{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T12:56:43Z","timestamp":1778158603069,"version":"3.51.4"},"reference-count":22,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,5,31]],"date-time":"2022-05-31T00:00:00Z","timestamp":1653955200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China under Grant","doi-asserted-by":"publisher","award":["61801372"],"award-info":[{"award-number":["61801372"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In MIMO-OFDM systems, pilot design and estimation algorithm jointly determine the reliability and effectiveness of pilot-based channel estimation methods. In order to improve the channel estimation accuracy with less pilot overhead, a deep learning scheme for joint pilot design and channel estimation is proposed. This new hybrid network structure is named CAGAN, which is composed of a concrete autoencoder (concrete AE) and a conditional generative adversarial network (cGAN). We first use concrete AE to find and select the most informative position in the time-frequency grid to achieve pilot optimization design and then input the optimized pilots to cGAN to complete channel estimation. Simulation experiments show that the CAGAN scheme outperforms the traditional LS and MMSE estimation methods with fewer pilots, and has good robustness to environmental noise.<\/jats:p>","DOI":"10.3390\/s22114188","type":"journal-article","created":{"date-parts":[[2022,5,31]],"date-time":"2022-05-31T09:24:29Z","timestamp":1653989069000},"page":"4188","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Deep Learning for Joint Pilot Design and Channel Estimation in MIMO-OFDM Systems"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1733-079X","authenticated-orcid":false,"given":"Xiao-Fei","family":"Kang","sequence":"first","affiliation":[{"name":"Affiliation College of Communication and Information Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}]},{"given":"Zi-Hui","family":"Liu","sequence":"additional","affiliation":[{"name":"Affiliation College of Communication and Information Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6729-9540","authenticated-orcid":false,"given":"Meng","family":"Yao","sequence":"additional","affiliation":[{"name":"Affiliation College of Communication and Information Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1317","DOI":"10.1109\/TSP.2021.3056591","article-title":"Bilinear Channel Estimation for MIMO OFDM: Lower Bounds and Training Sequence Optimization","volume":"69","author":"Elnakeeb","year":"2021","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ngo, H.Q., and Larsson, E.G. (2015, January 19\u201324). Blind estimation of effective downlink channel gains in massive MIMO. Proceedings of the 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), South Brisbane, Australia.","DOI":"10.1109\/ICASSP.2015.7178505"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2972","DOI":"10.1109\/TSP.2018.2821640","article-title":"Blind Estimation of Sparse Broadband Massive MIMO Channels with Ideal and One-bit ADCs","volume":"66","author":"Mezghani","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1109\/TWC.2006.1618919","article-title":"A new derivation of least-squares-fitting principle for OFDM channel estimation","volume":"5","author":"Chang","year":"2006","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_5","unstructured":"Minn, H., Bhargava, V.K., and Letaief, K.B. (2004, January 20\u201324). A combined timing and frequency synchronization and channel estimation for OFDM. Proceedings of the 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577), Paris, France."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Imko, M., Mehlfhrer, C., Wrulich, M., and Rupp, M. (2010, January 18\u201320). Doubly dispersive channel estimation with scalable complexity. Proceedings of the 2010 International ITG Workshop on Smart Antennas (WSA), Bremen, Germany.","DOI":"10.1109\/WSA.2010.5456443"},{"key":"ref_7","first-page":"612","article-title":"Pilot Allocation for Sparse Channel Estimation in MIMO-OFDM Systems","volume":"60","author":"He","year":"2013","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_8","first-page":"1027","article-title":"Experimental Demonstration of Compressive Sensing-Based Channel Estimation for MIMO-OFDM VLC","volume":"9","author":"Lin","year":"2020","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"8549","DOI":"10.1109\/TVT.2018.2851783","article-title":"Deep learning for super-resolution channel estimation and DOA estimation based massive MIMO systems","volume":"67","author":"Huang","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"852","DOI":"10.1109\/LWC.2018.2832128","article-title":"Deep Learning-Based Channel Estimation for Beamspace mmWave Massive MIMO Systems","volume":"7","author":"He","year":"2018","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2905","DOI":"10.1109\/TSP.2018.2799164","article-title":"Learning the MMSE Channel Estimator","volume":"66","author":"Neumann","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"748","DOI":"10.1109\/LWC.2018.2818160","article-title":"Deep Learning for Massive MIMO CSI Feedback","volume":"7","author":"Wen","year":"2018","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1109\/LWC.2018.2874264","article-title":"Deep learning-based CSI feedback approach. for time-varying massive MIMO channels","volume":"8","author":"Wang","year":"2019","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Mao, H., Lu, H., Lu, Y., and Zhu, D. (2019, January 21\u201323). RoemNet: Robust Meta Learning Based Channel Estimation in OFDM Systems. Proceedings of the ICC 2019 IEEE International Conference on Communications (ICC), Shanghai, China.","DOI":"10.1109\/ICC.2019.8761319"},{"key":"ref_15","unstructured":"Abid, A., Balin, M.F., and Zou, J. (2019). Concrete Autoencoders for Differentiable Feature Selection and Reconstruction. arXiv."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"106748","DOI":"10.1016\/j.knosys.2021.106748","article-title":"Unsupervised feature selection via transformed auto-encoder","volume":"215","author":"Zhang","year":"2021","journal-title":"Knowl.-Based Syst."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Cai, D., Zhang, C., and He, X. (2010, January 24\u201328). Unsupervised feature selection for multi-cluster data. Proceedings of the Sixteenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Washington, DC, USA.","DOI":"10.1145\/1835804.1835848"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Han, K., Wang, Y., Zhang, C., Li, C., and Xu, C. (2018, January 15\u201320). Autoencoder inspired unsupervised feature selection. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Calgary, AB, Canada.","DOI":"10.1109\/ICASSP.2018.8462261"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"854","DOI":"10.1109\/LCOMM.2020.3035326","article-title":"Channel Estimation for One-Bit. Multiuser Massive MIMO Using Conditional GAN","volume":"25","author":"Dong","year":"2020","journal-title":"IEEE Commun. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Yang, A., Sun, P., Rakesh, T., Sun, B., and Qin, F. (2021). Deep Learning Based OFDM Channel Estimation Using Frequency-Time Division and Attention Mechanism. arXiv.","DOI":"10.1109\/GCWkshps52748.2021.9682149"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1186\/1687-6180-2011-29","article-title":"The vienna lte simulators\u2014Enabling reproducibility in wireless communications research","volume":"2011","author":"Mehlfuhrer","year":"2011","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1109\/LCOMM.2019.2898944","article-title":"Deep Learning-Based Channel Estimation in OFDM Systems","volume":"23","author":"Soltani","year":"2019","journal-title":"IEEE Commun. Lett."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/11\/4188\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:22:48Z","timestamp":1760138568000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/11\/4188"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,31]]},"references-count":22,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["s22114188"],"URL":"https:\/\/doi.org\/10.3390\/s22114188","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,31]]}}}