利用参数结构的快速非酉联合对角化算法

刘文娟; 冯大政; 袁明冬

doi:10.7652/xjtuxb201612017

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利用参数结构的快速非酉联合对角化算法

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- 利用参数结构的快速非酉联合对角化算法
- A Fast Non-Unitary Joint Diagonalization Algorithm Based on Utilizations of Parametric Structures
- 西安交通大学学报 2016年50卷第12期页码：106-113
- 作者机构：
  
  西安电子科技大学雷达信号处理国家重点实验室,西安,710071
- 作者简介：
- 基金信息：
  
  : 2016-03-08。作者简介: 刘文娟(1986—),女,博士生;冯大政(通信作者),男,教授,博士生导师。基金项目: 国家自然科学基金资助项目(61271293,61373177)
- DOI：10.7652/xjtuxb201612017
  中图分类号： TN911.7
- 网络首发：2016-12-10，
  
  纸质出版：2016
- 稿件说明：
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刘文娟, 冯大政, 袁明冬. 利用参数结构的快速非酉联合对角化算法[J]. 西安交通大学学报, 2016,50(12):106-113.

A Fast Non-Unitary Joint Diagonalization Algorithm Based on Utilizations of Parametric Structures[J]. 2016, 50(12): 106-113.
刘文娟, 冯大政, 袁明冬. 利用参数结构的快速非酉联合对角化算法[J]. 西安交通大学学报, 2016,50(12):106-113. DOI： 10.7652/xjtuxb201612017.

A Fast Non-Unitary Joint Diagonalization Algorithm Based on Utilizations of Parametric Structures[J]. 2016, 50(12): 106-113. DOI： 10.7652/xjtuxb201612017.

摘要

针对基于快速Frobenius范数对角化(FFDIAG)的盲信号分离算法不能直接处理复数数据从而导致分离性能差的问题

提出一种利用参数结构的快速非酉联合对角化(PSJD)算法。该算法首先将由观测信号的统计量得到的复目标矩阵转化为实对称矩阵; 通过对代价函数的二阶近似

将解联合对角化问题转化为一系列的线性最小二乘问题

直接得到更新矩阵元素的估计。在每次迭代中

通过充分利用转化后的目标矩阵的结构信息

减少估计分离矩阵及更新目标矩阵的计算复杂度。同时

针对FFDIAG算法采用的固定步长难以兼顾收敛速度与更新矩阵严格对角占优性的问题

采用仅由当前更新矩阵的估计值决定的自适应学习率

提高算法的收敛性能。仿真实验表明

在一定的取值范围内

PSJD算法的收敛速度对步长参数的变化不敏感

在步长参数同为0.1的情况下

PSJD算法达到收敛所需的迭代次数比采用固定步长的算法减少了42%左右。

Abstract

A parametric structures based fast joint diagonalization(PSJD)algorithm for non-unitary diagonalization of a set of complex target matrices is presented to cope with the problem that the blind source separation by fast Frobenius diagonalization(FFDIAG)algorithm is not applicable in the complex-valued space and its separation performance is lower. The algorithm firstly transforms the complex target matrices into real-symmetric ones. Secondly

the problem of simultaneous diagonalization of matrices is transformed into a series of linear least-squares problems through second-order approximation to contract functions

and the elements of the updating matrix are directly estimated. The computational complexity for estimating the diagonalizer and for updating the target matrices is significantly reduced by making full use of the structure information of the transformed target matrices. In order to overcome the drawback of fixed step size adopted in the FFDIAG that may not strike a balance between the convergence rate and strictly diagonally dominant property of the update matrix

the proposed algorithm uses the adaptive learning rate determined from the estimation of the update matrix in each iteration to improve the convergence property. Results of numerical simulations show that the convergence rate of PSJD algorithm is not very sensitive in a wide range of step-size values. When the step size is 0.1

the number of iterations required to reach convergence is 42% less than that of the fixed step-size method.

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references

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