{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T18:20:34Z","timestamp":1772907634833,"version":"3.50.1"},"reference-count":60,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2021,12,10]],"date-time":"2021-12-10T00:00:00Z","timestamp":1639094400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A feature-based automatic modulation classification (FB-AMC) algorithm has been widely investigated because of its better performance and lower complexity. In this study, a deep learning model was designed to analyze the classification performance of FB-AMC among the most commonly used features, including higher-order cumulants (HOC), features-based fuzzy c-means clustering (FCM), grid-like constellation diagram (GCD), cumulative distribution function (CDF), and raw IQ data. A novel end-to-end modulation classifier based on deep learning, named CCT classifier, which can automatically identify unknown modulation schemes from extracted features using a general architecture, was proposed. Features except GCD are first converted into two-dimensional representations. Then, each feature is fed into the CCT classifier for modulation classification. In addition, Gaussian channel, phase offset, frequency offset, non-Gaussian channel, and flat-fading channel are also introduced to compare the performance of different features. Additionally, transfer learning is introduced to reduce training time. Experimental results showed that the features HOC, raw IQ data, and GCD obtained better classification performance than CDF and FCM under Gaussian channel, while CDF and FCM were less sensitive to the given phase offset and frequency offset. Moreover, CDF was an effective feature for AMC under non-Gaussian and flat-fading channels, and the raw IQ data can be applied to different channels\u2019 conditions. Finally, it showed that compared with the existing CNN and K-S classifiers, the proposed CCT classifier significantly improved the classification performance for MQAM at N = 512, reaching about 3.2% and 2.1% under Gaussian channel, respectively.<\/jats:p>","DOI":"10.3390\/s21248252","type":"journal-article","created":{"date-parts":[[2021,12,10]],"date-time":"2021-12-10T08:17:58Z","timestamp":1639124278000},"page":"8252","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Accuracy Analysis of Feature-Based Automatic Modulation Classification via Deep Neural Network"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6707-7457","authenticated-orcid":false,"given":"Zhan","family":"Ge","sequence":"first","affiliation":[{"name":"Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621000, China"}]},{"given":"Hongyu","family":"Jiang","sequence":"additional","affiliation":[{"name":"Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8174-9141","authenticated-orcid":false,"given":"Youwei","family":"Guo","sequence":"additional","affiliation":[{"name":"Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621000, China"}]},{"given":"Jie","family":"Zhou","sequence":"additional","affiliation":[{"name":"Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621000, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1049\/iet-com:20050176","article-title":"Survey of Automatic Modulation Classification Techniques: Classical Approaches and New Trends","volume":"1","author":"Dobre","year":"2007","journal-title":"IET Commun."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"5884","DOI":"10.1109\/TWC.2009.12.080883","article-title":"On the likelihood-based approach to modulation classification","volume":"8","author":"Hameed","year":"2009","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1109\/TSMCC.2010.2076347","article-title":"Likelihood-ratio approach to automatic modulation classification","volume":"41","author":"Xu","year":"2011","journal-title":"IEEE Trans. Syst. Man Cybern. C Appl. Rev."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1109\/26.823550","article-title":"Maximum-likelihood classification for digital amplitude-phase modulation","volume":"48","author":"Wei","year":"2000","journal-title":"IEEE Trans. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"8192","DOI":"10.1109\/TVT.2018.2839735","article-title":"Likelihood-based automatic modulation classification in OFDM with index modulation","volume":"67","author":"Zheng","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_6","unstructured":"Sills, J. (November, January 31). Maximum-likelihood modulation classification for PSK\/QAM. Proceedings of the MILCOM 1999, IEEE Military Communications, Conference Proceedings, Atlantic City, NJ, USA."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"19733","DOI":"10.1109\/ACCESS.2017.2746140","article-title":"Robust Automatic Modulation Classification Under Varying Noise Conditions","volume":"5","author":"Wu","year":"2017","journal-title":"IEEE Access"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Das, D., Anand, A., Bora, P., and Bhattacharjee, R. (2016, January 12\u201315). Cumulant based Automatic Modulation Classification of QPSK, OQPSK, \u03c0\/4-QPSK and 8-PSK in MIMO Environment. Proceedings of the 2016 International Conference on Signal Processing and Communications (SPCOM), Bangalore, India.","DOI":"10.1109\/SPCOM.2016.7746704"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1109\/26.664294","article-title":"Algorithms for automatic modulation recognition of communication signals","volume":"46","author":"Nandi","year":"1998","journal-title":"IEEE Trans. