多通道复信号检测中的几种常用复统计分布

doi:10.3969/j.issn.0372-2112.2013.06.031

电子学报 ›› 2013, Vol. 41 ›› Issue (6): 1238-1241.DOI: 10.3969/j.issn.0372-2112.2013.06.031

多通道复信号检测中的几种常用复统计分布

刘维建^1,2, 谢文冲², 王永良²

1. 国防科学技术大学电子科学与工程学院, 湖南长沙 410073;
2. 空军预警学院, 湖北武汉 430019

收稿日期:2012-01-12 修回日期:2012-08-27 出版日期:2013-06-25
- 作者简介:
- 刘维建男,1982年12月出生于山东省莱芜市.现为国防科技大学信号与信息处理专业博士研究生.主要研究方向:空时自适应检测、阵列信号处理. E-mail:liuvjian@163.com
- 基金资助:
- 国家杰出青年科学基金 (No.60925005); 国家青年科学基金 (No.61102169)

Some Complex Statistical Distributions in Multichannel Complex-Valued Signal Detection Theory

LIU Wei-jian^1,2, XIE Wen-chong², WANG Yong-liang²

1. College of Electronic Science and Engineering, NUDT, Changsha, Hu'nan 410073, China;
2. Key Lab, Air Force Early Warning Academy, Wuhan, Hubei 430019, China

Received:2012-01-12 Revised:2012-08-27 Online:2013-06-25 Published:2013-06-25
- Supported by:
- National Natural Science Foundation of China for Distinguished Young Schoolars (No.60925005); Youth Fund of National Natural Science Foundation of China (No.61102169)

摘要/Abstract

摘要： 复随机变量的概率密度函数(PDF)及其积累分布函数(CDF)是复值信号检测中计算虚警概率(PFA)和检测概率(PD)的基础.本文分析了复统计分布与实统计分布之间的关系,推导了复F分布和复贝塔分布(中心或者非中心)的PDF和CDF,推导了中心复t分布的PDF,并且给出了部分应用实例.

关键词: 复随机变量, 积累分布函数, 复值信号检测, 概率密度函数, 自适应检测

Abstract: The probability density functions(PDF's)and cumulative distribution functions(CDF's)of complex random variables RVA's)are basis for calculating the probabilities of false alarm(PFA's)and probabilities of detection(PD's)in complex-valued signal detection theory.In this paper,some relationship between the complex statistical distributions and the real ones is investigated.The PDF's and CDF's of the complex F and complex Beta distributions,both central and noncentral,and the PDF of the central complex t distribution are derived.

Key words: complex random variables, cumulative distribution function, complex-valued signal detection, probability density function, multichannel detection

中图分类号:

TN957

刘维建, 谢文冲, 王永良. 多通道复信号检测中的几种常用复统计分布[J]. 电子学报, 2013, 41(6): 1238-1241.

LIU Wei-jian, XIE Wen-chong, WANG Yong-liang . Some Complex Statistical Distributions in Multichannel Complex-Valued Signal Detection Theory[J]. Acta Electronica Sinica, 2013, 41(6): 1238-1241.

参考文献

[1] 简涛,何友,苏峰,长文,平殿发.距离扩展目标检测器的最优参数及鲁棒性分析[J].电子学报,2011,39(9):2090-2193. Jian Tao,He You,Su Feng,Qu Changwen,Ping Dianfa.Optimized parameters and robustness evaluation for range spread target detector[J].Acta Electronica Sinica,2011,39(9):2090-2193.(in Chinese)

[2] 王鞠庭,江胜利,何劲,刘中.基于对角加载的机载MIMO雷达GLRT检测器[J].电子学报,2009,37(12):2614-2619. Wang Juting,Jiang Shengli,He Jin,Liu Zhong,GLRT detector with diagonal loading for MIMO radars[J].Acta Electronica Sinica,2009,37(12):2614-2619.(in Chinese)

[3] Mandic D P,Goh V S L.Complex Valued Nonlinear Adaptive Filters:Noncircularity,Widely Linear and Neural Models[M].Chichester:Wiley,2009.

[4] Hjrungnes A.Complex-Valued Matrix Derivatives:With Applications in Signal Processing and Communications[M].New York:Cambridge University Press,2011.

[5] Vaidyanathan P P,Phoong S,Lin Y.Signal Processing and Optimization for Transceiver Systems[M].New York:Cambridge University Press,2010.

[6] Adali T,Haykin S.Adaptive Signal Processing,Next-Generation Solutions[M].Hoboken:Wiley-IEEE Press,2010.

[7] Schreier P J,Scharf L L.Statistical Signal Processing of Complex-Valued Data:the Theory of Improper and Noncircular Signals[M].New York:Cambridge University Press,2010.

[8] Wooding R A.The multivariate distribution of complex normal variables[J].Biometrika,1956,43(1/2):212-215.

[9] Goodman N R.Statistical analysis based on a certain multivariate complex Gaussian distribution(an introduction)[J].The Annals of Mathematical Statistics,1963,34(1):152-177.

[10] Kelly E J,Forsythe K M.Adaptive Detection and Parameter Estimation for Multidimensional Signal Models.Lexington:Lincoln Lab,1989.

[11] Picinbono B.Second-order complex random vectors and normal distributions[J].IEEE Transactions on Acoustics,Speech,and Signal Processing,1996,44(10):2637-2640.

[12] Pal N,Jin C,Lim W K.Handbook of Exponential and Related Distributions for Engineers and Scientists[M].London:Chapman & Hall/CRC,2006.

[13] Muirhead R J.Aspects of Multivariate Statistical Theory[M].2 nd.Hoboken:Wiley,2005.

[14] Press W H,Teukolsky S A,Vetterling W T,et al.Numerical Recipes:the Art of Scientific Computing[M].Third ed.Cambridge:Cambridge University Press,2007.

[15] Walck C,Fysikum.Hand-book on Statistical Distributions for Experimentalists[R].Sweden:Stockholm University,2007.

多通道复信号检测中的几种常用复统计分布

Some Complex Statistical Distributions in Multichannel Complex-Valued Signal Detection Theory

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