×10⁵	334	—	—	537	259
	CPU	1.2×10⁵	44.5	2,715	127	151	73.1
	DRAM	1.6×10⁴	5.93	222	10.4	11.8	5.71
	合计	1.0×10⁶	384	2,937	138	700	338
Transformer适配二	GPU	4.0×10⁵	333	—	—	520	212
	CPU	5.5×10⁴	46.8	1,830	126	186	75.7
	DRAM	6,975	5.88	141	9.79	14.3	5.84
	合计	4.6×10⁵	386	1,972	136	719	294
MDGNN	GPU	4.4×10⁴	51.9	—	—	83.2	21.1
	CPU	6.0×10⁴	71.9	233	89.4	271.4	68.8
	DRAM	4,920	5.86	14.6	5.60	22.2	5.63
	合计	1.1×10⁵	130	247.8	95.0	377	95.6
AGNN	GPU	1.1×10⁵	109	—	—	130	24.8
	CPU	7.0×10⁴	72.1	373	92.9	345	66.0
	DRAM	5,618	5.79	22.2	5.53	29.0	5.56
	合计	1.8×10⁵	187	395	98.4	503	96.4

下载: 导出CSV

表 6 MU-MIMO场景下的频谱效率、训练和推理复杂度比较

系统规模	$ N=32, 带宽51\mathrm{RB} $	$ N=128, 带宽273\mathrm{RB} $
预编码算法	ZFBD+Greedy	ZFBD+Greedy	AGNN
频谱效率 (bps/Hz)	53.9	118	124
和速率 (Gbps)	1.08	11.8	12.4
推理FLOPs	9.9×10⁷	7.9×10⁹	1.9×10⁸
CPU推理时间 (ms)	444	9,431	124
GPU推理时间 (ms)	—	—	15.1
训练时间 (s)	—	—	3,331
模型参数量	—	—	1.1×10⁴

下载: 导出CSV

表 7 MU-MIMO场景下训练与推理阶段的能耗与功耗比较

预编码算法	硬件组件	训练阶段		推理阶段(CPU)		推理阶段(GPU)
预编码算法	硬件组件	能耗 (J)	功耗 (W)	能耗 (mJ)	功耗 (W)	能耗 (mJ)	功耗 (W)
小规模ZFBD+Greedy	CPU	—	—	2.2×10⁴	49.9	—	—
	DRAM	—	—	2,408	5.43	—	—
	合计	—	—	2.5×10⁴	55.4	—	—
大规模ZFBD+Greedy	CPU	—	—	8.9×10⁵	94.9	—	—
	DRAM	—	—	5.3×10⁴	5.64	—	—
	合计	—	—	9.5×10⁵	101	—	—
大规模 AGNN	GPU	9.0×10⁵	271	—	—	3,795	251
	CPU	2.3×10⁵	68.8	1.5×10⁴	117	1,060	70.2
	DRAM	2.1×10⁴	6.22	1,871	15.1	95.8	6.35
	合计	1.2×10⁶	346	1.6×10⁴	132	4,950	328

下载: 导出CSV

表 8 大规模场景下各算法相对于小规模场景ZFBD+Greedy的对比

预编码算法	ZFBD+Greedy	AGNN
和速率	10.9倍	11.5倍
推理FLOPs	79.0倍	1.89倍
推理时间	21.3倍	0.03倍
推理能耗	38.6倍	0.20倍

下载: 导出CSV

表 9 非理想信道下MU-MIMO场景的频谱效率、训练和推理复杂度比较

系统规模	$ N=32, 带宽51\mathrm{RB} $	$ N=128, 带宽273\mathrm{RB} $
预编码算法	ZFBD+Greedy	ZFBD+Greedy	AGNN
频谱效率 (bps/Hz)	44.6	81.6	90.9
和速率 (Gbps)	0.892	8.16	9.09
推理FLOPs	9.9×10⁷	7.9×10⁹	2.8×10⁸
CPU推理时间 (ms)	444	9,431	260
GPU推理时间 (ms)	—	—	15.1
训练时间 (s)	—	—	31.75
模型参数量	—	—	3.6×10⁵

