基于随机矩阵理论的子空间加权改良算法

高雨濛; 李姜辉; 柏业超; 王琼; 张兴敢

doi:10.1631/FITEE.1900463

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基于随机矩阵理论的子空间加权改良算法

常规文章 | Updated：2022-05-19

- 基于随机矩阵理论的子空间加权改良算法
- An improved subspace weighting method using random matrix theory
- 信息与电子工程前沿（英文） 2020年21卷第9期页码：1302-1307
- Affiliations：
  
  School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China
  Institute of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, UK
- Author bio：
  
  Ye-chao BAI, E-mail: ychbai@nju.edu.cn
- Funds：
  
  Project supported by the National Natural Science Foundation of China (No.61976113)
- DOI：10.1631/FITEE.1900463
  中图分类号： TP319
- 收稿：2019-09-02，
  
  修回：2020-;8-10，
  
  纸质出版：2020-09
- Accepted：
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高雨濛, 李姜辉, 柏业超, 等. 基于随机矩阵理论的子空间加权改良算法[J]. 信息与电子工程前沿（英文）, 2020,21(9):1302-1307.

Yu-meng GAO, Jiang-hui LI, Ye-chao BAI, et al. An improved subspace weighting method using random matrix theory[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(9): 1302-1307.
高雨濛, 李姜辉, 柏业超, 等. 基于随机矩阵理论的子空间加权改良算法[J]. 信息与电子工程前沿（英文）, 2020,21(9):1302-1307. DOI： 10.1631/FITEE.1900463.

Yu-meng GAO, Jiang-hui LI, Ye-chao BAI, et al. An improved subspace weighting method using random matrix theory[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(9): 1302-1307. DOI： 10.1631/FITEE.1900463.

摘要

在低信噪比及信号相关情况下，加权子空间拟合（WSF）算法的性能优于多信号分类（MUSIC）算法。本文使用随机矩阵理论（RMT）改善加权子空间拟合。随机矩阵理论研究随机矩阵维数以同速率增加时，矩阵特征值和特征向量的渐近规律。加权子空间拟合中，运用近似一阶扰动计算样本协方差矩阵特征向量的统计特性。利用随机矩阵理论中关于样本协方差矩阵信号子空间向真实信号投影的范数的渐进结果，获得加权子空间拟合计算方法。仿真结果表明，在低快拍数及低信噪比情况下，本文所提方法具有优越性。

Abstract

The weighting subspace fitting (WSF) algorithm performs better than the multi-signal classification (MUSIC) algorithm in the case of low signal-to-noise ratio (SNR) and when signals are correlated. In this study

we use the random matrix theory (RMT) to improve WSF. RMT focuses on the asymptotic behavior of eigenvalues and eigenvectors of random matrices with dimensions of matrices increasing at the same rate. The approximative first-order perturbation is applied in WSF when calculating statistics of the eigenvectors of sample covariance. Using the asymptotic results of the norm of the projection from the sample covariance matrix signal subspace onto the real signal in the random matrix theory

the method of calculating WSF is obtained. Numerical results are shown to prove the superiority of RMT in scenarios with few snapshots and a low SNR.

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references

NA Asendorf . . Informative Data Fusion: Beyond Canonical Correlation Analysis. PhD Thesis . . University of Michigan, State of Michigan, USA , , . .

XJ Bai , , , YA Li , , , W Zhang , , , 等 . . Direction of arrival estimation of two wide-band sources with small array based on beam-space coherent signal-subspace method. In: Xing S, Chen S, Wei Z (Eds.), Unifying Electrical Engineering and Electronics Engineering . . Springer, New York , , 2014 . . 7 p.1415 - - 1423 . . DOI: 10.1007/978-1-4614-4981-2-155 http://doi.org/10.1007/978-1-4614-4981-2-155 . .

YC Bai , , , JH Li , , , Y Wu , , , 等 . . Weighted incoherent signal subspace method for DOA estimation on wideband colored signals . . IEEE Access , , 2018 . . 7 1224 - - 1233 . . DOI: 10.1109/ACCESS.2018.2886250 http://doi.org/10.1109/ACCESS.2018.2886250 . .

