基于改进Kolmogorov-Arnold混合卷积神经网络的调制识别方法

郑庆河; 刘方霖; 余礼苏; 姜蔚蔚; 黄崇文; 李斌; 束锋

doi:10.11999/JEIT250161

基于改进Kolmogorov-Arnold混合卷积神经网络的调制识别方法

doi: 10.11999/JEIT250161 cstr: 32379.14.JEIT250161

郑庆河^1, ,,
刘方霖¹,
余礼苏²,
姜蔚蔚³,
黄崇文⁴,
李斌⁵,
束锋⁶

1.
山东管理学院智能工程学院济南 250357
2.
南昌大学信息工程学院南昌 330031
3.
北京邮电大学信息与通信工程学院北京 100876
4.
浙江大学信息与电子工程学院杭州 310058
5.
南京信息工程大学计算机学院南京 210044
6.
海南大学信息与通信工程学院海口 570228

基金项目: 国家重点研发计划(2018YFF01014304)，国家自然科学基金(62401070)，山东省重点研发计划(2024TSGC0055)，山东省自然科学基金(ZR2019ZD01, ZR2023QF125)，山东省高等学校青年创新团队计划(2024KJH005)

详细信息

作者简介:
郑庆河：男，副教授，研究方向为无线通信、认知无线电、机器学习、调制识别、信道估计

刘方霖：男，本科生，研究方向为无线通信、认知无线电、深度学习、调制识别

余礼苏：男，副教授，研究方向为射频光载无线通信、非正交多址接入、无人机通信、人工智能

姜蔚蔚：男，讲师，研究方向为卫星通信、无线通信、物联网、人工智能

黄崇文：男，教授，研究方向为6G无线通信、智能协同感知、智能天线

李斌：男，副教授，研究方向为物理层通信、边缘计算、无人机通信

束锋：男，教授，研究方向为智能通信、调制识别、深度学习、认知计算

通讯作者:
郑庆河　zqh@sdmu.edu.cn

中图分类号: TN929.5
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- 被引次数: 0
出版历程
- 收稿日期: 2025-03-17
- 修回日期: 2025-04-10
- 网络出版日期: 2025-04-28
- 刊出日期: 2025-08-27

An Improved Modulation Recognition Method Based on Hybrid Kolmogorov-Arnold Convolutional Neural Network

1.
School of Intelligent Engineering, Shandong Management University, Jinan 250357, China
2.
School of Information Engineering, Nanchang University, Nanchang 330031, China
3.
School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China
4.
School of Information and Electronic Engineering, Zhejiang University, Hangzhou 310058, China
5.
School of Computer Science, Nanjing University of Information Science and Technology, Nanjing 210044, China
6.
School of Information and Communication Engineering, Hainan University, Haikou 570228, China

Funds: The National Key R&D Program (2018YFF01014304), The National Natural Science Foundation of China (62401070), Shandong Provincial Key R&D Program (2024TSGC0055), Shandong Provincial Natural Science Foundation (ZR2019ZD01, ZR2023QF125), Shandong Provincial Youth Innovation Team Plan of Higher Education Institutions (2024KJH005)

