DOA Estimation of Regularization Backtracking Algorithms Based on QR Decomposition

ZHANG Ningning, ZHANG Jiao

PDF(2669 KB)
PDF(2669 KB)
Journal of Shanxi University(Natural Science Edition) ›› 2025, Vol. 48 ›› Issue (3) : 565-577. DOI: 10.13451/j.sxu.ns.2024034
Physics

DOA Estimation of Regularization Backtracking Algorithms Based on QR Decomposition

Author information +
History +

Abstract

A matching pursuit algorithm for regularization backtracking based on QR decomposition (QR-RBMP) is proposed in this paper to solve the problems of low precision of directional of arrival (DOA) estimation in the cases of low signal noise ratio (SNR), small snapshot and coherent signals. Firstly, the algorithm is performed on sensing matrix by QR decomposition to increase the independence of the sensing matrix. Then, the regularization idea and backtracking mechanism are used to optimize matching pursuit algorithm to improve the signal reconstruction precision. The regularization idea carries out secondary screening on the atoms initially selected by the matching tracking algorithm, and selects the most relevant atoms with the largest energy. The backtracking idea carries out secondary screening on the atoms selected by the regularization, deletes the incorrect atoms, improves the correctness of the selected atoms, and thus improves the reconstruction accuracy of the matching tracking algorithm. Finally, we obtain the reconstructed signal. The position of the non-zero element of the signal is the result of DOA estimation. Through a series of simulation experiments, the proposed algorithm is compared with MUSIC algorithm, regularized orthogonal matching pursuit algorithm (ROMP), subspace tracking algorithm, SP algorithm without Square Root (ISP) and energy sorting based backtracking regularized matching pursuit algorithm (ESBRMP) based on RMSE and POR. The results show that the proposed algorithm reduces the RMSE by 42% and improves the POR by 8% compared with the existing optimal methods under the same conditions.

Key words

DOA estimation / nested array / matrix decomposition / regularization idea / backtracking mechanism / compressed sensing

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations
ZHANG Ningning , ZHANG Jiao. DOA Estimation of Regularization Backtracking Algorithms Based on QR Decomposition. Journal of Shanxi University(Natural Science Edition). 2025, 48(3): 565-577 https://doi.org/10.13451/j.sxu.ns.2024034

