{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:58:55Z","timestamp":1760151535032,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T00:00:00Z","timestamp":1648684800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Compressed sensing theory has been widely used for data aggregation in WSNs due to its capability of containing much information but with light load of transmission. However, there still exist some issues yet to be solved. For instance, the measurement matrix is complex to construct, and it is difficult to implement in hardware and not suitable for WSNs with limited node energy. To solve this problem, a random measurement matrix construction method based on Time Division Multiple Access (TDMA) is proposed based on the sparse random measurement matrix combined with the data transmission method of the TDMA of nodes in the cluster. The reconstruction performance of the number of non-zero elements per column in this matrix construction method for different signals was compared and analyzed through extensive experiments. It is demonstrated that the proposed matrix can not only accurately reconstruct the original signal, but also reduce the construction complexity from O(MN) to O(d2N) (d\u226aM), on the premise of achieving the same reconstruction effect as that of the sparse random measurement matrix. Moreover, the matrix construction method is further optimized by utilizing the correlation theory of nested matrices. A TDMA-based semi-random and semi-deterministic measurement matrix construction method is also proposed, which significantly reduces the construction complexity of the measurement matrix from O(d2N) to O(dN), and improves the construction efficiency of the measurement matrix. The findings in this work allow more flexible and efficient compressed sensing for data aggregation in WSNs.<\/jats:p>","DOI":"10.3390\/e24040493","type":"journal-article","created":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T21:33:03Z","timestamp":1648762383000},"page":"493","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Compressed Sensing Measurement Matrix Construction Method Based on TDMA for Wireless Sensor Networks"],"prefix":"10.3390","volume":"24","author":[{"given":"Yan","family":"Yang","sequence":"first","affiliation":[{"name":"School of Electronic Information, Northwestern Polytechnical University, Xi\u2019an 710000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haoqi","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Electronic Information, Northwestern Polytechnical University, Xi\u2019an 710000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3331-559X","authenticated-orcid":false,"given":"Jing","family":"Hou","sequence":"additional","affiliation":[{"name":"School of Electronic Information, Northwestern Polytechnical University, Xi\u2019an 710000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,31]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Forster, A. (2016). Introduction to Wireless Sensor Networks, John Wiley & Sons.","key":"ref_1","DOI":"10.1002\/9781119345343"},{"doi-asserted-by":"crossref","unstructured":"Singh, P.K., and Paprzycki, M. (2020). Introduction on wireless sensor networks issues and challenges in current era. Handbook of Wireless Sensor Networks: Issues and Challenges in Current Scenario\u2019s, Springer.","key":"ref_2","DOI":"10.1007\/978-3-030-40305-8"},{"doi-asserted-by":"crossref","unstructured":"Roy, N.R., and Chandra, P. (2019, January 21\u201322). Analysis of data aggregation techniques in WSN. Proceedings of the International Conference on Innovative Computing and Communications, Ostrava, Czech Republic.","key":"ref_3","DOI":"10.1007\/978-981-15-0324-5_48"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1851","DOI":"10.1002\/int.22363","article-title":"Multisource basic probability assignment fusion based on information quality","volume":"36","author":"Li","year":"2021","journal-title":"Int. J. Intell. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7443","DOI":"10.1002\/int.22593","article-title":"Combining conflicting evidence based on Pearson correlation coefficient and weighted graph","volume":"36","author":"Deng","year":"2021","journal-title":"Int. J. Intell. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.inffus.2020.02.003","article-title":"Multi-classifier information fusion in risk analysis","volume":"60","author":"Pan","year":"2020","journal-title":"Inf. Fusion"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2063","DOI":"10.1109\/TFUZZ.2019.2929024","article-title":"Improved fuzzy Bayesian network-based risk analysis with interval-valued fuzzy sets and D\u2013S evidence theory","volume":"28","author":"Pan","year":"2019","journal-title":"IEEE Trans. Fuzzy Syst."},{"doi-asserted-by":"crossref","unstructured":"Eldar, Y.C., and Kutyniok, G. (2012). Compressed Sensing: Theory and Applications, Cambridge University Press.","key":"ref_8","DOI":"10.1017\/CBO9780511794308"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3629","DOI":"10.1109\/TIT.2007.904835","article-title":"Joint Source-Channel Communication for Distributed Estimation in Sensor Networks","volume":"53","author":"Bajwa","year":"2007","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1016\/j.sigpro.2005.05.029","article-title":"Extensions of compressed sensing","volume":"86","author":"Tsaig","year":"2006","journal-title":"Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/s00365-007-9005-8","article-title":"Uniform uncertainty principle for Bernoulli and subgaussian ensembles","volume":"28","author":"Mendelson","year":"2008","journal-title":"Constr. Approx."