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
- 收稿日期: 2025-09-02
- 修回日期: 2025-11-20
- 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

Funds: The National Natural Science Foundation of China (62331027)

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。该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3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 and designing effective dictionary and measurement matrices, compressed sensing enables reconstruction below the Nyquist sampling rate, making it suitable for resource-constrained environments; (2)Smaller pilot overhead: With sparse prior information and optimized observation design, compressed sensing reduces pilot overhead compared with traditional schemes. This saving releases spectrum resources and improves transmission efficiency; (3)Higher signal processing efficiency: Compressed sensing enhances channel estimation performance by approximately 3$ \sim $5 dB under the same data volume and achieves linear computational complexity, which is markedly lower than that of conventional super-linear approaches. Progress Between 2006 and 2009, compressed sensing progressed rapidly. Candès established the theoretical basis by converting zero-norm sparsity into a convex one-norm formulation under the Restricted Isometry Property (RIP). Aharon et al. then introduced dictionary matrices to strengthen sparse representation, and Needell et al. applied greedy algorithms to speed up reconstruction. From 2010 to 2020, research shifted toward engineering application and algorithm refinement. Wu et al. proposed more robust recovery strategies to improve adaptability, and Zayyani et al. later advanced AI-based dictionary learning. Since 2020, compressed sensing has integrated with deep learning for data-driven sparse modelling and reconstruction. Liu’s work in Integrated Sensing-And-Communication (ISAC) systems demonstrates this trend and supports deployment in next-generation communication networks. Conclusion This paper reviews compressed sensing for efficient receiving and processing of communication signal across three dimensions: current progress, key technical challenges, and future directions. It highlights three main research pathways, including dictionary matrix design, measurement matrix development, and reconstruction strategies. The review also shows that compressed sensing is moving toward greater adaptiveness, lightweight design, and intelligence. Current challenges are also summarized, including high computational cost, limited adaptability, and reduced performance under non-ideal conditions. These observations provide guidance for further study. Prospects (1)Research on relaxed sparse condition: Existing sparsity assumptions remain strict and constrain the use of compressed sensing in high-dimensional or non-stationary scenarios where ideal sparse representations are difficult to obtain. Loosening sparse requirements is therefore essential. Present work explores adaptive dictionary learning, structured sparse priors, and neural-network-driven relaxation, yet issues persist, such as dependence on prior assumptions, insufficient interpretability, and lack of theoretical convergence. Future work may refine optimization objectives, develop neural models with clear mathematical interpretation, and establish sparse representation methods that do not rely on rigid sparsity priors. (2)Research on algorithm complexity: Further complexity reduction is required in non-stationary time-varying channels, high-dimensional processing, and long-sequence reconstruction. Promising directions include pre-trained dictionary models, deep-learning-based structured measurement matrices, and robust deep reconstruction networks. (3)Research on algorithm adaptability: Practical systems face noise, spectrum fragmentation, fading, and multipath propagation, with stronger effects in cognitive radio and integrated sensing applications. Adaptive strategies should therefore be prioritized. Possible solutions include dynamic sliding-window modelling or optimized regularization for adaptive dictionaries, structured measurement matrices with tunable parameters, and semi-supervised reconstruction algorithms. (4)Research on non-cooperative user detection: Spectrum scarcity heightens the need for efficient sensing to manage uncoordinated users and prevent high-frequency occupancy. Future research may integrate deep learning with statistical models or embed time-frequency information in online dictionary learning to enhance generalization. Multi-objective design of adaptive measurement matrices may further support reliable detection of non-cooperative users.
- Compressed sensing /
- Dictionary learning /
- Measurement matrix /
- Signal reconstruction

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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

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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
${\boldsymbol{\varPhi}} $	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
$ {\boldsymbol{\varTheta}} $	$ {\boldsymbol{\varTheta}} = {\boldsymbol{\varPhi}}{\boldsymbol{D}} $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

字典类型	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

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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