基于张量分析的欠定混合矩阵估计算法

doi:10.11959/j.issn.1000-436x.2022206

通信学报 ›› 2022, Vol. 43 ›› Issue (11): 35-43.doi: 10.11959/j.issn.1000-436x.2022206

基于张量分析的欠定混合矩阵估计算法

马宝泽¹^,²^,³, 李国军¹^,², 向翠玲¹^,², 徐阳¹^,²

¹ 重庆邮电大学光电工程学院，重庆 400065
² 重庆邮电大学超视距可信信息传输研究所，重庆 400065
³ 重庆邮电大学光电信息感测与传输技术重庆市重点实验室博士后科研工作站，重庆 400065

修回日期:2022-10-09 出版日期:2022-11-25 发布日期:2022-11-01
作者简介:马宝泽（1990− ），男，河北廊坊人，博士，重庆邮电大学讲师，主要研究方向为盲源分离、信道辨识、数据分析、深度学习等
李国军（1978− ），男，四川资阳人，博士，重庆邮电大学教授、博士生导师，主要研究方向为复杂恶劣环境超视距无线通信与网络
向翠玲（1996− ），女，重庆人，重庆邮电大学硕士生，主要研究方向为信道估计与均衡、短波建链技术
徐阳（1998− ），男，湖南常德人，重庆邮电大学硕士生，主要研究方向为信道估计与均衡、自适应迭代算法
基金资助:
国家重点研发计划基金资助项目(2019YFC1511300);国家自然科学基金资助项目(62201113);重庆市重点研发计划基金资助项目(cstc2017zdcy-zdyfX0011)

Underdetermined mixing matrix estimation algorithm based on tensor analysis

Baoze MA¹^,²^,³, Guojun LI¹^,², Cuiling XIANG¹^,², Yang XU¹^,²

¹ School of Electro-optics Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
² Lab of Beyond LOS Reliable Information Transmission, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
³ Postdoctoral Research Workstation of Chongqing Key Laboratory of Optoelectronic Information Sensing and Transmission Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Revised:2022-10-09 Online:2022-11-25 Published:2022-11-01
Supported by:
The National Key Research and Development Program of China(2019YFC1511300);The National Natural Science Foundation of China(62201113);Chongqing Key Research and Development Program(cstc2017zdcy-zdyfX0011)

摘要/Abstract

摘要：

针对欠定矩阵估计中存在有效特征信息提取难和算法收敛速度慢等问题，提出基于张量分析的瞬时混合欠定矩阵估计算法，旨在克服信号稀疏性约束。该算法通过信号分割子段的自协方差构造对称三阶张量，并压缩为核张量降低数据规模，利用增强线性搜索技术加速交替最小二乘算法的收敛速度，将因子矩阵作为混合矩阵估计的测度，但分割子段数选取是个开放问题。仿真表明，所提算法在估计欠定混合矩阵时性能优于稀疏变换法和传统高阶统计量法。

关键词: 欠定矩阵估计, 对称张量, 分割策略, 自协方差矩阵

Abstract:

Aiming at the problems of difficult to extract effective feature information and the slow convergence speed of the underdetermined matrix estimation, an underdetermined matrix estimation algorithm of instantaneous mixtures based on tensor analysis was proposed to overcome the constraint of signal sparsity.In the proposed algorithm, the symmetric third-order tensor was constructed via the autocovariance matrix of segmentation sub-block, which was compressed into a kernel tensor to reduce the size of the data.An enhanced line search technology was applied to speed up the convergence of alternating least squares method, and the factor matrix was used as the measure of the mixing matrix estimation, but the selection of the number of segmentation sub-blocks was an open problem.Experimental results demonstrate that the proposed algorithm outperforms the sparse transformation method and the traditional high-order statistical method in handling the underdetermined mixing matrix estimation.

Key words: underdetermined matrix estimation, symmetric tensor, segmentation strategy, autocovariance matrix

中图分类号:

TN911.6

马宝泽, 李国军, 向翠玲, 徐阳. 基于张量分析的欠定混合矩阵估计算法[J]. 通信学报, 2022, 43(11): 35-43.

Baoze MA, Guojun LI, Cuiling XIANG, Yang XU. Underdetermined mixing matrix estimation algorithm based on tensor analysis[J]. Journal on Communications, 2022, 43(11): 35-43.

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算法	混合矩阵(m×n)平均相对误差/dB
算法	3×4	4×5	5×6
LI-TIFROM	-25.85	-20.23	-15.40
UBSS-SCA	-14.87	-13.79	-14.76
SOBIUM	-26.05	-20.86	-18.25
本文算法	-29.34	-25.17	-19.49

基于张量分析的欠定混合矩阵估计算法

Underdetermined mixing matrix estimation algorithm based on tensor analysis

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