},{"doi-asserted-by":"crossref","unstructured":"Bajwa, W.U., Haupt, J.D., Raz, G.M., Wright, S.J., and Nowak, R.D. (2007, January 26\u201329). Toeplitz-structured compressed sensing matrices. Proceedings of the IEEE\/SP 14th Workshop on Statistical Signal Processing, Madison, WI, USA.","key":"ref_12","DOI":"10.1109\/SSP.2007.4301266"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"918","DOI":"10.1016\/j.jco.2007.04.002","article-title":"Deterministic constructions of compressed sensing matrices","volume":"23","author":"DeVore","year":"2007","journal-title":"J. Complex."},{"unstructured":"Berinde, R., and Indyk, P. (2008). Sparse recovery using sparse random matrices. LATIN, preprint.","key":"ref_14"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1109\/LSP.2010.2052243","article-title":"Compressive sensing with chaotic sequence","volume":"17","author":"Yu","year":"2010","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.acha.2008.08.002","article-title":"Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery","volume":"26","author":"Applebaum","year":"2009","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"56081","DOI":"10.1109\/ACCESS.2019.2913396","article-title":"V-matrix-based scalable data aggregation scheme in WSN","volume":"7","author":"Wang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1186\/s13638-018-1176-4","article-title":"A kind of effective data aggregating method based on compressive sensing for wireless sensor network","volume":"2018","author":"Zhang","year":"2018","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"106875","DOI":"10.1016\/j.measurement.2019.106875","article-title":"Energy-efficient data gathering algorithm relying on compressive sensing in lossy WSNs","volume":"147","author":"Zhang","year":"2019","journal-title":"Measurement"},{"doi-asserted-by":"crossref","unstructured":"Qiao, J., and Zhang, X. (2016, January 1\u20133). The design of a dual-structured measurement matrix in compressed sensing. Proceedings of the 2016 IEEE International Conference on Information and Automation (ICIA), Ningbo, China.","key":"ref_20","DOI":"10.1109\/ICInfA.2016.7831819"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2448","DOI":"10.1108\/EC-09-2015-0269","article-title":"A novel compressive sensing method based on SVD sparse random measurement matrix in wireless sensor network","volume":"33","author":"Ma","year":"2016","journal-title":"Eng. Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","article-title":"Compressed sensing","volume":"52","author":"Donoho","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/MSP.2007.914731","article-title":"An introduction to compressive sampling","volume":"25","author":"Wakin","year":"2008","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4655","DOI":"10.1109\/TIT.2007.909108","article-title":"Signal recovery from random measurements via orthogonal matching pursuit","volume":"53","author":"Tropp","year":"2007","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_25","first-page":"1360","article-title":"A Construction Algorithm of Measurement Matrix with Low Power Average Column Coherence","volume":"42","author":"Li","year":"2014","journal-title":"Acta Electron. Sin."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.acha.2010.10.002","article-title":"Compressed Sensing with Coherent and Redundant Dictionaries","volume":"31","author":"Candes","year":"2011","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.sigpro.2015.12.016","article-title":"The construction of measurement matrices based on block weighing matrix in compressed sensing","volume":"123","author":"Zhao","year":"2016","journal-title":"Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1016\/j.cam.2018.11.011","article-title":"Circulant preconditioners for functions of Hermitian Toeplitz matrices","volume":"352","author":"Hon","year":"2019","journal-title":"J. Comput. Appl. Math."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"100","DOI":"10.2174\/1872212115666201230091420","article-title":"Contactless Core-temperature Monitoring by Infrared Thermal Sensor using Mean Absolute Error Analysis","volume":"15","author":"Malallah","year":"2021","journal-title":"Recent Pat. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1647","DOI":"10.1007\/s00500-019-03993-6","article-title":"Correlation coefficients for T-spherical fuzzy sets and their applications in clustering and multi-attribute decision making","volume":"24","author":"Ullah","year":"2020","journal-title":"Soft Comput."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1007\/s40815-020-00803-2","article-title":"Evaluation of the performance of search and rescue robots using T-spherical fuzzy hamacher aggregation operators","volume":"22","author":"Ullah","year":"2020","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_32","first-page":"72","article-title":"CEQD: A complex mass function to predict interference effects","volume":"5","author":"Xiao","year":"2021","journal-title":"IEEE Trans. Cybern."},{"key":"ref_33","first-page":"1","article-title":"CaFtR: A fuzzy complex event processing method","volume":"11","author":"Xiao","year":"2021","journal-title":"Int. J. Fuzzy Syst."},{"unstructured":"(2021, June 03). Available online: https:\/\/www.kaggle.com\/garystafford\/environmental-sensor-data-132k.","key":"ref_34"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/4\/493\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:47:37Z","timestamp":1760136457000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/4\/493"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,31]]},"references-count":34,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["e24040493"],"URL":"https:\/\/doi.org\/10.3390\/e24040493","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,3,31]]}}}