{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:46:36Z","timestamp":1760237196297,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,3,20]],"date-time":"2020-03-20T00:00:00Z","timestamp":1584662400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003453","name":"Natural Science Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2018A030313736"],"award-info":[{"award-number":["2018A030313736"]}],"id":[{"id":"10.13039\/501100003453","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Perfect channel state information (CSI) is required in most of the classical physical-layer security techniques, while it is difficult to obtain the ideal CSI due to the time-varying wireless fading channel. Although imperfect CSI has a great impact on the security of MIMO communications, deep learning is becoming a promising solution to handle the negative effect of imperfect CSI. In this work, we propose two types of deep learning-based secure MIMO detectors for heterogeneous networks, where the macro base station (BS) chooses the null-space eigenvectors to prevent information leakage to the femto BS. Thus, the bit error rate of the associated user is adopted as the metric to evaluate the system performance. With the help of deep convolutional neural networks (CNNs), the macro BS obtains the refined version from the imperfect CSI. Simulation results are provided to validate the proposed algorithms. The impacts of system parameters, such as the correlation factor of imperfect CSI, the normalized doppler frequency, the number of antennas is investigated in different setup scenarios. The results show that considerable performance gains can be obtained from the deep learning-based detectors compared with the classical maximum likelihood algorithm.<\/jats:p>","DOI":"10.3390\/s20061730","type":"journal-article","created":{"date-parts":[[2020,3,20]],"date-time":"2020-03-20T07:29:07Z","timestamp":1584689347000},"page":"1730","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Deep Learning-Based Secure MIMO Communications with Imperfect CSI for Heterogeneous Networks"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7760-5663","authenticated-orcid":false,"given":"Dan","family":"Deng","sequence":"first","affiliation":[{"name":"School of Information Engineering, Guangzhou Panyu Polytechnic, Guangzhou 511406, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0907-6517","authenticated-orcid":false,"given":"Xingwang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454000, China"}]},{"given":"Ming","family":"Zhao","sequence":"additional","affiliation":[{"name":"CAS Key Laboratory of Wireless-Optical Communications, University of Science and Technology of China, Hefei 230027, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9784-3703","authenticated-orcid":false,"given":"Khaled M.","family":"Rabie","sequence":"additional","affiliation":[{"name":"Department of Engineering, Manchester Metropolitan University, Manchester M15 6BH, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8632-7439","authenticated-orcid":false,"given":"Rupak","family":"Kharel","sequence":"additional","affiliation":[{"name":"Department of Computing and Mathematics, Manchester Metropolitan University, Manchester M15 6BH, UK"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"54508","DOI":"10.1109\/ACCESS.2019.2913438","article-title":"Enhancing Information Security via Physical Layer Approaches in Heterogeneous IoT With Multiple Access Mobile Edge Computing in Smart City","volume":"7","author":"Wang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_2","first-page":"680","article-title":"Residual Transceiver Hardware Impairments on Cooperative NOMA Networks","volume":"19","author":"Li","year":"2020","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_3","first-page":"13329","article-title":"A Unified Framework for HS-UAV NOMA Networks: Performance Analysis and Location Optimization","volume":"8","author":"Li","year":"2020","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"6585","DOI":"10.1109\/TVT.2018.2812742","article-title":"Bandwidth Efficiency and Service Adaptiveness Oriented Data Dissemination in Heterogeneous Vehicular Networks","volume":"67","author":"Dai","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"11339","DOI":"10.1109\/TVT.2017.2737028","article-title":"Resource Allocation for Information-Centric Virtualized Heterogeneous Networks With In-Network Caching and Mobile Edge Computing","volume":"66","author":"Zhou","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Zhong, Z., Peng, J., Huang, K., and Zhong, Z. (2016, January 15\u201318). Analysis on Physical-Layer Security for Internet of Things in Ultra Dense Heterogeneous Networks. Proceedings of the 2016 IEEE International Conference on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData), Chengdu, China.","DOI":"10.1109\/iThings-GreenCom-CPSCom-SmartData.2016.34"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1204","DOI":"10.1109\/TCOMM.2016.2519402","article-title":"Physical Layer Security in Heterogeneous Cellular Networks","volume":"64","author":"Wang","year":"2016","journal-title":"IEEE Trans. Commun."