- ISSN 0258-2724
- CN 51-1277/U
- EI Compendex
- Scopus
- Indexed by Core Journals of China, Chinese S&T Journal Citation Reports
- Chinese S&T Journal Citation Reports
- Chinese Science Citation Database
| Citation: | YANG Liu, BAI Chaoyuan, FAN Pingzhi. Co-optimization Algorithm for Measurement Matrix of Compressive Sensing[J]. Journal of Southwest Jiaotong University, 2025, 60(2): 454-461. doi: 10.3969/j.issn.0258-2724.20230032
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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.
| [1] |
DONOHO D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306. doi: 10.1109/TIT.2006.871582
|
| [2] |
SENEL K, LARSSON E G. Grant-free massive MTC-enabled massive MIMO: a compressive sensing approach[J]. IEEE Transactions on Communications, 2018, 66(12): 6164-6175. doi: 10.1109/TCOMM.2018.2866559
|
| [3] |
ROBAEI M, AKL R, CHATAUT R, et al. Adaptive millimeter-wave channel estimation and tracking[C]//2022 24th International Conference on Advanced Communication Technology (ICACT). PyeongChang: IEEE, 2022: 23-28.
|
| [4] |
DUAN L G, YANG X Y, LI A P. WSN data compression model based on K-SVD dictionary and compressed sensing[C]//International Conference of Pioneering Computer Scientists, Engineers and Educators. Singapore: Springer, 2021: 429-442.
|
| [5] |
JIANG R K, WANG X T, CAO S, et al. Joint compressed sensing and enhanced whale optimization algorithm for pilot allocation in underwater acoustic OFDM systems[J]. IEEE Access, 2019, 7: 95779-95796. doi: 10.1109/ACCESS.2019.2929305
|
| [6] |
曾祥洲. 基于压缩感知块结构信号的稀疏表示与重构算法研究[D]. 广州: 华南理工大学,2016.
|
| [7] |
XU Q R, SHENG Z C, FANG Y, et al. Measurement matrix optimization for compressed sensing system with constructed dictionary via Takenaka-Malmquist functions[J]. Sensors, 2021, 21(4): 1229.1-1229.14.
|
| [8] |
宋儒瑛,张朝阳. 基于分块矩阵法优化测量矩阵的研究[J]. 太原师范学院学报(自然科学版),2022,21(2): 1-7.
|
| [9] |
魏从静. 压缩感知中测量矩阵的构造与优化研究[D]. 南京: 南京邮电大学,2016.
|
| [10] |
HE J A, WANG T, WANG C F, et al. Improved measurement matrix construction with pseudo-random sequence in compressed sensing[J]. Wireless Personal Communications, 2022, 123(4): 3003-3024. doi: 10.1007/s11277-021-09274-6
|
| [11] |
BARANIUK R G. Compressive sensing[J]. IEEE Signal Processing Magazine, 2007, 24(4): 118-121. doi: 10.1109/MSP.2007.4286571
|
| [12] |
DONOHO D L, ELAD M. Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization[J]. Proceedings of the National Academy of Sciences of the United States of America, 2003, 100(5): 2197-2202.
|
| [13] |
TROPP J A. Greed is good: algorithmic results for sparse approximation[J]. IEEE Transactions on Information Theory, 2004, 50(10): 2231-2242. doi: 10.1109/TIT.2004.834793
|
| [14] |
郭桂祥. 基于非凸优化方法的压缩感知SAR成像研究[D]. 南京: 南京信息工程大学,2022.
|
| [15] |
WU Q S, FU Y, ZHANG Y D, et al. Structured Bayesian compressive sensing exploiting dirichlet process priors[J]. Signal Processing, 2022, 201: 108680.1-108680.15.
|
| [16] |
WANG B C, MIR T, JIAO R C, et al. Dynamic multi-user detection based on structured compressive sensing for IoT-oriented 5G systems[C]//2016 URSI Asia-Pacific Radio Science Conference (URSI AP-RASC). Seoul: IEEE, 2016: 431-434.
|
| [17] |
JIANG X H, LI N, GUO Y, et al. Sensing matrix optimization for multi-target localization using compressed sensing in wireless sensor network[J]. China Communications, 2022, 19(3): 230-244. doi: 10.23919/JCC.2022.03.017
|
| [18] |
TSILIGIANNI E, KONDI L P, KATSAGGELOS A K. Approximate equiangular tight frames for compressed sensing and CDMA applications[J]. EURASIP Journal on Applied Signal Processing, 2017, 2017(1): 66.1-66.14.
|
| [19] |
ELAD M. Optimized projections for compressed sensing[J]. IEEE Transactions on Signal Processing, 2007, 55(12): 5695-5702. doi: 10.1109/TSP.2007.900760
|
| [20] |
SARDY S, BRUCE A G, TSENG P. Block coordinate relaxation methods for nonparametric wavelet denoising[J]. Journal of Computational and Graphical Statistics, 2000, 9(2): 361-379. doi: 10.1080/10618600.2000.10474885
|
| [21] |
WANG G, NIU M Y, FU F W. Deterministic constructions of compressed sensing matrices based on codes[J]. Cryptography and Communications, 2019, 11(4): 759-775. doi: 10.1007/s12095-018-0328-z
|
| [22] |
YI R J, CUI C, WU B, et al. A new method of measurement matrix optimization for compressed sensing based on alternating minimization[J]. Mathematics, 2021, 9(4): 329.1-329.19.
|
| [23] |
YU L F, LI G, CHANG L P. Optimizing projection matrix for compressed sensing systems[C]//2011 8th International Conference on Information, Communications & Signal Processing. Singapore: IEEE, 2011: 1-5.
|
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YANG Liu, BAI Chaoyuan, FAN Pingzhi. Co-optimization Algorithm for Measurement Matrix of Compressive Sensing[J]. Journal of Southwest Jiaotong University, 2025, 60(2): 454-461. doi: 10.3969/j.issn.0258-2724.20230032
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