{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T07:41:54Z","timestamp":1765438914578,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T00:00:00Z","timestamp":1695945600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"US National Science Foundation","award":["1910812"],"award-info":[{"award-number":["1910812"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Many physical-layer security works in the literature rely on purely theoretical work or simulated results to establish the value of physical-layer security in securing communications. We consider the secrecy capacity of a wireless Gaussian wiretap channel using channel sounding measurements to analyze the potential for secure communication in a real-world scenario. A multi-input, multi-output, multi-eavesdropper (MIMOME) system is deployed using orthogonal frequency division multiplexing (OFDM) over an 802.11n wireless network. Channel state information (CSI) measurements were taken in an indoor environment to analyze time-varying scenarios and spatial variations. It is shown that secrecy capacity is highly affected by environmental changes, such as foot traffic, network congestion, and propagation characteristics of the physical environment. We also present a numerical method for calculating MIMOME secrecy capacity in general and comment on the use of OFDM with regard to calculating secrecy capacity.<\/jats:p>","DOI":"10.3390\/e25101397","type":"journal-article","created":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T05:48:13Z","timestamp":1695966493000},"page":"1397","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Physical Layer Security: Channel Sounding Results for the Multi-Antenna Wiretap Channel"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-7443-453X","authenticated-orcid":false,"given":"Daniel","family":"Harman","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karl","family":"Knapp","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tyler","family":"Sweat","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8276-4842","authenticated-orcid":false,"given":"Philip","family":"Lundrigan","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Rice","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9375-9440","authenticated-orcid":false,"given":"Willie","family":"Harrison","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,29]]},"reference":[{"key":"ref_1","unstructured":"Shor, P. (1994, January 20\u201322). Algorithms for quantum computation: Discrete logarithms and factoring. Proceedings of the 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM, USA."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bloch, M., and Barros, J. (2011). Physical-Layer Security: From Information Theory to Security Engineering, Cambridge University Press.","DOI":"10.1017\/CBO9780511977985"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhou, X., Song, L., and Zhang, Y. (2016). Physical Layer Security in Wireless Communications, CRC Press.","DOI":"10.1201\/b15496"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Mucchi, L., Nizzi, F., Pecorella, T., Fantacci, R., and Esposito, F. (2019, January 3\u20136). Benefits of Physical Layer Security to Cryptography: Tradeoff and Applications. Proceedings of the IEEE International Black Sea Conference on Communications and Networking (BlackSeaCom), Sochi, Russia.","DOI":"10.1109\/BlackSeaCom.2019.8812778"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1550","DOI":"10.1109\/SURV.2014.012314.00178","article-title":"Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey","volume":"16","author":"Mukherjee","year":"2014","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1109\/MSP.2013.2265141","article-title":"Coding for Secrecy: An Overview of Error-Control Coding Techniques for Physical-Layer Security","volume":"30","author":"Harrison","year":"2013","journal-title":"IEEE Sign Process. Mag."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1002\/j.1538-7305.1949.tb00928.x","article-title":"Communication theory of secrecy systems","volume":"28","author":"Shannon","year":"1949","journal-title":"Bell Syst. Tech. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1002\/j.1538-7305.1975.tb02040.x","article-title":"The wire-tap channel","volume":"54","author":"Wyner","year":"1975","journal-title":"Bell Syst. Tech. J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5515","DOI":"10.1109\/TIT.2010.2068852","article-title":"Secure Transmission With Multiple Antennas\u2014Part II: The MIMOME Wiretap Channel","volume":"56","author":"Khisti","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4961","DOI":"10.1109\/TIT.2011.2158487","article-title":"The Secrecy Capacity of the MIMO Wiretap Channel","volume":"57","author":"Oggier","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2547","DOI":"10.1109\/TIT.2008.2011448","article-title":"A Note on the Secrecy Capacity of the Multiple-Antenna Wiretap Channel","volume":"55","author":"Liu","year":"2009","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Duong, T.Q., Zhou, X.S., and Poor, H.V. (2017). Trusted Communications with Physical Layer Security for 5G and Beyond, The Institution of Engineering and Technology.","DOI":"10.1049\/PBTE076E"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Jensen, B., Clark, B., Flanary, D., Norman, K., Rice, M., and Harrison, W.K. (2019, January 20\u201324). Physical-Layer Security: Does it Work in a Real Environment?. Proceedings of the IEEE International Conference on Communications (ICC), Shanghai, China.","DOI":"10.1109\/ICC.2019.8761418"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1109\/MVT.2020.3002494","article-title":"Physical-Layer Security for Vehicle-to-Everything Networks: Increasing Security While Maintaining Reliable Communications","volume":"15","author":"Rice","year":"2020","journal-title":"IEEE Veh. Technol. Mag."},{"key":"ref_16","unstructured":"Li, Z., Yates, R., and Trappe, W. (2010). Securing Wireless Communications at the Physical Layer, Springer."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1354","DOI":"10.1109\/TIFS.2012.2195491","article-title":"Physical-Layer Secrecy for OFDM Transmissions Over Fading Channels","volume":"7","author":"Renna","year":"2012","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_18","unstructured":"Tse, D., and Viswanath, P. (2013). Fundamentals of Wireless Communication, Cambridge University Press."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Brown, T., DeCarvalho, E., and Kyritsi, P. (2012). Practical Guide to the MIMO Radio Channel: With MATLAB Examples, Wiley.","DOI":"10.1002\/9781119944966"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Yang, T., Taghizadeh, O., and Mathar, R. (2019, January 15\u201318). SEE of Full-Duplex Multi-carrier Bidirectional Wiretap Channels with Multiple Eavesdroppers. Proceedings of the 2019 IEEE Wireless Communications and Networking Conference (WCNC), Marrakesh, Morocco.","DOI":"10.1109\/WCNC.2019.8886111"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1109\/JSAC.2003.810294","article-title":"Capacity limits of MIMO channels","volume":"21","author":"Goldsmith","year":"2003","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_22","first-page":"288","article-title":"MIMO channel capacity using antenna selection and water pouring","volume":"2014","year":"2014","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"6865","DOI":"10.1109\/TCOMM.2021.3098700","article-title":"On the Secrecy Capacity of MIMO Wiretap Channels: Convex Reformulation and Efficient Numerical Methods","volume":"69","author":"Mukherjee","year":"2021","journal-title":"IEEE Trans. Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1109\/LWC.2021.3128331","article-title":"On the Optimality of the Stationary Solution of Secrecy Rate Maximization for MIMO Wiretap Channel","volume":"11","author":"Mukherjee","year":"2022","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1114","DOI":"10.1109\/TCOMM.2012.021712.090634","article-title":"Secure Communication in the Low-SNR Regime","volume":"60","author":"Gursoy","year":"2012","journal-title":"IEEE Trans. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1342","DOI":"10.1109\/TMC.2018.2860991","article-title":"Precise Power Delay Profiling with Commodity Wi-Fi","volume":"18","author":"Xie","year":"2019","journal-title":"IEEE Trans. Mob. Comput."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/10\/1397\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:01:49Z","timestamp":1760130109000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/10\/1397"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,29]]},"references-count":26,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2023,10]]}},"alternative-id":["e25101397"],"URL":"https:\/\/doi.org\/10.3390\/e25101397","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2023,9,29]]}}}