面向通信信号高效接收处理的压缩感知技术综述

程伊婷; 董涛; 苏昱玮; 文霄杰; 杨陶隽; 李逸博

doi:10.11999/JEIT250855

面向通信信号高效接收处理的压缩感知技术综述

doi: 10.11999/JEIT250855 cstr: 32379.14.JEIT250855

程伊婷^{1, 2, 3},
董涛^{1, 2, 3, ,},
苏昱玮^{1, 2, 3},
文霄杰^{1, 2, 3},
杨陶隽^{1, 2, 3},
李逸博^{2, 3}

1.
空间信息体系与融合应用全国重点实验室北京 100095
2.
北京卫星信息工程研究所北京 100095
3.
航天恒星科技有限公司北京 100095

基金项目: 国家自然科学基金62331027

详细信息

作者简介:
程伊婷：女，硕士生，研究方向为卫星通信信号接收处理等

董涛：男，博士，研究员，研究方向为卫星通信网络、卫星通信信号处理等

苏昱玮：男，博士，高级工程师，研究方向为卫星通信与信号处理等

文霄杰：女，博士，研究员，研究方向为卫星通信、移动通信等

杨陶隽：男，博士生，研究方向为卫星通信与信号处理等

李逸博：男，硕士，工程师，研究方向为卫星通信信道设备研制等

通讯作者:
董涛　dongtaoandy@163.com

中图分类号: TN911.7
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- 被引次数: 0
出版历程
- 修回日期: 2025-11-21
- 录用日期: 2025-11-21
- 网络出版日期: 2025-11-28

A Review of Compressed Sensing Technology for Efficient Receiving and Processing of Communication Signal

CHENG Yiting^{1, 2, 3},
DONG Tao^{1, 2, 3
, ,},
SU Yuwei^{1, 2, 3},
WEN Xiaojie^{1, 2, 3},
YANG Taojun^{1, 2, 3},
LI Yibo^{2, 3}

1.
State Key Laboratory of Space Information System and Integrated Application, Beijing 100095, China
2.
Beijing Institute of Satellite Information Engineering, Beijing 100095, China
3.
Space Star Technology Co., Ltd., Beijing 100095, China

