{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T12:32:53Z","timestamp":1763728373978,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,10]],"date-time":"2023-01-10T00:00:00Z","timestamp":1673308800000},"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>Nonorthogonal multiple access (NOMA) is a relevant technology for realizing the primary goals of next-generation wireless networks, such as high connectivity and stability. Because a rising number of users are becoming connected, user data security has become a critical issue. Many chaotic communication systems have been established to address this important issue via exhibition of affordable physical-layer-security solutions. In this study, we propose a chaotic downlink NOMA (C-DL-NOMA) system over the additive white Gaussian noise and Rayleigh-fading channels to enhance the security of the DL-NOMA system. The proposed algorithm is based on a coherent analog modulation technique that combines various chaotic maps for chaotic masking of encrypted data. On the transmitter, chaotic encryption was used for transmitted data with fixed power-allocation-level control, whereas on the receiver, successive interference-cancellation demodulation was utilized to detect multiple users, after which chaotic decryption was performed. Simulation results were evaluated based on security analyses, such as statistical analysis (histogram and correlation analyses and information entropy), bit-error-rate performance, and achievable-data-rate performance. According to these security analyses and numerical results, the proposed C-DL-NOMA system outperformed traditional unencrypted NOMA systems.<\/jats:p>","DOI":"10.3390\/e25010140","type":"journal-article","created":{"date-parts":[[2023,1,11]],"date-time":"2023-01-11T02:06:03Z","timestamp":1673402763000},"page":"140","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Physical-Layer Security in Power-Domain NOMA Based on Different Chaotic Maps"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6206-7265","authenticated-orcid":false,"given":"Mariam","family":"Abu Al-Atta","sequence":"first","affiliation":[{"name":"Electronics and Communications Department, Faculty of Engineering, Delta University for Science and Technology, Gamsaa 35712, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karim A.","family":"Said","sequence":"additional","affiliation":[{"name":"Electronics and Communication Engineering Department, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed A.","family":"Mohamed","sequence":"additional","affiliation":[{"name":"Electronics and Communication Engineering Department, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Walid","family":"Raslan","sequence":"additional","affiliation":[{"name":"Electronics and Communications Department, Faculty of Engineering, Delta University for Science and Technology, Gamsaa 35712, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,10]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Zhang, Z., Sun, H., and Lei, X. (2020). Non-orthogonal Multiple Access. Encycl. Wirel. Netw., 1\u20134.","key":"ref_1","DOI":"10.1007\/978-3-319-32903-1_57-1"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"102867","DOI":"10.1109\/ACCESS.2019.2930990","article-title":"Performance enhancement using receive diversity with power adaptation in the NOMA system","volume":"7","author":"Kim","year":"2019","journal-title":"IEEE Access"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1109\/MCOM.2017.1601065","article-title":"Non-orthogonal multiple access in multi-cell networks: Theory, performance, and practical challenges","volume":"55","author":"Shin","year":"2017","journal-title":"IEEE Commun. Mag."},{"doi-asserted-by":"crossref","unstructured":"Ghous, M., Abbas, Z.H., Hassan, A.K., Abbas, G., Baker, T., and Al-Jumeily, D. (2021). Performance analysis and beamforming design of a secure cooperative miso-noma network. Sensors, 21.","key":"ref_4","DOI":"10.3390\/s21124180"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/s12243-020-00819-7","article-title":"Physical layer security for NOMA: Limitations, issues, and recommendations","volume":"76","author":"Melki","year":"2021","journal-title":"Ann. Telecommun."