西南交通大学学报2025，Vol.60Issue(2)：454-461,8.DOI:10.3969/j.issn.0258-2724.20230032
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
摘要
Abstract
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Key words
compressed sensing/matrix decomposition/equiangular tight frame theory/channel estimation/active user detection分类
电子信息工程引用本文复制引用
杨柳,白朝元,范平志..一种压缩感知测量矩阵的联合优化算法[J].西南交通大学学报,2025,60(2):454-461,8.基金项目
国家自然科学基金项目(62020106001,U2468201) （62020106001,U2468201）
