一种压缩感知测量矩阵的联合优化算法  

Co-optimization Algorithm for Measurement Matrix of Compressive Sensing

作　　者：杨柳[1,2,3] 白朝元[1,2] 范平志 YANG Liu;BAI Chaoyuan;FAN Pingzhi(School of Information Science and Technology,Southwest Jiaotong University,Chengdu 611756,China;Information Coding&Transmission Key Lab of Sichuan Province,Southwest Jiaotong University,Chengdu 611756,China;National Engineering Laboratory of Integrated Transportation Big Data Application Technology,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学信息科学与技术学院,四川成都611756 [2]西南交通大学四川省信息编码与传输重点实验室,四川成都611756 [3]西南交通大学综合交通大数据应用技术国家工程实验室,四川成都611756

出　　处：《西南交通大学学报》2025年第2期454-461,共8页Journal of Southwest Jiaotong University

基　　金：国家自然科学基金项目(62020106001,U2468201)。

摘　　要：对于压缩感知算法,其测量矩阵与稀疏基之间的相关性往往决定了信号恢复精度.为提升大规模通信场景下压缩感知算法重构信号的性能,基于矩阵分解与等角紧框架理论对测量矩阵进行改进.首先,基于测量矩阵和稀疏基构造字典矩阵,并进一步构造Gram矩阵,利用特征值分解降低Gram矩阵的平均相关性;然后,基于等角紧框架理论与梯度缩减理论,通过使Gram矩阵逼近等角紧框架矩阵来减小Gram矩阵非主对角线元素的最大值,从而降低测量矩阵与稀疏基之间的最大相关性;最后,以正交匹配追踪(orthogonal matching pursuit,OMP)为重构算法进行仿真验证.仿真结果表明:相比于优化前,矩阵相关系数降低40%~50%;在信道估计与活跃用户检测中,本文在较高稀疏度下的算法错误估计数比其他优化算法降低50%以上,信道估计的均方误差相比其他矩阵提升3 dB,误码率性能提升2 dB.For the compressive sensing algorithm,the correlation between measurement matrix and sparse base always determines the accuracy of signal recovery.In order to improve the performance of the compressive sensing algorithm in signal reconstruction in large-scale communication scenarios,the measurement matrix was improved based on matrix decomposition and equiangular tight frame(ETF)theory.Firstly,a dictionary matrix was constructed based on the measurement matrix and sparse base,and a Gram matrix was constructed.Eigenvalue decomposition was used to reduce the average correlation of the Gram matrix.Then,based on the ETF theory and gradient reduction theory,the Gram matrix was pushed to approach the ETF matrix to reduce the maximum value of the non-principal diagonal elements of the Gram matrix and the maximum correlation between the measurement matrix and the sparse basis.The orthogonal matching pursuit(OMP)algorithm was used as the reconstruction algorithm for simulation and verification,and the simulation results show that after optimization,the correlation coefficient of the matrix is reduced by 40%-50%.In channel estimation and active user detection,the estimation error of active user number by the proposed algorithm is more than 50%lower than that by other optimization algorithms under high sparsity;compared with other matrices,the mean square error of channel estimation is improved by 3 dB,and the bit error rate performance is improved by 2 dB.

关 键 词：压缩感知 矩阵分解 等角紧框架理论 信道估计 活跃用户检测 

分 类 号：TN929.5[电子电信—通信与信息系统]