},{"doi-asserted-by":"crossref","unstructured":"Al-Musawi, I., Al-Hussaibi, W., and Ali, F. (2021, January 14\u201323). Chaos-Based Physical Layer Security in NOMA Networks over Rician Fading Channels. Proceedings of the 2021 IEEE International Conference on Communications Workshops (ICC Workshops), Montreal, QC, Canada.","key":"ref_6","DOI":"10.1109\/ICCWorkshops50388.2021.9473862"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1186\/s13638-018-1156-8","article-title":"A downlink non-orthogonal multiple access scheme having physical layer security","volume":"2018","author":"Horiike","year":"2018","journal-title":"Eurasip J. Wirel. Commun. Netw."},{"doi-asserted-by":"crossref","unstructured":"Masuda, Y., Okamoto, E., Ito, K., and Yamamoto, T. (2019, January 9\u201311). An uplink non-orthogonal multiple access scheme having physical layer security based on chaos modulation. Proceedings of the International Conference on Information Networking, Kuala Lumpur, Malaysia.","key":"ref_8","DOI":"10.1109\/ICOIN.2019.8718195"},{"unstructured":"Stallings, W. (2017). Cryptography and Network Security: Principles and Practice 7th Global Edition, William Stallings.","key":"ref_9"},{"doi-asserted-by":"crossref","unstructured":"Horiike, N., Kitagawa, H., Okamoto, E., and Yamamoto, T. (2018, January 12\u201315). Chaos MIMO-based downlink non-orthogonal multiple access scheme with physical layer security. Proceedings of the 2018 15th IEEE Annual Consumer Communications & Networking Conference (CCNC), Las Vegas, NV, USA.","key":"ref_10","DOI":"10.1109\/CCNC.2018.8319189"},{"doi-asserted-by":"crossref","unstructured":"Masuda, Y., Okamoto, E., and Yamamoto, T. (2020, January 10\u201313). Low Complexity Decoding of Downlink Chaos NOMA Scheme with Physical Layer Security. Proceedings of the 2020 IEEE 17th Annual Consumer Communications & Networking Conference (CCNC), Las Vegas, NV, USA.","key":"ref_11","DOI":"10.1109\/CCNC46108.2020.9045697"},{"doi-asserted-by":"crossref","unstructured":"Almusawi, I., Al-Hussaibi, W., and Tahir, Y. (2020, January 28\u201330). Chaos-Based NOMA for Secure Wireless Communications over Rayleigh Fading Channels. Proceedings of the 1st International Multi-Disciplinary Conference Theme: Sustainable Development and Smart Planning, IMDC-SDSP 2020, Cyperspace.","key":"ref_12","DOI":"10.4108\/eai.28-6-2020.2297909"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1155\/2018\/1907506","article-title":"Nonorthogonal Multiple Access for 5G and Beyond","volume":"2018","author":"Kucur","year":"2018","journal-title":"Wirel. Commun. Mob. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"52851","DOI":"10.1109\/ACCESS.2021.3070147","article-title":"Performance Analysis of Multi-User Downlink PD-NOMA under sui Fading Channel Models","volume":"9","author":"Mahmood","year":"2021","journal-title":"IEEE Access"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"220461","DOI":"10.1109\/ACCESS.2020.3042993","article-title":"Outage Probability Analysis for NOMA Downlink and Uplink Communication Systems with Generalized Fading Channels","volume":"8","author":"Agarwal","year":"2020","journal-title":"IEEE Access"},{"unstructured":"Mohammad, M., Alav\u0131, R., Pehlivan, H., and Pour, S.H. (2011). Kaos Tabanl\u0131 Bir \u015eifreleme Y\u00f6ntemi ve Analizi. Proceedings of the Akademik Bili\u015fim Konferans\u0131 Bildirileri, 2\u20134 February, 2011, \u0130n\u00f6n\u00fc University.","key":"ref_16"},{"doi-asserted-by":"crossref","unstructured":"Akg\u00fcl, A., Ka\u00e7ar, S., Aricioglu, B., and Pehlivan, I. (2013, January 28\u201330). Text encryption by using one-dimensional chaos generators and nonlinear equations. Proceedings of the 2013 8th International Conference on Electrical and Electronics Engineering (ELECO), Bursa, Turkey.","key":"ref_17","DOI":"10.1109\/ELECO.2013.6713853"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1336","DOI":"10.1002\/cae.22038","article-title":"Chaos-based encryption of multimedia data and design of security analysis interface as an educational tool","volume":"26","author":"Akgul","year":"2018","journal-title":"Comput. Appl. Eng. Educ."