摘要

摘要: 针对苛刻通信场景下调制方式识别精度低且泛化难的问题，该文提出一种改进Kolmogorov-Arnold混合卷积神经网络模型KA-CNN。首先，通过双树复小波包变换将信号分解至多维小波域，结合不同频率分量构建多尺度信号表征，促使神经网络模型学习各频率下的一致性特征；然后设计集成样条函数和非线性激活函数的深度学习结构，利用样条函数解决维度诅咒问题，增强周期性特征的持续学习能力；最后，采用Lipschitz正则化约束的多级网格训练，改善模型面对不同信号参数的适应性，增强跨通信场景的泛化能力。在公开数据集RadioML 2016.10a, RadioML 2018.01a和CSPB.ML.2023的实验表明，KA-CNN具有优异的调制识别精度，当信噪比在16 dB时能够取得90%以上的识别准确率。相较于其它深度学习方法，整体识别精度提升3%～10%，并在各种信噪比条件下具备更强的特征学习能力和泛化性。
- 调制识别 /
- 深度学习 /
- Kolmogorov-Arnold模型 /
- 卷积神经网络
Abstract: Objective With the rapid growth of communication devices and increasing complexity of electromagnetic environments, spectrum efficiency has become a critical performance metric for sixth-generation communication systems. Modulation recognition is an essential function of dynamic spectrum access, aiming to automatically identify the modulation scheme of received signals to enhance spectrum utilization. In practice, wireless signals are often affected by multipath propagation, interference, and noise, which pose challenges for accurate recognition. To address these issues, this study proposes a deep learning-based approach using an end-to-end model that eliminates manual feature extraction, mitigates limitations of handcrafted features, and improves recognition accuracy. By transferring general knowledge from signal classification to modulation recognition, a well-generalized method based on a hybrid Kolmogorov-Arnold Convolutional Neural Network (KA-CNN) is developed. This approach supports reliable communication in applications such as intelligent transportation, the Internet of Things (IoT), vehicular ad hoc networks, and satellite communication. Methods The proposed modulation recognition method first decomposes the signal into a multi-dimensional wavelet domain using a dual-tree complex wavelet packet transform. Different frequency components are then combined to construct a multi-scale signal representation, enabling the neural network to learn consistent features across frequencies. A deep learning structure, KA-CNN, is designed by integrating spline functions with nonlinear activation functions to enhance nonlinear fitting and continuous learning of periodic features. Spline functions are used to address the curse of dimensionality. To improve adaptability to varying signal parameters and enhance generalization across communication scenarios, multilevel grid training with Lipschitz regularization constraints is applied. In KA-CNN, the hybrid module transfers the characteristics of the spline function into convolution operations, which improves the model’s capacity to capture complex mappings between input signals and modulation schemes while retaining the efficiency of the Kolmogorov-Arnold network. This enhances both the expressive power and adaptability of deep learning models under complex communication conditions. Results and Discussions During the experimental phase, modulation recognition performance testing, ablation study, and comparative analysis are conducted on three publicly available datasets (RadioML 2016.10a, RadioML 2018.01a, and CSPB.ML.2023) to evaluate the performance of KA-CNN. Results show that KA-CNN achieves modulation recognition accuracies of 65.14%, 65.56%, and 78.40% on RadioML 2016.10a, RadioML 2018.01a, and CSPB.ML.2023, respectively (Figure 6). The main performance limitation arises in the classification of QPSK versus 8PSK, AM-DSB versus WBFM, and high-order QAM modulation types (Figure 7). Maximum differences in recognition accuracy of KA-CNN driven by different signal representations reach 2.04%, 3.46%, and 4.54% across the three datasets, demonstrating the effect of signal representation (Figure 8). The wavelet packet transform constructs a multi-scale time-frequency representation of signals that is insensitive to the maximum decomposition scale L and supports complementary learning of different modulation features. The hybrid Kolmogorov-Arnold convolutional module and the multi-dimensional perceptual cascade attention mechanism play key roles in enhancing modulation recognition accuracy, particularly under relatively high Signal-To-Noise Ratio (SNR) conditions (Figure 9). Additionally, finer grids and higher decomposition orders improve the model’s ability to extract discriminative signal features, thereby increasing recognition accuracy (Figure 10). Finally, a comparative evaluation against several deep learning models, including GGCNN, Transformer, PR-LSTM, and MobileViT, confirms the superior performance of KA-CNN (Figure 11). Conclusions This study proposes a hybrid KA-CNN to address the reduced modulation recognition accuracy caused by noise and parameter variation, as well as the limited generalization across communication scenarios in existing deep learning models. By integrating spline functions with nonlinear activation functions, KA-CNN mitigates the curse of dimensionality and improves its capacity for continuous learning of periodic features. A dual-tree complex wavelet packet transform is used to construct a multi-scale signal representation, enabling the model to extract consistent features across frequencies. The model is trained using multilevel grids with Lipschitz regularization constraints to enhance adaptability to varying signal parameters and improve generalization. Experimental results on three public datasets demonstrate that KA-CNN improves modulation recognition accuracy and exhibits robust generalization, particularly under low SNRs.
- Modulation recognition /
- Deep learning /
- Kolmogorov-Arnold model /
- Convolutional neural network

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图 1 通信系统模型

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图 2 基于KA-CNN的调制识别整体框架

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图 3 信号多尺度时频表征构建过程

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图 4 KA-CNN的非线性变换示意图

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图 5 用于捕获空间、通道和频率信息的多维感知层结构

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图 6 不同信噪比下的调制识别准确率

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图 7 典型信噪比下的调制识别混淆矩阵

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图 8 不同信号表征下的调制识别准确率

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图 9 不同模块组合下的调制识别准确率

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图 10 不同参数下的调制识别准确率

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图 11 不同模型的调制识别性能对比

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表 1 信号模型参数

参数类型	RadioML 2016.10a	RadioML 2018.01a	CSPB.ML.2023
符号率偏移(kHz)	0.1～0.4	0.1～0.4	0.1～0.6
频率偏移(kHz)	0～0.01	0.0001～0.01	–0.2～0.2
相位偏移	0～0.01×2π	0.0001～0.01×2π	–0.1～0.1×2π
时钟误差	0～0.02	0～0.02	0～0.25
采样点数	2×128	2×1024	2×128
信噪比(dB)	–20:2:18	–20:2:30	2～20
噪声类型	加性高斯白噪声	加性高斯白噪声	加性高斯白噪声
信道环境	莱斯+瑞利	莱斯+瑞利	莱斯+瑞利
调制类型	11种	24种	9种
样本数量	2.2×10⁶	2.56×10⁷	1.2×10⁶(非重叠)

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表 2 训练过程的超参数

数据集	分解尺度L	迭代周期	批量大小$ \varOmega $	学习率	惩罚因子$ \lambda $	网格大小G	样条阶数D	丢弃率$ \rho $
RadioML 2016.10a	3	80	64	0.001	0.0001	5	3	0.2
RadioML 2018.01a	4	100	128	0.0001	0.0001	6	4	0.3
CSPB.ML.2023	3	100	64	0.0001	0.00001	5	3	0.2

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