摘要

摘要: 压缩感知凭借其突破奈奎斯特采样定理限制、实现超低采样率的高质量信号处理与重构的优势，成为通信信号高效接收处理的研究热点。本文依据压缩感知原理，按照字典矩阵设计、测量矩阵设计和信号重构三个主要研究方向对技术发展脉络进行了梳理，提出了当前压缩感知技术研究面临的挑战。基于现阶段工程应用面临的问题，对压缩感知技术发展趋势进行展望。
- 压缩感知 /
- 字典矩阵 /
- 测量矩阵 /
- 信号重构
Abstract: Significance ① Lower data acquisition and storage costs: By exploiting signal sparsity, designing dictionary and measurement matrices, compressed sensing enables signal reconstruction below the Nyquist rate, making it valuable in resource-constrained environments; ② Smaller pilot overhead: Through sparse prior information and intelligent observation design, compressed sensing leverages pilot overhead compared to traditional technologies. This reduction saves spectrum resources, improving spectrum transmission efficiency; ③ Higher signal processing efficiency: Compressed sensing improves channel estimation performance by 3–5 dB under equivalent data volume, and achieve linear computational complexity markedly lower than traditional super-linear approaches. Progress From 2006 to 2009, compressed sensing matured rapidly: Candès and others established its theoretical foundation by reformulating zero-norm sparsity into a convex one-norm problem under the Restricted Isometry Property (RIP). Furthermore, Aharon introduced dictionary matrices to enhance sparse representation. Moreover, Needell applied greedy algorithms to accelerate reconstruction; Between 2010 and 2020, the focus shifted to practical deployment and algorithmic refinement: Wu proposed robust recovery to enhance algorithm adaptability. Then, Zayyani developed AI-driven dictionary learning; Since 2020, compressed sensing has fused with deep learning for data-driven sparse modelling and reconstruction, notably with Liu’s work in integrated sensing-and-communication (ISAC) systems, driving its adoption in future communication networks. Conclusion This paper analyzes compressed sensing methods for efficient receiving and processing of communication signal from three aspects: status review, technical challenges, and future outlook. It identifies three research directions: dictionary matrix design, measurement matrix design, and signal-reconstruction techniques. After reviewing mainstream approaches, this paper argues that compressed sensing is evolving toward adaptiveness, lightweight design and intelligence. This paper also analyses current challenges: high computational complexity, limited adaptability and degraded performance under non-ideal algorithm-complexity reduction, enhanced adaptability and non-cooperative user detection, offering guidance for future research. Prospects ① Research on Relaxed Sparse Condition: The sparsity constraints in current compressed sensing theory is strict, greatly limiting its application in scenarios such as high-dimensional data and non-stationary signals that lack ideal sparse representations. Therefore, loosening sparse conditions become a core issue. Existing research primarily focuses on adaptive dictionary learning, introducing structured sparse priors, and using neural networks to loosen sparse conditions. However, these methods still have limitations, such as excessive dependence on prior model assumptions, poor interpretability of neural networks, and lack of strict theoretical convergence guarantees. Future research should focus on three aspects: improve optimization models and objective functions, research deep neural network models with clear mathematical interpretations, design sparse representation methods without strict sparse priors. ② Research on Algorithm Complexity: Current compressed sensing techniques need to further reduce algorithm complexity while ensuring performance, especially in complex applications such as non-stationary time-varying channels, high-dimensional signal processing, and long-sequence response signal processing. Future research should focus on three aspects: introduce pre-trained models in dictionary learning, generate more general structured measurement matrices with deep learning, establish robust deep reconstruction networks. ③ Research on Algorithm Adaptability: In practical scenarios, noise interference, frequency spectrum discontinuity, channel fading, and multipath effects are unavoidable. Especially, the impact of non-ideal channels is more pronounced in fields such as cognitive radio and integrated communication sensing. There is an urgent need to study adaptive algorithms to handle dynamic channel changes. Future research should focus on three aspects: introduce a dynamic sliding window or optimize regularization constraints to design adaptive dictionary matrices; design structured measurement matrices with updating parameters, or design adaptive measurement matrices based on statistical analysis; introduce semi-supervised learning algorithms to design adaptive reconstruction algorithms. ④ Research on Non-cooperative User Detection: As spectrum resources become increasingly scarce, there is an urgent need for efficient spectrum sensing techniques to solve the problem of non-cooperative user detection and avoid high-frequency point occupation, enabling dynamic and efficient sharing of spectrum resources. Future research should focus on two aspects: combine deep learning and statistical model or introduce time-frequency domain information in online dictionary learning algorithm to improve generalization ability for non-cooperative user detection; research multi-objective optimization for adaptive measurement matrices to improve generalization ability for non- cooperative user detection.
- Compressed Sensing /
- Dictionary learning /
- Measurement matrix /
- Signal reconstruction

HTML全文

图 1 面向通信信号高效接收处理的压缩感知技术发展历程图

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图 2 压缩感知技术结构框图

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图 3 固定正交基字典矩阵设计算法流程图

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图 4 固定冗余字典矩阵设计算法流程图

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图 5 自适应字典矩阵设计算法流程图

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图 6 随机测量矩阵设计算法流程图

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图 7 结构化测量矩阵设计算法流程图

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图 8 自适应测量矩阵设计算法流程图

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表 1 文献涉及符号阐释表

符号	解释
Φ	测量矩阵
X	需要恢复的目标原始信号
x	需要恢复的目标原始信号样本
Y	接收端测得的测量数据
y	接收端测得的测量数据样本
P	样本数
N	目标原始信号长度
M	测量数据长度
D	字典矩阵
A	目标原始信号 X 对应的稀疏向量
a	每一目标原始信号样本对应的稀疏向量
K	字典原子数
s	稀疏度
θ	Θ = ΦD传感矩阵
λ	稀疏表示变换产生的冗余噪声
i, j	矩阵索引号

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表 2 主流固定字典类型及特性表述表

字典类型表	表述
傅里叶基	由正弦和余弦函数组成，适用于平稳信号
离散余弦变换基	傅里叶基的实数对称形式，适用于具有平滑区域的信号
小波基	通过母小波的缩放和平移生成，适用于非平稳信号

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表 3 不同测量矩阵的计算复杂度与应用场景说明表

测量矩阵类型	计算复杂度	应用场景
随机测量矩阵	O(MN)	适用于对信号先验信息了解较少，且计算资源相对充足的场景
结构化测量矩阵	O(N) ~ O(N²)	对于计算资源有限制，且信号稀疏结构有一定的预测性场景中应用广泛
自适应测量矩阵	> O(N²)	信号特征复杂多变时，对重构精度要求高的场景中表现出色

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