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1109\/JSAC.2018.2825560","article-title":"A Survey of Physical Layer Security Techniques for 5G Wireless Networks and Challenges Ahead","volume":"36","author":"Wu","year":"2018","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"7982","DOI":"10.1109\/TWC.2017.2755640","article-title":"Physical Layer Security in Heterogeneous Networks With Jammer Selection and Full-Duplex Users","volume":"16","author":"Tang","year":"2017","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Ma, Z., Lu, Y., Shen, L., Liu, Y., and Wang, N. (2018, January 18\u201320). Cooperative Jamming and Relay Beamforming Design for Physical Layer Secure Two-Way Relaying. Proceedings of the 2018 International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery (CyberC), Zhengzhou, China.","DOI":"10.1109\/CyberC.2018.00066"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1771","DOI":"10.1109\/TCOMM.2015.2419634","article-title":"Artificial Noise: Transmission Optimization in Multi-Input Single-Output Wiretap Channels","volume":"63","author":"Yang","year":"2015","journal-title":"IEEE Trans. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4347","DOI":"10.1109\/TCOMM.2015.2474390","article-title":"Multi-Antenna Transmission With Artificial Noise Against Randomly Distributed Eavesdroppers","volume":"63","author":"Zheng","year":"2015","journal-title":"IEEE Trans. Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"6437","DOI":"10.1109\/TCOMM.2018.2859954","article-title":"Physical Layer Security in Heterogeneous Networks With Pilot Attack: A Stochastic Geometry Approach","volume":"66","author":"Wang","year":"2018","journal-title":"IEEE Trans. Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"68920","DOI":"10.1109\/ACCESS.2018.2880339","article-title":"Caching-Aided Physical Layer Security in Wireless Cache-Enabled Heterogeneous Networks","volume":"6","author":"Zhao","year":"2018","journal-title":"IEEE Access"},{"key":"ref_15","first-page":"1","article-title":"Foundation study on wireless big data: Concept, mining, learning and practices","volume":"15","author":"Zhu","year":"2018","journal-title":"Chin. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1002\/ett.2985","article-title":"Secure communications in multiple amplify-and-forward relay networks with outdated channel state information","volume":"27","author":"Deng","year":"2016","journal-title":"Trans. Emerging Telecommun. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1278","DOI":"10.1109\/TCOMM.2012.032012.110430","article-title":"Amplify-and-Forward Relay Selection with Outdated Channel Estimates","volume":"60","author":"Michalopoulos","year":"2012","journal-title":"IEEE Trans. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"638","DOI":"10.1109\/LCOMM.2012.031212.112448","article-title":"Outage probability analysis and power allocation for two-way relay networks with user selection and outdated channel state information","volume":"16","author":"Fan","year":"2012","journal-title":"IEEE Commun. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1109\/JSYST.2019.2919654","article-title":"Performance Analysis of Impaired SWIPT NOMA Relaying Networks Over Imperfect Weibull Channels","volume":"99","author":"Li","year":"2020","journal-title":"IEEE Syst. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/LWC.2019.2939309","article-title":"Full-Duplex Cooperative NOMA Relaying Systems With I\/Q Imbalance and Imperfect SIC","volume":"9","author":"Li","year":"2020","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"10605","DOI":"10.1109\/ACCESS.2017.2705018","article-title":"Effective Rate of MISO Systems Over \u03ba - \u03bc Shadowed Fading Channels","volume":"5","author":"Li","year":"2017","journal-title":"IEEE Access"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1447","DOI":"10.1109\/TSP.2012.2237167","article-title":"Analysis and Design of Wireless Ad Hoc Networks With Channel Estimation Errors","volume":"61","author":"Wu","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1098","DOI":"10.1109\/TSP.2008.2009270","article-title":"Optimizing Training Lengths and Training Intervals in Time-Varying Fading Channels","volume":"57","author":"Savazzi","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2837","DOI":"10.1109\/TVT.2011.2151216","article-title":"User-Specified Training Symbol Placement for Channel Prediction in TDD MIMO Systems","volume":"60","author":"Han","year":"2011","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1109\/LCOMM.2019.2898944","article-title":"Deep Learning-Based Channel Estimation","volume":"23","author":"Soltani","year":"2019","journal-title":"IEEE Commun. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4326","DOI":"10.1109\/TCOMM.2019.2903811","article-title":"One-Bit OFDM Receivers via Deep Learning","volume":"67","author":"Balevi","year":"2019","journal-title":"IEEE Trans. Commun."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Wu, Y., Li, X., and Fang, J. (2018, January 25\u201328). A Deep Learning Approach for Modulation Recognition via Exploiting Temporal Correlations. Proceedings of the 2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), kalamata, Greece.","DOI":"10.1109\/SPAWC.2018.8445938"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Yuan, J., Ngo, H.Q., and Matthaiou, M. (2020). Machine Learning-Based Channel Prediction in Massive MIMO with Channel Aging. IEEE Trans. Wireless Commun., 1.","DOI":"10.1109\/SPAWC.2019.8815557"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Amirabadi, M.A. (2020). Deep learning for channel estimation in FSO communication system. arXiv.","DOI":"10.1016\/j.optcom.2019.124989"},{"key":"ref_30","unstructured":"Amirabadi, M.A. (2020). A deep learning based solution for imperfect CSI problem in correlated FSO communication channel. arXiv."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2170","DOI":"10.1109\/TVT.2015.2419318","article-title":"Optimal Transmission With Artificial Noise in MISOME Wiretap Channels","volume":"65","author":"Yang","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Fritschek, R., Schaefer, R.F., and Wunder, G. (2019, January 20\u201324). Deep Learning for the Gaussian Wiretap Channel. Proceedings of the 2019 IEEE International Conference on Communications (ICC), Shanghai, China.","DOI":"10.1109\/ICC.2019.8761681"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Xing, J., Lv, T., and Zhang, X. (2019, January 8\u201311). Cooperative Relay Based on Machine Learning for Enhancing Physical Layer Security. Proceedings of the 2019 IEEE 30th Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), Istanbul, Turkey.","DOI":"10.1109\/PIMRC.2019.8904319"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"6994","DOI":"10.1109\/TCOMM.2019.2930247","article-title":"Deep Reinforcement Learning-Enabled Secure Visible Light Communication Against Eavesdropping","volume":"67","author":"Xiao","year":"2019","journal-title":"IEEE Trans. Commun."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/LWC.2018.2881976","article-title":"Learning-Based Wireless Powered Secure Transmission","volume":"8","author":"He","year":"2019","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1109\/TIFS.2017.2737968","article-title":"A Secure Mobile Crowdsensing Game With Deep Reinforcement Learning","volume":"13","author":"Xiao","year":"2018","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Simon, M.K., and Alouini, M.S. (2005). Digital Communication Over Fading, Wiley. [2nd ed.].","DOI":"10.1002\/0471715220"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2567","DOI":"10.1109\/LAWP.2019.2943413","article-title":"Antenna Correlation Under Geometry-Based Stochastic Channel Models","volume":"18","author":"Ji","year":"2019","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/MCOM.2019.1800581","article-title":"Exploiting Wireless Channel State Information Structures Beyond Linear Correlations: A Deep Learning Approach","volume":"57","author":"Jiang","year":"2019","journal-title":"IEEE Commun. Mag."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Jayne, C., and Iliadis, L. (2016). Convolutional Radio Modulation Recognition Networks. Engineering Applications of Neural Networks, Springer International Publishing.","DOI":"10.1007\/s00521-016-2318-4"},{"key":"ref_41","unstructured":"Simonyan, K., and Zisserman, A. (2015, January 7\u20139). Very Deep Convolutional Networks for Large-Scale Image Recognition. Proceedings of the International Conference on Learning Representations, San Diego, CA, USA."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Jian, S. (July, January 26). Deep Residual Learning for Image Recognition. Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_43","unstructured":"Goodfellow, I., Bengio, Y., and Courville, A. (2016). Deep Learning, MIT Press."},{"key":"ref_44","unstructured":"Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G.S., Davis, A., Dean, J., and Devin, M. (2020, March 20). TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems. Available online: http:\/\/download.tensorflow.org\/paper\/whitepaper2015.pdf."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/6\/1730\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:09:55Z","timestamp":1760173795000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/6\/1730"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,20]]},"references-count":44,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["s20061730"],"URL":"https:\/\/doi.org\/10.3390\/s20061730","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,3,20]]}}}