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1109\/26.837045","article-title":"Hierarchical Digital Modulation Classification using Cumulants","volume":"48","author":"Swami","year":"2000","journal-title":"IEEE Trans. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1109\/TCCN.2018.2824326","article-title":"Cooperative Cumulants-Based Modulation Classification in Distributed Networks","volume":"4","author":"Abdelbar","year":"2018","journal-title":"IEEE Trans. Cogn. Commun. Netw."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"946","DOI":"10.1109\/LCOMM.2018.2809732","article-title":"Robust automatic VHF modulation recognition based on deep neural networks","volume":"22","author":"Li","year":"2018","journal-title":"IEEE Commun. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Wu, H., Li, Y., Guo, Y., Zhou, L., and Meng, J. (2019, January 3\u20137). Modulation Classification of VHF Communication System based on CNN and Cyclic Spectrum Graphs. Proceedings of the 2019 Joint International Symposium on Electromagnetic Compatibility, Sapporo and Asia-Pacific International Symposium on Electromagnetic Compatibility (EMC Sapporo\/APEMC), Sapporo, Japan.","DOI":"10.23919\/EMCTokyo.2019.8893723"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Park, C., Choi, J., Nah, S., Jang, W., and Kim, D. (2008, January 17\u201320). Automatic Modulation Recognition of Digital Signals using Wavelet Features and SVM. Proceedings of the 2008 10th International Conference on Advanced Communication Technology, Gangwon, Korea.","DOI":"10.1109\/ICACT.2008.4493784"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1109\/LWC.2017.2697853","article-title":"Cyclic Feature based Modulation Recognition using Compressive Sensing","volume":"6","author":"Xie","year":"2017","journal-title":"IEEE Wirele. Commun. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Dobre, O., Bar-Ness, Y., and Su, W. (2004, January 21\u201325). Robust QAM modulation classification algorithm using cyclic cumulants. Proceedings of the 2004 IEEE Wireless Communications and Networking Conference, Atlanta, GA, USA.","DOI":"10.1109\/WCNC.2004.1311279"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1109\/LCOMM.2011.112311.112006","article-title":"Cyclostationarity-Based Robust Algorithms for QAM Signal Identification","volume":"16","author":"Dobre","year":"2012","journal-title":"IEEE Commun. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"79636","DOI":"10.1109\/ACCESS.2019.2921988","article-title":"Automatic modulation classification using compressive convolutional neural network","volume":"7","author":"Huang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1109\/TNNLS.2018.2850703","article-title":"Modulation classification based on signal constellation diagrams and deep learning","volume":"30","author":"Peng","year":"2019","journal-title":"IEEE Trans. Neural Netw. Learn Syst."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Wang, F., Wang, Y., and Chen, X. (2017, January 4\u20137). Graphic constellations and DBN based automatic modulation classification. Proceedings of the 2017 IEEE 85th Vehicular Technology Conference (VTC Spring), Sydney, NSW, Australia.","DOI":"10.1109\/VTCSpring.2017.8108670"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2324","DOI":"10.1109\/TCOMM.2010.08.090481","article-title":"Fast and robust modulation classification via Kolomogorov-Smirnov test","volume":"58","author":"Wang","year":"2010","journal-title":"IEEE Trans. Commun."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Im, C., Ahn, S., and Yoon, D. (2020, January 25\u201329). Modulation classification based on Kullback-Leibler divergence. Proceedings of the 2020 IEEE 15th International Conference on Advanced Trends in Radio electronics, Telecommunications and Computer Engineering (TCSET), Lviv-Slavske, Ukraine.","DOI":"10.1109\/TCSET49122.2020.235457"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Wang, F., and Chan, C. (2012, January 10\u201315). Variational-distance-based modulation classifier. Proceedings of the2012 IEEE International Conference on Communications (ICC), Ottawa, ON, Canada.","DOI":"10.1109\/ICC.2012.6364879"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1109\/LCOMM.2011.032811.110316","article-title":"Computationally Efficient Modulation Level Classification Based on Probability Distribution Distance Functions","volume":"15","author":"Urriza","year":"2011","journal-title":"IEEE Commun. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.sigpro.2013.05.024","article-title":"Genetric algorithm optimized distribution sampling test for QAM modulation classification","volume":"94","author":"Zhu","year":"2014","journal-title":"Signal Process."