{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T10:57:35Z","timestamp":1768820255960,"version":"3.49.0"},"reference-count":30,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2019,10,25]],"date-time":"2019-10-25T00:00:00Z","timestamp":1571961600000},"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>In this paper, we propose a pseudo-random beamforming (PRBF) technique for improving physical-layer security (PLS) in multiple input multiple output (MIMO) downlink cellular networks consisting of a legitimate base station (BS), multiple legitimate mobile stations (MSs) and potential eavesdroppers. The legitimate BS can obtain available potential eavesdroppers\u2019 channel state information (CSI), which is registered in an adjacent cell. In the proposed PRBF technique, the legitimate BS pseudo-randomly generates multiple candidates of the transmit beamforming (BF) matrix, in which each transmit BF matrix consists of multiple orthonormal BF vectors and shares BF information with legitimate MSs before data transmission. Each legitimate MS generates receive BF vectors to maximize the receive signal-to-interference-plus-noise (SINR) for all pseudo-randomly generated transmit beams and calculates the corresponding SINR. Then, each legitimate MS sends a single beam index and the corresponding SINR value of the BF vector that maximizes the received SINR for each BF matrix since a single spatial stream is sent to each legitimate MS. Based on the feedback information from legitimate MSs and the CSI from the legitimate BS to eavesdroppers, the legitimate BS selects the optimal transmit BF matrix and the legitimate MSs that maximizes secrecy sum-rate. We also propose a codebook-based opportunistic feedback (CO-FB) strategy to reduce feedback overhead at legitimate MSs. Based on extensive computer simulations, the proposed PRBF with the proposed CO-FB significantly outperforms the conventional random beamforming (RBF) with the conventional opportunistic feedback (O-FB) strategies in terms of secrecy sum-rate and required feedback bits.<\/jats:p>","DOI":"10.3390\/e21111038","type":"journal-article","created":{"date-parts":[[2019,10,25]],"date-time":"2019-10-25T11:05:18Z","timestamp":1572001518000},"page":"1038","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Pseudo-Random Beamforming Technique for Improving Physical-Layer Security of MIMO Cellular Networks"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9332-2102","authenticated-orcid":false,"given":"Woong","family":"Son","sequence":"first","affiliation":[{"name":"Department of Electronics Engineering, Chungnam National University, Daejeon 34134, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9024-8952","authenticated-orcid":false,"given":"Han Seung","family":"Jang","sequence":"additional","affiliation":[{"name":"School of Electrical, Electronic Communication and Computer Engineering, Chonnam National University, Yeosu 59626, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4485-9592","authenticated-orcid":false,"given":"Bang Chul","family":"Jung","sequence":"additional","affiliation":[{"name":"Department of Electronics Engineering, Chungnam National University, Daejeon 34134, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1002\/j.1538-7305.1949.tb00928.x","article-title":"Communication theory of secrecy systems","volume":"10","author":"Shannon","year":"1949","journal-title":"Bell Syst. Tech. J."},{"key":"ref_2","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_3","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1109\/TIT.1978.1055917","article-title":"The Gaussian wire-tap channel","volume":"24","author":"Hellman","year":"1978","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_4","first-page":"451","article-title":"Wireless information-theoretic security","volume":"24","author":"Bloch","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1109\/MWC.2011.5751298","article-title":"Physical layer security in wireless networks: A tutorial","volume":"18","author":"Shiu","year":"2011","journal-title":"IEEE Wirel. Commun."},{"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. Tuts."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1778","DOI":"10.1109\/LCOMM.2013.071813.131158","article-title":"On the multi-user diversity with secrecy in uplink wiretap networks","volume":"17","author":"Jin","year":"2013","journal-title":"IEEE Commun. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Jin, H., Jung, B.C., and Shin, W.-Y. (2016, January 22\u201327). On the secrecy capacity of multi-cell uplink networks with opportunistic scheduling. Proceedings of the 2016 IEEE International Conference on Communications (ICC), Kuala Lumpur, Malaysia.","DOI":"10.1109\/ICC.2016.7510753"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1109\/LCOMM.2016.2629483","article-title":"Artificial noise-aided user scheduling for optimal secrecy multiuser diversity","volume":"21","author":"Bang","year":"2017","journal-title":"IEEE Commun. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1109\/LCOMM.2013.112513.131926","article-title":"On ergodic secrecy rate for MISO wiretap broadcast channels with opportunistic scheduling","volume":"18","author":"Pei","year":"2014","journal-title":"IEEE Commum. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wang, L., Wang, Z., and Pei, M. (2016, January 14\u201317). Orthogonal random beamforming with beam selection for MISO wiretap broadcast channels. Proceedings of the 2016 2nd IEEE International Conference on Computer and Communications (ICCC), Chengdu, China.","DOI":"10.1109\/CompComm.2016.7924950"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1128","DOI":"10.1109\/JSYST.2015.2413843","article-title":"Mode selection in MU-MIMO downlink networks: A physical-layer security perspective","volume":"11","author":"Chen","year":"2015","journal-title":"IEEE Syst. J."