下载: 导出CSV

表 10 非理想信道下MU-MIMO场景训练与推理阶段的能耗与功耗比较

预编码算法	硬件组件	训练阶段		推理阶段(CPU)		推理阶段(GPU)
预编码算法	硬件组件	能耗 (J)	功耗 (W)	能耗 (mJ)	功耗 (W)	能耗 (mJ)	功耗 (W)
小规模ZFBD+Greedy	CPU	—	—	2.2×10⁴	49.9	—	—
	DRAM	—	—	2,408	5.43	—	—
	合计	—	—	2.5×10⁴	55.4	—	—
大规模ZFBD+Greedy	CPU	—	—	8.9×10⁵	94.9	—	—
	DRAM	—	—	5.3×10⁴	5.64	—	—
	合计	—	—	9.5×10⁵	101	—	—
大规模 AGNN	GPU	6.0×10⁵	264	—	—	7,625	240
	CPU	2.0×10⁵	66.8	3.0×10⁴	113	2,125	68.4
	DRAM	1.5×10⁴	6.48	4120	16.1	215.5	6.79
	合计	1.2×10⁶	338	3.4×10⁴	129	9,966	315

下载: 导出CSV

表 11 非理想信道下大规模场景各算法相对于小规模场景ZFBD+Greedy的对比

预编码算法	ZFBD+Greedy	AGNN
和速率	9.1倍	10.2倍
推理FLOPs	79.0倍	2.83倍
推理时间	21.3倍	0.03倍
推理能耗	38.6倍	0.40倍

下载: 导出CSV

参考文献(20)

