α稳定分布特征指数估计算法

doi:10.13229/j.cnki.jdxbgxb20170185

吉林大学学报(工学版) ›› 2018, Vol. 48 ›› Issue (2): 618-624.doi: 10.13229/j.cnki.jdxbgxb20170185

α稳定分布特征指数估计算法

关济实^{1, 2}, 石要武¹, 邱建文², 单泽彪³, 史红伟³

1.吉林大学通信工程学院,长春 130022;
2.中广核研究院有限公司北京分公司北京 100083;
3.长春理工大学电子信息工程学院,130022

收稿日期:2017-02-14 出版日期:2018-03-01 发布日期:2018-03-01
通讯作者: 史红伟(1978-),男,讲师,博士. 研究方向:雷达信号处理. E-mail:qitiand@qq.com
作者简介:关济实(1977-),男,高级工程师,博士研究生. 研究方向:雷达阵列信号处理. E-mail:guanjishi@sina.com
基金资助:
国家自然科学基金项目(61571462)

New algorithm to estimate characteristic exponent of α-stable distribution

GUAN Ji-shi^{1, 2}, SHI Yao-wu¹, QIU Jian-wen², SHAN Ze-biao³, SHI Hong-wei³

1. College of Communication Engineering, Jilin University,Changchun 130022,China;
2.Beijing Branch,China Nuclear Power Technology Research Institute Co. Ltd., Beijing 100083, China;
3. School of Electronic and Information Engineering, Changchun University of Science and Technology, Changchun 130022,China

Received:2017-02-14 Online:2018-03-01 Published:2018-03-01

摘要/Abstract

摘要： 针对α稳定分布信号参数估计问题,提出一种基于α稳定分布叠加性质和p范数性质的特征指数估计算法。该算法利用多个同分布的α稳定分布变量组合相加结果的p范数与原变量p范数之间的关系实现对特征指数α的估计。介绍了α稳定分布的定义和基本性质,说明了估计算法的原理和估计步骤,证明了估计算法的无偏性和一致性。仿真实验表明,该算法不需要稳定分布的其他先验知识,在很大的范围内可以有效地估计α稳定分布的特征指数,在高斯噪声掺杂的情况下仍可准确估计信号的α值,为α稳定分布噪声下的信号处理方法提供支持。

关键词: 通信技术, α, 稳定分布, 参数估计, 叠加性质, p范数

Abstract: To estimate the parameter of α-stable distribution signal, this paper proposes an algorithm based on the plus property and p-norm property of α-stable distribution. The characteristic exponent α is estimated using the relationship between the p-norm of original variable and the new p-norm of variable, which is the combination of several variables with the same α-stable distribution. The definition and the properties of the α-stable distribution are introduced, and then the principle and execution steps of the proposed algorithm are explained. The unbiaseness and uniformity of the algorithm in estimation of the characteristic exponent are discussed. Simulation results show that this method can estimate the characteristics exponent of α-stable distribution in a wide range without any more information of the distribution. It works well even Gaussian noise is added to the α-stable variable. The estimation results can support the subsequent signal processing algorithm with α-stable noise.

Key words: communication technology, α-stable distribution, parameter estimation, plus property, p-norm

中图分类号:

TN911

关济实, 石要武, 邱建文, 单泽彪, 史红伟. α稳定分布特征指数估计算法[J]. 吉林大学学报(工学版), 2018, 48(2): 618-624.

GUAN Ji-shi, SHI Yao-wu, QIU Jian-wen, SHAN Ze-biao, SHI Hong-wei. New algorithm to estimate characteristic exponent of α-stable distribution[J]. 吉林大学学报(工学版), 2018, 48(2): 618-624.

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α稳定分布特征指数估计算法

New algorithm to estimate characteristic exponent of α-stable distribution

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