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Gao, C., Han, S., Wang, X., Meng, W., and Gao, F. (2018, January 25\u201329). Performance Analysis of Beamforming Algorithms In Physical Layer Security. Proceedings of the 2018 14th International Wireless Communications & Mobile Computing Conference (IWCMC), Limassol, Cyprus.","DOI":"10.1109\/IWCMC.2018.8450291"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Mukherjee, A., and Swindlehurst, A.L. (2012, January 25\u201330). Detecting passive eavesdroppers in the MIMO wiretap channel. Proceedings of the 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Kyoto, Japan.","DOI":"10.1109\/ICASSP.2012.6288501"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Chorti, A., Perlaza, S.M., Han, Z., and Poor, H.V. (2012, January 3\u20137). Physical layer security in wireless networks with passive and active eavesdroppers. Proceedings of the 2012 IEEE Global Communications Conference (GLOBECOM), Anaheim, CA, USA.","DOI":"10.1109\/GLOCOM.2012.6503890"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/MCOM.2015.7120012","article-title":"Physical layer security for massive MIMO: An overview on passive eavesdropping and active attacks","volume":"53","author":"Kapetanovic","year":"2015","journal-title":"IEEE Commun. Mag."},{"key":"ref_17","first-page":"58","article-title":"Massive MIMO pilot retransmission strategies for robustification against jamming","volume":"6","author":"Do","year":"2017","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"24908","DOI":"10.1109\/ACCESS.2017.2764914","article-title":"Jamming resilient cross-layer resource allocation in uplink HARQ-based SIMO OFDMA video transmission systems","volume":"5","author":"Tseng","year":"2017","journal-title":"IEEE Access"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"7500204","DOI":"10.1109\/LSENS.2017.2707280","article-title":"Disrupting Anti-Jamming Interference Alignment Sensor Networks with Optimal Signal Design","volume":"1","author":"Guo","year":"2017","journal-title":"IEEE Sens. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"7018","DOI":"10.1109\/TVT.2018.2825539","article-title":"Mode hopping for anti-jamming in radio vortex wireless communications","volume":"67","author":"Liang","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1109\/TGCN.2019.2914698","article-title":"Power Minimization Precoding in Uplink Multi-Antenna NOMA Systems With Jamming","volume":"3","author":"Wang","year":"2019","journal-title":"IEEE Trans. Green Commun. Netw."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1109\/LSP.2012.2234109","article-title":"Secrecy sum-rate for orthogonal random beamforming with opportunistic scheduling","volume":"20","author":"Krikidis","year":"2012","journal-title":"IEEE Signal Process Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1109\/MWC.2016.7462485","article-title":"Secrecy wireless information and power transfer: Challenges and opportunities","volume":"23","author":"Chen","year":"2016","journal-title":"IEEE Wirel. Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1109\/TIFS.2018.2868494","article-title":"Opportunistic scheduling for average secrecy rate enhancement in fading downlink channel with potential eavesdroppers","volume":"14","author":"Abbas","year":"2019","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"127078","DOI":"10.1109\/ACCESS.2019.2939048","article-title":"Secrecy Rate Analysis of Opportunistic User Scheduling in Uplink Networks With Potential Eavesdroppers","volume":"7","author":"Bang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Son, W., Jung, B.C., Shin, W.-Y., and Shin, Y. (2017, January 18\u201320). Multi-cell pseudo-random beamforming: Opportunistic feedback and beam selection. Proceedings of the 2017 International Conference on Information and Communication Technology Convergence (ICTC), Jeju, South Korea.","DOI":"10.1109\/ICTC.2017.8190757"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Son, W., Jung, B.C., Kim, C.-Y., and Kim, J.M. (2018, January 3\u20136). Pseudo-Random Beamforming with Beam Selection for Improving Physical-Layer Security. Proceedings of the 2018 Tenth International Conference on Ubiquitous and Future Networks (ICUFN), Prague, Czech Republic.","DOI":"10.1109\/ICUFN.2018.8436732"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2180","DOI":"10.1109\/TWC.2013.032113.120673","article-title":"Opportunistic interference alignment for MIMO interfering multiple-access channels","volume":"12","author":"Yang","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1109\/TWC.2017.2647942","article-title":"Opportunistic downlink interference alignment for multi-cell MIMO networks","volume":"16","author":"Yang","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1109\/LCOMM.2018.2803813","article-title":"Distributed interference alignment for multi-antenna cellular networks with dynamic time division duplex","volume":"22","author":"Ko","year":"2018","journal-title":"IEEE Commun. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/11\/1038\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:29:20Z","timestamp":1760189360000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/11\/1038"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,25]]},"references-count":30,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2019,11]]}},"alternative-id":["e21111038"],"URL":"https:\/\/doi.org\/10.3390\/e21111038","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,25]]}}}