},{"key":"ref_26","first-page":"469","article-title":"Automatic modulation classification using convolutional neural network with features fusion of SPWVD and BJD","volume":"5","author":"Zhang","year":"2019","journal-title":"IEEE Trans. Signal Inf. Proc."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1109\/TWC.2016.2623716","article-title":"Low complexity automatic modulation classification based on order-statistics","volume":"16","author":"Han","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1885","DOI":"10.1109\/LCOMM.2013.082113.131131","article-title":"Optimal Discriminant Functions Based on Sampled Distribution Distance for Modulation Classification","volume":"17","author":"Urriza","year":"2013","journal-title":"IEEE Commun. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.dsp.2017.09.005","article-title":"Automatic modulation classification of digital modulation signals with stacked autoencoder","volume":"71","author":"Ali","year":"2017","journal-title":"Digit. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2162","DOI":"10.1109\/LCOMM.2017.2717821","article-title":"k-Sparse autoencoder-based automatic modulation classification with low complexity","volume":"21","author":"Ali","year":"2017","journal-title":"IEEE Commun. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"705021","DOI":"10.3389\/fpls.2021.705021","article-title":"Multi-Target Recognition of Bananas and Automatic Positioning for the Inflorescence Axis Cutting Point","volume":"12","author":"Wu","year":"2021","journal-title":"Front. Plant Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1626","DOI":"10.1109\/LSP.2017.2752459","article-title":"Automatic modulation classification using deep learning based on sparse autoencoders with nonnegativity constraints","volume":"24","author":"Ali","year":"2017","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"63760","DOI":"10.1109\/ACCESS.2019.2916833","article-title":"Deep Learning in Digital Modulation Recognition Using High Order Cumulants","volume":"7","author":"Xie","year":"2019","journal-title":"IEEE Access"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"O\u2019Shea, T., Corgan, J., and Clancy, T. (2016, January 2). Convolutional radio modulation recognition networks. Proceedings of the International Conference on Engineering Applications of Neural Networks, Aberdeen, UK.","DOI":"10.1007\/978-3-319-44188-7_16"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"4074","DOI":"10.1109\/TVT.2019.2900460","article-title":"Data-driven Deep Learning for Automatic Modulation Recognition in Cognitive Radios","volume":"68","author":"Wang","year":"2019","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"10760","DOI":"10.1109\/TVT.2018.2868698","article-title":"Automatic modulation classification: A deep learning enabled approach","volume":"67","author":"Meng","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Lee, J., Kim, J., Kim, B., Yoon, D., and Choi, J. (2017). Robust automatic modulation classification technique for fading channels via deep neural network. Entropy, 19.","DOI":"10.3390\/e19090454"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Hong, D., Zhang, Z., and Xu, X. (2017, January 3\u201316). Automatic modulation classification using recurrent neural networks. Proceedings of the 2017 3rd IEEE International Conference on Computer and Communications (ICCC), Chengdu, China.","DOI":"10.1109\/CompComm.2017.8322633"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"13521","DOI":"10.1109\/TVT.2020.3030018","article-title":"Automatic Modulation Classification Using CNN-LSTM Based Dual-Stream Structure","volume":"69","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1109\/TVT.2019.2951594","article-title":"Deep neural network for robust modulation classification under uncertain noise conditions","volume":"69","author":"Hu","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1109\/TCCN.2018.2835460","article-title":"Deep learning models for wireless signal classification with distributed lowcost spectrum sensors","volume":"4","author":"Rajendran","year":"2018","journal-title":"IEEE Trans. Cogn. Commun. Netw."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Zhang, D., Ding, W., Zhang, B., Xie, C., Li, H., Liu, C., and Han, J. (2018). Automatic modulation classification based on deep learning for unmaned aerial vehicles. Sensors, 18.","DOI":"10.3390\/s18030924"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"15713","DOI":"10.1109\/ACCESS.2018.2815741","article-title":"Digital Signal Modulation Classification with Data Augmentation Using Generative Adversarial Nets in Cognitive Radio Networks","volume":"6","author":"Tang","year":"2018","journal-title":"IEEE Access"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"106350","DOI":"10.1016\/j.compag.2021.106350","article-title":"Collision-free path planning for a guava-harvesting robot based on recurrent deep reinforcement learning","volume":"188","author":"Lin","year":"2021","journal-title":"Comput. Electron. Agric."