},{"key":"ref_19","first-page":"11","article-title":"Image Encryption Using Henon Chaotic Map With Byte Sequence","volume":"3","author":"Raghava","year":"2013","journal-title":"Int. J. Comput. Sci. Eng. Inf. Technol. Res. (IJCSEITR)"},{"key":"ref_20","first-page":"1900","article-title":"An Image Cryptography using Henon Map and Arnold Cat Map","volume":"5","author":"Sankhe","year":"2018","journal-title":"Int. Res. J. Eng. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"316","DOI":"10.25046\/aj060136","article-title":"Chaos-based image encryption using Arnold\u2019s cat map confusion and Henon map diffusion","volume":"6","author":"Ratna","year":"2021","journal-title":"Adv. Sci. Technol. Eng. Syst."},{"doi-asserted-by":"crossref","unstructured":"Lozi, R. (2011). Complexity Leads to Randomness in Chaotic Systems. Math. Sci. Technol., 93\u2013125.","key":"ref_22","DOI":"10.1142\/9789814338820_0005"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.jprocont.2005.04.002","article-title":"Modelling and control of chaotic processes through their Bifurcation Diagrams generated with the help of Recurrent Neural Network models: Part 1-simulation studies","volume":"16","author":"Krishnaiah","year":"2006","journal-title":"J. Process Control"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1007\/s13319-015-0062-7","article-title":"An Efficient Image Encryption Scheme Based on: Henon Map, Skew Tent Map and S-Box","volume":"6","author":"Hanchinamani","year":"2015","journal-title":"3D Res."},{"unstructured":"Varvoglis, H. (2022, November 17). Chaos, Random Walks and Diffusion in Hamiltonian Systems. Available online: https:\/\/www.researchgate.net\/publication\/264419522_Chaos_random_walks_and_diffusion_in_Hamiltonian_systems.","key":"ref_25"},{"key":"ref_26","first-page":"603","article-title":"Period of a Discrete Cat Mapping","volume":"99","author":"Dyson","year":"2013","journal-title":"JSTOR"},{"key":"ref_27","first-page":"1","article-title":"A new 4D hyperchaotic system and its generalized function projective synchronization","volume":"2013","author":"Gao","year":"2013","journal-title":"Math. Probl. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"23319","DOI":"10.1007\/s11042-021-10527-6","article-title":"An efficient DNA-inspired image encryption algorithm based on hyper-chaotic maps and wavelet fusion","volume":"80","author":"Mohamed","year":"2021","journal-title":"Multimed. Tools Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4655","DOI":"10.1007\/s11042-013-1828-7","article-title":"Selective encryption for gray images based on chaos and DNA complementary rules","volume":"74","author":"Rehman","year":"2015","journal-title":"Multimed. Tools Appl."},{"key":"ref_30","first-page":"1","article-title":"A new hyperchaotic system and its adaptive tracking control","volume":"61","author":"Li","year":"2012","journal-title":"Wuli Xuebao\/Acta Phys. Sin."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"013021","DOI":"10.1117\/1.JEI.26.1.013021","article-title":"Cross-utilizing hyperchaotic and DNA sequences for image encryption","volume":"26","author":"Zhan","year":"2017","journal-title":"J. Electron. Imaging"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1038\/171737a0","article-title":"Molecular Structure of Nucleic Acids","volume":"171","author":"Watson","year":"1953","journal-title":"Nature"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1757","DOI":"10.1007\/s00371-020-01936-z","article-title":"A new one-dimensional chaotic map and its application in a novel permutation-less image encryption scheme","volume":"37","author":"Talhaoui","year":"2021","journal-title":"Vis. Comput."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1109\/TWC.2020.3031809","article-title":"A dCDD-Based Transmit Diversity Scheme for Downlink Pseudo-NOMA Systems","volume":"20","author":"Kim","year":"2021","journal-title":"IEEE Trans. Wirel. Commun."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/1\/140\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:05:35Z","timestamp":1760119535000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/1\/140"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,10]]},"references-count":34,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["e25010140"],"URL":"https:\/\/doi.org\/10.3390\/e25010140","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2023,1,10]]}}}