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

作　　者：马宝泽 李国军 向翠玲[1,2] 徐阳 MA Baoze;LI Guojun;XIANG Cuiling;XU Yang(School of Electro-optics Engineering,Chongqing University of Posts and Telecommunications,Chongqing 400065,China;Lab of Beyond LOS Reliable Information Transmission,Chongqing University of Posts and Telecommunications,Chongqing 400065,China;Postdoctoral Research Workstation of Chongqing Key Laboratory of Optoelectronic Information Sensing and Transmission Technology,Chongqing University of Posts and Telecommunications,Chongqing 400065,China)

机构地区：[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

出　　处：《通信学报》2022年第11期35-43,共9页Journal on Communications

基　　金：国家重点研发计划基金资助项目(No.2019YFC1511300);国家自然科学基金资助项目(No.62201113);重庆市重点研发计划基金资助项目(No.cstc2017zdcy-zdyfX0011)。

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。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.

关 键 词：欠定矩阵估计 对称张量 分割策略 自协方差矩阵 

分 类 号：TN911.6[电子电信—通信与信息系统]