Fourth-Order Sparse Array Design From a Sum-Difference Co-Array Perspective

Hua Chen; Haodong Guo; Wei Liu; Qing Shen; Gang Wang; Hing Cheung So

doi:10.1109/TSP.2025.3575079

Fourth-Order Sparse Array Design From a Sum-Difference Co-Array Perspective

Hua Chen^*, Haodong Guo, Wei Liu, Qing Shen, Gang Wang, Hing Cheung So

^*Corresponding author for this work

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

4 Citations (Scopus)

Abstract

Sparse arrays designed based on fourth-order difference co-array (DCA) can achieve significantly higher uniform degrees-of-freedom (uDOFs). However, most existing fourth-order sparse arrays do not fully utilize the properties of the second-order sum co-array (SCA) that is also closely related to the fourth-order DCA. In this paper, a fourth-order sparse array design scheme from the sum-difference co-array perspective is proposed, which can be generated by two arbitrary arrays called generator arrays. Once the two generator arrays are determined, all sensor positions can be obtained with a closed-form expression. If the second-order SCA and DCA of the generator arrays have long consecutive segments without holes, the derived sparse array obtained through this scheme can achieve a large number of uDOFs. Besides, other characteristics of the generator arrays can also be inherited, such as robustness against mutual coupling or sensor failures. Simulation results are provided to demonstrate the performance of the proposed design in different applications. © 2025 IEEE.

Original language	English
Pages (from-to)	2243-2254
Number of pages	12
Journal	IEEE Transactions on Signal Processing
Volume	73
Online published	4 Jun 2025
DOIs	https://doi.org/10.1109/TSP.2025.3575079
Publication status	Published - 2025

Funding

This work was supported in part by Zhejiang Provincial Natural Science Foundation of China under Grant LY23F010003; in part by “Pioneer” and “Leading Goose” R&D Program of Zhejiang Province under Grant 2024C01105; in part by the National Natural Science Foundation of China under Grant U24A20217, Grant 62222109, and Grant 62001256; in part by U.K. Engineering and Physical Sciences Research Council (EPSRC) under Grant EP/V009419/2; and in part by China Scholarship Council under Grant 202408330215.

Research Keywords

Mutual coupling
Sensor arrays
Generators
Robustness
Vectors
Direction-of-arrival estimation
Estimation
Array signal processing
Couplings
Training
Sparse arrays
fourth-order difference co-array
sum-difference analysis
direction-of-arrival estimation

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title = "Fourth-Order Sparse Array Design From a Sum-Difference Co-Array Perspective",

abstract = "Sparse arrays designed based on fourth-order difference co-array (DCA) can achieve significantly higher uniform degrees-of-freedom (uDOFs). However, most existing fourth-order sparse arrays do not fully utilize the properties of the second-order sum co-array (SCA) that is also closely related to the fourth-order DCA. In this paper, a fourth-order sparse array design scheme from the sum-difference co-array perspective is proposed, which can be generated by two arbitrary arrays called generator arrays. Once the two generator arrays are determined, all sensor positions can be obtained with a closed-form expression. If the second-order SCA and DCA of the generator arrays have long consecutive segments without holes, the derived sparse array obtained through this scheme can achieve a large number of uDOFs. Besides, other characteristics of the generator arrays can also be inherited, such as robustness against mutual coupling or sensor failures. Simulation results are provided to demonstrate the performance of the proposed design in different applications. {\textcopyright} 2025 IEEE.",

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author = "Hua Chen and Haodong Guo and Wei Liu and Qing Shen and Gang Wang and So, {Hing Cheung}",

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T1 - Fourth-Order Sparse Array Design From a Sum-Difference Co-Array Perspective

AU - Chen, Hua

AU - Guo, Haodong

AU - Liu, Wei

AU - Shen, Qing

AU - Wang, Gang

AU - So, Hing Cheung

PY - 2025

Y1 - 2025

N2 - Sparse arrays designed based on fourth-order difference co-array (DCA) can achieve significantly higher uniform degrees-of-freedom (uDOFs). However, most existing fourth-order sparse arrays do not fully utilize the properties of the second-order sum co-array (SCA) that is also closely related to the fourth-order DCA. In this paper, a fourth-order sparse array design scheme from the sum-difference co-array perspective is proposed, which can be generated by two arbitrary arrays called generator arrays. Once the two generator arrays are determined, all sensor positions can be obtained with a closed-form expression. If the second-order SCA and DCA of the generator arrays have long consecutive segments without holes, the derived sparse array obtained through this scheme can achieve a large number of uDOFs. Besides, other characteristics of the generator arrays can also be inherited, such as robustness against mutual coupling or sensor failures. Simulation results are provided to demonstrate the performance of the proposed design in different applications. © 2025 IEEE.

AB - Sparse arrays designed based on fourth-order difference co-array (DCA) can achieve significantly higher uniform degrees-of-freedom (uDOFs). However, most existing fourth-order sparse arrays do not fully utilize the properties of the second-order sum co-array (SCA) that is also closely related to the fourth-order DCA. In this paper, a fourth-order sparse array design scheme from the sum-difference co-array perspective is proposed, which can be generated by two arbitrary arrays called generator arrays. Once the two generator arrays are determined, all sensor positions can be obtained with a closed-form expression. If the second-order SCA and DCA of the generator arrays have long consecutive segments without holes, the derived sparse array obtained through this scheme can achieve a large number of uDOFs. Besides, other characteristics of the generator arrays can also be inherited, such as robustness against mutual coupling or sensor failures. Simulation results are provided to demonstrate the performance of the proposed design in different applications. © 2025 IEEE.

KW - Mutual coupling

KW - Sensor arrays

KW - Generators

KW - Robustness

KW - Vectors

KW - Direction-of-arrival estimation

KW - Estimation

KW - Array signal processing

KW - Couplings

KW - Training

KW - Sparse arrays

KW - fourth-order difference co-array

KW - sum-difference analysis

KW - direction-of-arrival estimation

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DO - 10.1109/TSP.2025.3575079

M3 - RGC 21 - Publication in refereed journal

SN - 1053-587X

VL - 73

SP - 2243

EP - 2254

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

ER -

Fourth-Order Sparse Array Design From a Sum-Difference Co-Array Perspective

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