Spectral Distribution of Wigner Matrices in Finite Dimensions and Its Application to LPI Performance Evaluation of Radar Waveforms

Jun CHEN; Fei WANG; Jianjiang ZHOU; Chenguang SHI

doi:10.1587/transfun.E100.A.2021

Spectral Distribution of Wigner Matrices in Finite Dimensions and Its Application to LPI Performance Evaluation of Radar Waveforms

Jun CHEN, Fei WANG, Jianjiang ZHOU, Chenguang SHI

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Recent research on the assessment of low probability of interception (LPI) radar waveforms is mainly based on limiting spectral properties of Wigner matrices. As the dimension of actual operating data is constrained by the sampling frequency, it is very urgent and necessary to research the finite theory of Wigner matrices. This paper derives a closed-form expression of the spectral cumulative distribution function (CDF) for Wigner matrices of finite sizes. The expression does not involve any derivatives and integrals, and therefore can be easily computed. Then we apply it to quantifying the LPI performance of radar waveforms, and the Kullback-Leibler divergence (KLD) is also used in the process of quantification. Simulation results show that the proposed LPI metric which considers the finite sample size and signal-to-noise ratio is more effective and practical.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.9 pp.2021-2025

Publication Date: 2017/09/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E100.A.2021

Type of Manuscript: LETTER

Category: Digital Signal Processing

Authors

Jun CHEN
  Nanjing University of Aeronautics and Astronautics
Fei WANG
  Nanjing University of Aeronautics and Astronautics
Jianjiang ZHOU
  Nanjing University of Aeronautics and Astronautics
Chenguang SHI
  Nanjing University of Aeronautics and Astronautics

Keyword

Wigner matrices, finite dimension, spectral CDF, LPI metric, radar waveform

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Jun CHEN, Fei WANG, Jianjiang ZHOU, Chenguang SHI, "Spectral Distribution of Wigner Matrices in Finite Dimensions and Its Application to LPI Performance Evaluation of Radar Waveforms" in IEICE TRANSACTIONS on Fundamentals, vol. E100-A, no. 9, pp. 2021-2025, September 2017, doi: 10.1587/transfun.E100.A.2021.
Abstract: Recent research on the assessment of low probability of interception (LPI) radar waveforms is mainly based on limiting spectral properties of Wigner matrices. As the dimension of actual operating data is constrained by the sampling frequency, it is very urgent and necessary to research the finite theory of Wigner matrices. This paper derives a closed-form expression of the spectral cumulative distribution function (CDF) for Wigner matrices of finite sizes. The expression does not involve any derivatives and integrals, and therefore can be easily computed. Then we apply it to quantifying the LPI performance of radar waveforms, and the Kullback-Leibler divergence (KLD) is also used in the process of quantification. Simulation results show that the proposed LPI metric which considers the finite sample size and signal-to-noise ratio is more effective and practical.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.2021/_p

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@ARTICLE{e100-a_9_2021,
author={Jun CHEN, Fei WANG, Jianjiang ZHOU, Chenguang SHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Spectral Distribution of Wigner Matrices in Finite Dimensions and Its Application to LPI Performance Evaluation of Radar Waveforms},
year={2017},
volume={E100-A},
number={9},
pages={2021-2025},
abstract={Recent research on the assessment of low probability of interception (LPI) radar waveforms is mainly based on limiting spectral properties of Wigner matrices. As the dimension of actual operating data is constrained by the sampling frequency, it is very urgent and necessary to research the finite theory of Wigner matrices. This paper derives a closed-form expression of the spectral cumulative distribution function (CDF) for Wigner matrices of finite sizes. The expression does not involve any derivatives and integrals, and therefore can be easily computed. Then we apply it to quantifying the LPI performance of radar waveforms, and the Kullback-Leibler divergence (KLD) is also used in the process of quantification. Simulation results show that the proposed LPI metric which considers the finite sample size and signal-to-noise ratio is more effective and practical.},
keywords={},
doi={10.1587/transfun.E100.A.2021},
ISSN={1745-1337},
month={September},}

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TY - JOUR
TI - Spectral Distribution of Wigner Matrices in Finite Dimensions and Its Application to LPI Performance Evaluation of Radar Waveforms
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2021
EP - 2025
AU - Jun CHEN
AU - Fei WANG
AU - Jianjiang ZHOU
AU - Chenguang SHI
PY - 2017
DO - 10.1587/transfun.E100.A.2021
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2017
AB - Recent research on the assessment of low probability of interception (LPI) radar waveforms is mainly based on limiting spectral properties of Wigner matrices. As the dimension of actual operating data is constrained by the sampling frequency, it is very urgent and necessary to research the finite theory of Wigner matrices. This paper derives a closed-form expression of the spectral cumulative distribution function (CDF) for Wigner matrices of finite sizes. The expression does not involve any derivatives and integrals, and therefore can be easily computed. Then we apply it to quantifying the LPI performance of radar waveforms, and the Kullback-Leibler divergence (KLD) is also used in the process of quantification. Simulation results show that the proposed LPI metric which considers the finite sample size and signal-to-noise ratio is more effective and practical.
ER -