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Dobre, O.A., and Hameed, F. (2006, January 7\u201310). Likelihood-Based Algorithms for Linear Digital Modulation Classification in Fading Channels. Proceedings of the 2006 Canadian Conference on Electrical and Computer Engineering, Ottawa, ON, Canada.","DOI":"10.1109\/CCECE.2006.277525"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1109\/LCOMM.2009.12.091711","article-title":"Automatic modulation classification algorithm using higher-order cumulants under real-world channel conditions","volume":"13","author":"Orlic","year":"2009","journal-title":"IEEE Commun. Lett."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2051","DOI":"10.1109\/TCOMM.2011.051711.100184","article-title":"Maximum-likelihood classification of digital amplitude-phase modulation signals in flat fading non-Gaussian channels","volume":"59","author":"Chavali","year":"2011","journal-title":"IEEE Trans. Commun."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1109\/LCOMM.2019.2894400","article-title":"A faster maximum-likelihood modulation classification in flat fading non-Gaussian channels","volume":"23","author":"Chen","year":"2019","journal-title":"IEEE Commun. Lett."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"2408","DOI":"10.1109\/TCOMM.2013.041113.120548","article-title":"Classification of digital amplitude phase modulated signals in time-correlated non-Gaussian channels","volume":"61","author":"Chavali","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Helmy, M., and Zaki, F. (2009, January 14\u201316). Identification of Linear bi-dimensional digital modulation schemes via clustering algorithms. Proceedings of the 2009 International Conference on Computer Engineering & Systems, Cairo, Egypt.","DOI":"10.1109\/ICCES.2009.5383234"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Kalam, L., and Theagarajan, L. (May, January 28). Multistage Clustering Based Automatic Modulation Classification. Proceedings of the 2019 IEEE 89th Vehicular Technology Conference (VTC2019-Spring), Kuala Lumpur, Malaysia.","DOI":"10.1109\/VTCSpring.2019.8746390"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Zhang, H., Liao, H., and Gan, L. (2014, January 5\u20137). Robust classification of quadrature amplitude modulation constellations based on GMM. Proceedings of the 2014 IEEE International Conference on Communication Problem-Solving, Beijing, China.","DOI":"10.1109\/ICCPS.2014.7062342"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/0167-8655(90)90050-C","article-title":"Cluster validity based on the hard tendency of the fuzzy classification","volume":"11","author":"FRivera","year":"1990","journal-title":"Pattern Recognit. Lett."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Lea, C., Vidal, R., Reiter, A., and Hager, G. (2016, January 8\u201316). Temporal convolutional networks: A unified approach to action segmentation. Proceedings of the European Conference on Computer Vision, Amsterdam, Netherlands.","DOI":"10.1007\/978-3-319-49409-8_7"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Pandey, A., and Wang, D. (2019, January 12\u201317). TCNN: Temporal Convolutional Neural Network for Real-time Speech Enhancement in the Time Domain. Proceedings of the 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brighton, UK.","DOI":"10.1109\/ICASSP.2019.8683634"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.1109\/TKDE.2009.191","article-title":"A survey on transfer learning","volume":"22","author":"Pan","year":"2010","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1098","DOI":"10.1109\/LSP.2014.2323241","article-title":"Blind Modulation Classification Algorithm for Single and Multiple-Antenna Systems over Frequency-Selective Channels","volume":"21","author":"Marey","year":"2014","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.patrec.2020.07.028","article-title":"Deep k-Means: Jointly clustering with k-Means and learning representations","volume":"138","author":"Farda","year":"2020","journal-title":"Pattern Recognit. Lett."},{"key":"ref_59","first-page":"1420","article-title":"Deep Fuzzy Clustering\u2014A Representation Learning Approach","volume":"28","author":"Feng","year":"2020","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1109\/TNSE.2018.2848960","article-title":"Channel State Information Prediction for 5G Wireless Communications: A Deep Learning Approach","volume":"7","author":"Luo","year":"2020","journal-title":"IEEE Trans. Netw. Sci. Eng."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/24\/8252\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:44:50Z","timestamp":1760168690000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/24\/8252"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,10]]},"references-count":60,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["s21248252"],"URL":"https:\/\/doi.org\/10.3390\/s21248252","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,10]]}}}