Tensor Array Signal Processing for Structured Sparse Sensing

ZHENG Hang; SHI Zhi-guo; WANG Yong; ZHOU Cheng-wei

doi:10.12263/DZXB.20240504

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Tensor Array Signal Processing for Structured Sparse Sensing

SURVEYS AND REVIEWS | 更新时间：2025-12-08

- Tensor Array Signal Processing for Structured Sparse Sensing
- ACTA ELECTRONICA SINICA Vol. 53, Issue 3, Pages: 1040-1062(2025)
- 作者机构：
  
  1.浙江大学信息与电子工程学院，浙江杭州 310027
  2.浙江省协同感知与自主无人系统重点实验室，浙江杭州 310015
  3.浙江大学金华研究院，浙江金华 321000
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(U21A20456;62271444);Natural Science Foundation of Zhejiang Province(LZ23F010007)
- DOI：10.12263/DZXB.20240504
  CLC： TN911;
- Received：02 June 2024，
  
  Revised：2024-11-13，
  
  Published：25 March 2025
- 稿件说明：
移动端阅览
郑航, 史治国, 王勇, 等. 面向结构化稀疏感知的张量阵列信号处理[J]. 电子学报, 2025, 53(03): 1040-1062.

ZHENG Hang, SHI Zhi-guo, WANG Yong, et al. Tensor Array Signal Processing for Structured Sparse Sensing[J]. Acta Electronica Sinica, 2025, 53(03): 1040-1062.
郑航, 史治国, 王勇, 等. 面向结构化稀疏感知的张量阵列信号处理[J]. 电子学报, 2025, 53(03): 1040-1062. DOI：10.12263/DZXB.20240504

ZHENG Hang, SHI Zhi-guo, WANG Yong, et al. Tensor Array Signal Processing for Structured Sparse Sensing[J]. Acta Electronica Sinica, 2025, 53(03): 1040-1062. DOI：10.12263/DZXB.20240504

摘要

随着新一代信息基础设施建设的持续推进，多维阵列信号处理在雷达、通信、遥感等领域发挥着越发关键的基础性作用.多维阵列信号涵盖了丰富的空域/时域/频域/极化等参数信息，蕴含着巨大的经济和社会价值.为了解决传统矢量/矩阵模型在表征多维阵列信号时存在的结构化信息损失问题，张量代数逐步成为多维信号特征提取和利用的有力数理工具.然而，随着信号维度的扩张，遵循奈奎斯特采样定理所获取的信号规模在张量空间以指数级别膨胀，而现有系统所能提供的算力资源却在逼近物理极限，造成计算过载、时延过长等问题的出现.针对这些问题，稀疏感知利用信号在物理空间的稀疏性实现欠奈奎斯特采样信号处理，其从一维到多维空间的拓展为大规模张量信号的高效处理提供了可能.同时，引入互质、嵌套等结构化稀疏感知模式，可从增广虚拟域信号处理的角度提升系统性能.因此，本文面向多维阵列信号特征的高经济性获取需求，以“理论基础—算法设计—鲁棒机理”为主线，介绍结构化稀疏阵列张量信号处理的新理论与新方法.本文介绍了稀疏张量信号处理的高阶统计处理理论，通过构建虚拟域张量模型并设计其对应的信源辨识能力优化策略，保障了多维虚拟域上的奈奎斯特匹配处理和欠定参数估计；在此理论基础上，围绕波达方向估计和波束成形这两个基本问题，介绍了基于虚拟域张量填充的稀疏阵列波达方向估计算法，充分利用全部的非连续多维虚拟域信息实现高精度、超分辨信源测向，并介绍了基于互质张量权重优化的稀疏阵列波束成形算法，实现波束方向图上的虚峰消除和主瓣尖锐化，提高了稀疏阵列的信号增强与抗干扰性能；在此基础上，从提高非理想条件下的稀疏张量信号处理鲁棒性角度出发，介绍了一种资源集约型张量化神经网络架构，克服了非理想张量统计模型失配带来的性能衰落问题，从数据驱动层面实现面向稀疏张量信号特征开展机器学习的高效性、鲁棒性.

Abstract

With the continuous construction of new information infrastructures

multi-dimensional array signal processing plays a fundamental role in the filed of radar

wireless communication

remote sensing and so on. Multidimensional ar

ray signals contain rich spatial/temporal/frequentiol/polarization parametric information

offering great economic and social values. To deal with the problem of structural information loss inherent in traditional vector/matrix models

the tensor algebra has been adopted to effectively retrieve multi-dimensional signal features. However

as the dimension of signals increases

the tensor signal volume following the Nyquist sampling theorem exponentially expands. Unfortunately

computation resources of the system are approaching the physical limit

resulting in computational overload and high latency. Concerning these issues

the sparse sensing theory has been developed to exploit the spatial sparsity of signals for sub-Nyquist processing. The extension from one-dimensional sparse sensing to multi-dimensional sparse sensing becomes a promising solution to efficient tensor signal processing. Meanwhile

by imposing structured sparse sensing paradigm such as coprime and nested sensing

the performance of the system can be enhanced via augmented coarray signal processing. Thus

to pursue the high economy of multi-dimensional array signal processing

this paper endeavors to the research on

Structured Sparse Tensor Signal Processing for Sensor Arrays. In particular

the paper introduces the statistical theory of sub-Nyquist tensor signals. By deriving the augmented coarray tensor model and devising the corresponding strategy of source identifiability enhancement

this theory facilitates Nyquist matching in the virtual domain and underdetermined parameter estimation. Based upon this theory

this paper introduces a coarray tensor completion algorithm for sparse array DOA estimation

exploiting the full information of the discontinuous virtual array to achieve high accuracy and resolution. Meanwhile

this paper introduces a coprime tensor weights optimization algorithm for sparse array beamforming

which yields a beampatten with a sharper mainlobe and lower sidelobes

and increases the output signal-to-inte

rference-plus-noise ratio. Furthermore

this paper introduces a resource-efficient tensorized neural network for robust sparse tensor signal processing

which compensates the performance deterioration for the model-driven methods in non-ideal conditions by efficiently learning tensor signal features.

关键词

Keywords

references

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