References

List( Publishing order | Descend order by publishing year | Descend order by cited within ) Chart analysis
1
HU N, YE Z F, XU X, et al. DOA Estimation for Sparse Array via Sparse Signal Reconstruction[J]. IEEE Trans Aerosp Electron Syst, 2013, 49(2): 760-773. DOI: 10.1109/TAES.2013.6494379 .
本文引用 [1]
2
KRIM H, VIBERG M. Two Decades of Array Signal Processing Research: The Parametric Approach[J]. IEEE Signal Process Mag, 1996, 13(4): 67-94. DOI: 10.1109/79.526899 .
本文引用 [1]
3
SCHMIDT R. Multiple Emitter Location and Signal Parameter Estimation[J]. IEEE Trans Anntenas Propag, 1986, 34(3): 276-280. DOI: 10.1109/TAP.1986.1143830 .
本文引用 [1]
4
ROY R, KAILATH T. ESPRIT-estimation of Signal Parameters via Rotational Invariance Techniques[J]. IEEE Trans Acoust Speech Signal Process, 1989, 37(7): 984-995. DOI: 10.1109/29.32276 .
本文引用 [1]
5
STOICA P, NEHORAI A. Performance Study of Conditional and Unconditional Direction-of-arrival Estimation[J]. IEEE Trans Acoust Speech Signal Process, 1990, 38(10): 1783-1795. DOI: 10.1109/29.60109 .
本文引用 [1]
6
TSAKALIDES P, NIKIAS C L. Maximum Likelihood Localization of Sources in Noise Modeled as a Stable Process[J]. IEEE Trans Signal Process, 1995, 43(11): 2700-2713. DOI: 10.1109/78.482119 .
7
OTTERSTEN B, VIBERG M, STOICA P, et al. Exact and Large Sample Maximum Likelihood Techniques for Parameter Estimation and Detection in Array Processing[M]//HAYKIN S, LITVA J, SHEPHERD T J. Radar Array Processing. Berlin, Heidelberg: Springer, 1993: 99-151. DOI: 10.1007/978-3-642-77347-1_4 .
本文引用 [1]
8
HAMZA R, BUCKLEY K. Second-order Statistical Analysis of Totally Weighted Subspace Fitting Methods[J]. IEEE Trans Signal Process, 1994, 42(9): 2520-2524. DOI: 10.1109/78.317877 .
本文引用 [1]
9
ÇALıK S K. UAV Path Planning with Multiagent Ant Colony System Approach[C]//2016 24th Signal Processing and Communication Application Conference (SIU). Zonguldak, Turkey: IEEE, 2016: 1409-1412. DOI: 10.1109/SIU.2016.7496013 .
本文引用 [1]
10
WAGNER M, PARK Y, GERSTOFT P. Gridless DOA Estimation and Root-MUSIC for Non-uniform Linear Arrays[J]. IEEE Trans Signal Process, 2021, 69: 2144-2157. DOI: 10.1109/TSP.2021.3068353 .
本文引用 [1]
11
TOTA R, HOSSAIN M S. Multiple Near-field Sources Localization by Optimal Beamformer Using Minimum Norm Method[C]//2021 International Conference on Electronics, Communications and Information Technology (ICECIT). Khulna, Bangladesh: IEEE, 2021: 1-4. DOI: 10.1109/ICECIT54077.2021.9641373 .
本文引用 [1]
12
QI B B, LI W. An Improved Multiple-toeplitz Matrices Reconstruction Algorithm for DOA Estimation of Coherent Signals[J]. Radioengineering, 2021, 30(3): 532-539. DOI: 10.13164/re.2021.0532 .
本文引用 [1]
13
DONOHO D L. Compressed Sensing[J]. IEEE Trans Inf Theory, 2006, 52(4): 1289-1306. DOI: 10.1109/TIT.2006.871582 .
本文引用 [2]
14
WANG H B. Compressed Sensing: Theory and Applications[J]. J Phys: Conf Ser, 2023, 2419(1): 012042. DOI: 10.1088/1742-6596/2419/1/012042 .
本文引用 [1]
15
MALLOY M L, NOWAK R D. Near-optimal Adaptive Compressed Sensing[J]. IEEE Trans Inf Theory, 2014, 60(7): 4001-4012. DOI: 10.1109/TIT.2014.2321552 .
本文引用 [1]
16
陈健, 庄耀宇, 杨丹, 等. 基于FPGA的改进的排序QR分解实现[J]. 湖南大学学报(自然科学版), 2022, 49(10): 8-16. DOI: 10.16339/j.cnki.hdxbzkb.2022351 .
CHEN J, ZHUANG Y Y, YANG D, et al. Implementation of Improved Sorted QR Decomposition on FPGA[J]. J Hunan Univ Nat Sci, 2022, 49(10): 8-16. DOI: 10.16339/j.cnki.hdxbzkb.2022351 .