TSG Basha , , , PV Sridevi , , , MNG Prasad . . Beam forming in smart antenna with precise direction of arrival estimation using improved music . . Wirel Person Commun , , 2013 . . 71 ( ( 2 ): ): 1353 - - 1364 . . DOI: 10.1007/s11277-012-0879-9 http://doi.org/10.1007/s11277-012-0879-9 . .

F Benaych-Georges , , , RR Nadakuditi . . The eigenvalues and eigenvectors of finite low rank perturbations of large random matrices . . Adv Math , , 2011 . . 227 ( ( 1 ): ): 494 - - 521 . . DOI: 10.1016/j.aim.2011.02.007 http://doi.org/10.1016/j.aim.2011.02.007 . .

H Chen , , , XG Zhang , , , QS Wang , , , 等 . . Efficient data fusion using random matrix theory . . IEEE Signal Process Lett , , 2018 . . 25 ( ( 5 ): ): 605 - - 609 . . DOI: 10.1109/LSP.2018.2815557 http://doi.org/10.1109/LSP.2018.2815557 . .

X He , , , Q Ai , , , RC Qiu , , , 等 . . A big data architecture design for smart grids based on random matrix theory . . IEEE Trans Smart Grid , , 2017 . . 8 ( ( 2 ): ): 674 - - 686 . . DOI: 10.1109/TSG.2015.2445828 http://doi.org/10.1109/TSG.2015.2445828 . .

H Krim , , , M Viberg . . Two decades of array signal processing research: the parametric approach . . IEEE Signal Process Mag , , 1996 . . 13 ( ( 4 ): ): 67 - - 94 . . DOI: 10.1109/79.526899 http://doi.org/10.1109/79.526899 . .

S Li , , , W He , , , XG Yang , , , 等 . . Direction-of-arrival estimation of quasi-stationary signals using two-level Khatri-Rao subspace and four-level nested array . . J Cent South Univ , , 2014 . . 21 ( ( 7 ): ): 2743 - - 2750 . . DOI: 10.1007/s11771-014-2236-5 http://doi.org/10.1007/s11771-014-2236-5 . .

AH Liu , , , Q Yang , , , X Zhang , , , 等 . . Modified root music for co-prime linear arrays . . Electron Lett , , 2018 . . 54 ( ( 15 ): ): 949 - - 950 . . DOI: 10.1049/el.2018.1125 http://doi.org/10.1049/el.2018.1125 . .

R Schmidt . . Multiple emitter location and signal parameter estimation . . IEEE Trans Antenn Propag , , 1986 . . 34 ( ( 3 ): ): 276 - - 280 . . DOI: 10.1109/TAP.1986.1143830 http://doi.org/10.1109/TAP.1986.1143830 . .

M Viberg , , , B Ottersten , , , T Kailath . . Detection and estimation in sensor arrays using weighted subspace fitting . . IEEE Trans Signal Process , , 1991 . . 39 ( ( 11 ): ): 2436 - - 2449 . . DOI: 10.1109/78.97999 http://doi.org/10.1109/78.97999 . .

LT Wan , , , GJ Han , , , JF Jiang , , , 等 . . DOA estimation for coherently distributed sources considering circular and noncircular signals in massive MIMO systems . . IEEE Syst J , , 2017 . . 11 ( ( 1 ): ): 41 - - 49 . . DOI: 10.1109/JSYST.2015.2445052 http://doi.org/10.1109/JSYST.2015.2445052 . .

XG Wu , , , TW Guo . . DOA estimation under sensor gain and phase uncertainties . . Int Conf on Estimation, Detection and Information Fusion , , 2011 . . p.147 - - 156 . . DOI: 10.1007/978-3-642-25188-7_18 http://doi.org/10.1007/978-3-642-25188-7_18 . .

LM Zhao , , , HQ Liu , , , Y Li , , , 等 . . DOA estimation under sensor gain and phase uncertainties . . Int Conf on Estimation, Detection and Information Fusion , , 2015 . . p.209 - - 213 . . DOI: 10.1109/ICEDIF.2015.7280192 http://doi.org/10.1109/ICEDIF.2015.7280192 . .

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