[1]	WANG Chengxiang, YOU Xiaohu, GAO Xiqi, et al. On the road to 6G: Visions, requirements, key technologies, and testbeds[J]. IEEE Communications Surveys & Tutorials, 2023, 25(2): 905–974. doi: 10.1109/COMST.2023.3249835.
[2]	沈璐瑶, 周星光, 许子乐, 等. 无蜂窝大规模MIMO系统中下行短包传输的叠加导频功率分配[J]. 电子与信息学报, 2026, 48(1): 57–66. doi: 10.11999/JEIT250655. SHEN Luyao, ZHOU Xingguang, XU Zile, et al. Power allocation for downlink short packet transmission with superimposed pilots in cell-free massive MIMO[J]. Journal of Electronics & Information Technology, 2026, 48(1): 57–66. doi: 10.11999/JEIT250655.
[3]	霍如, 吕科呈, 黄韬. 车联网中路径预测驱动的任务切分与计算资源分配方法[J]. 电子与信息学报, 2025, 47(10): 3658–3669. doi: 10.11999/JEIT250135. HUO Ru, LV Kecheng, and HUANG Tao. Task segmentation and computing resource allocation method driven by path prediction in internet of vehicles[J]. Journal of Electronics & Information Technology, 2025, 47(10): 3658–3669. doi: 10.11999/JEIT250135.
[4]	邢智童, 李云, 吴广富, 等. 智能反射面辅助的无线通信系统波束赋形及智能反射面相移技术综述[J]. 电子与信息学报, 2026, 48(2): 697–712. doi: 10.11999/JEIT250790. XING Zhitong, LI Yun, WU Guangfu, et al. A review on phase rotation and beamforming scheme for intelligent reflecting surface assisted wireless communication systems[J]. Journal of Electronics & Information Technology, 2026, 48(2): 697–712. doi: 10.11999/JEIT250790.
[5]	HUANG Zhaohui, WANG Zhaocheng, and HAN Zhu. Graph neural network empowered wireless communications: Fundamentals, state-of-the-art, challenges, and opportunities[J]. IEEE Wireless Communications, 2025, 32(5): 162–168. doi: 10.1109/MWC.002.2400327.
[6]	ZHAO Baichuan, GUO Jia, and YANG Chenyang. Understanding the performance of learning precoding policies with graph and convolutional neural networks[J]. IEEE Transactions on Communications, 2024, 72(9): 5657–5673. doi: 10.1109/TCOMM.2024.3388506.
[7]	LIU Shengjie, GUO Jia, and YANG Chenyang. Multidimensional graph neural networks for wireless communications[J]. IEEE Transactions on Wireless Communications, 2024, 23(4): 3057–3073. doi: 10.1109/TWC.2023.3305124.
[8]	DUAN Yuxuan, GUO Jia, and YANG Chenyang. Learning precoding in multi-user multi-antenna systems: Transformer or graph transformer?[J]. IEEE Transactions on Wireless Communications, 2026, 25: 6284–6300. doi: 10.1109/TWC.2025.3624290.
[9]	KASALAEE G, KARKAN A H, FRIGON J F, et al. Compression of site-specific deep neural networks for massive MIMO precoding[C]. 2025 IEEE International Conference on Machine Learning for Communication and Networking, Barcelona, Spain, 2025: 1–6. doi: 10.1109/ICMLCN64995.2025.11140523.
[10]	HAN Song, POOL J, TRAN J, et al. Learning both weights and connections for efficient neural networks[C]. NIPS'15: Proceedings of the 29th International Conference on Neural Information Processing Systems - Volume 1, Montreal, Canada, 2015: 1135–1143.
[11]	LI Chen, TSOURDOS A, and GUO Weisi. A transistor operations model for deep learning energy consumption scaling law[J]. IEEE Transactions on Artificial Intelligence, 2024, 5(1): 192–204. doi: 10.1109/TAI.2022.3229280.
[12]	VELIČKOVIĆ P, CASANOVA A, LIÒ P, et al. Graph attention networks[C]. 6th International Conference on Learning Representations ICLR 2018 Conference Track Proceedings, Vancouver, Canada, 2018. doi: 10.17863/CAM.48429. (查阅网上资料,未找到本条文献出版地信息,请确认).
[13]	GUO Jia and YANG Chenyang. A model-based GNN for learning precoding[J]. IEEE Transactions on Wireless Communications, 2024, 23(7): 6983–6999. doi: 10.1109/TWC.2023.3336911.
[14]	ZHANG Lin, HAN Shengqian, and YANG Chenyang. Gradient-driven graph neural networks for learning digital and hybrid precoder[J]. IEEE Transactions on Communications, 2026, 74: 706–722. doi: 10.1109/TCOMM.2025.3628767.
[15]	SUN Liang and MCKAY M R. Eigen-based transceivers for the MIMO broadcast channel with semi-orthogonal user selection[J]. IEEE Transactions on Signal Processing, 2010, 58(10): 5246–5261. doi: 10.1109/TSP.2010.2053709.
[16]	VASWANI A, SHAZEER N, PARMAR N, et al. Attention is all you need[C]. NIPS'17: Proceedings of the 31st International Conference on Neural Information Processing Systems, Long Beach, USA, 2017: 6000–6010.
[17]	3GPP. TR 138. 901 Study on channel model for frequencies from 0.5 to 100 GHz[S]. Cedex: ETSI, 2025.
[18]	3GPP. TS 38. 101-1 User Equipment (UE) radio transmission and reception; Part 1: Range 1 standalone[S]. Cedex: ETSI, 2025.
[19]	3GPP. TR 36. 873 Study on 3D channel model for LTE[S]. Cedex: ETSI, 2017. (查阅网上资料, 未找到本条文献年份信息, 请确认).
[20]	ZHU Fenghao, WANG Xinquan, HUANG Chongwen, et al. Robust beamforming for RIS-aided communications: Gradient-based manifold meta learning[J]. IEEE Transactions on Wireless Communications, 2024, 23(11): 15945–15956. doi: 10.1109/TWC.2024.3435023.