本文引用 [1]
17
CANDES E J, ROMBERG J, TAO T. Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information[J]. IEEE Trans Inf Theory, 2006, 52(2): 489-509. DOI: 10.1109/TIT.2005.862083 .
本文引用 [1]
18
LI Y Q, WANG J. Time-frequency Analysis of Seismic Data Based on Basis Pursuit[C]//2014 12th International Conference on Signal Processing (ICSP). Hangzhou, China: IEEE, 2014: 175-179. DOI: 10.1109/ICOSP.2014.7014992 .
本文引用 [1]
19
TROPP J A, GILBERT A C. Signal Recovery from Random Measurements via Orthogonal Matching Pursuit[J]. IEEE Trans Inf Theory, 2007, 53(12): 4655-4666. DOI: 10.1109/TIT.2007.909108 .
本文引用 [1]
20
NEEDELL D, VERSHYNIN R. Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit[J]. Found Comput Math, 2009, 9(3): 317-334. DOI: 10.1007/s10208-008-9031-3 .
本文引用 [1]
21
DAI W, MILENKOVIC O. Subspace Pursuit for Compressive Sensing Signal Reconstruction[J]. IEEE Trans Inf Theory, 2009, 55(5): 2230-2249. DOI: 10.1109/TIT.2009.2016006 .
本文引用 [1]
22
DO T T, GAN L, NGUYEN N, et al. Sparsity Adaptive Matching Pursuit Algorithm for Practical Compressed Sensing[C]//2008 42nd Asilomar Conference on Signals, Systems and Computers. Pacific Grove, CA, USA: IEEE, 2008: 581-587. DOI: 10.1109/ACSSC.2008.5074472 .
本文引用 [1]
23
NEEDELL D, TROPP J A. CoSaMP: Iterative Signal Recovery from Incomplete and Inaccurate Samples[J]. Appl Comput Harmon Anal, 2009, 26(3): 301-321. DOI: 10.1016/j.acha.2008.07.002 .
本文引用 [1]
24
ZHAO J, BAI X. An Improved Orthogonal Matching Pursuit Based on Randomly Enhanced Adaptive Subspace Pursuit[C]//2017 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC). Kuala Lumpur, Malaysia: IEEE, 2017: 437-441. DOI: 10.1109/APSIPA.2017.8282071 .
本文引用 [1]
25
ZHANG C J. An Orthogonal Matching Pursuit Algorithm Based on Singular Value Decomposition[J]. Circuits Syst Signal Process, 2020, 39(1): 492-501. DOI: 10.1007/s00034-019-01182-2 .
本文引用 [1]
26
LIU Y Z, SONG T, ZHUANG Y Q. A High-throughput Subspace Pursuit Processor for ECG Recovery in Compressed Sensing Using Square-root-free MGS QR Decomposition[J]. IEEE Trans Very Large Scale Integr VLSI Syst, 2020, 28(1): 174-187. DOI: 10.1109/TVLSI.2019.2936867 .
本文引用 [2]
27
LI L X, XU D F, PENG H P, et al. Reconstruction of Complex Network Based on the Noise via QR Decomposition and Compressed Sensing[J]. Sci Rep, 2017, 7(1): 15036. DOI: 10.1038/s41598-017-15181-3 .
本文引用 [1]
28
ZHANG H F, XIAO S G, ZHOU P. A Matching Pursuit Algorithm for Backtracking Regularization Based on Energy Sorting[J]. Symmetry, 2020, 12(2): 231. DOI: 10.3390/sym12020231 .
本文引用 [2]
29
ZHENG Z, YANG C L, WANG W Q, et al. Robust DOA Estimation Against Mutual Coupling with Nested Array[J]. IEEE Signal Process Lett, 2020, 27: 1360-1364. DOI: 10.1109/LSP.2020.3011314 .
本文引用 [1]
30
JIANG G J, YANG Y L. Synthetic Sparse Nested Array with Extended Aperture and Reduced Mutual Coupling for DOA Estimation[J]. Signal Process, 2023, 204: 108849. DOI: 10.1016/j.sigpro.2022.108849 .
本文引用 [1]
31
CANDÈS E, ROMBERG J. Sparsity and Incoherence in Compressive Sampling[J]. Inverse Probl Int J Inverse Probl Inverse Meth Comput Inversion Data, 2007, 23(3): 969-985. DOI:10.1088/0266-5611/23/3/008 .
本文引用 [1]

Comments

PDF(2669 KB)

Accesses

Citation

Detail
Sections
Recommended
Copyright © Journal of Shanxi University(Natural Science Edition), All Rights Reserved.
Powered by Beijing Magtech Co. Ltd.

/

〈 〉