{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T13:40:08Z","timestamp":1761745208383,"version":"build-2065373602"},"reference-count":55,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,2,29]],"date-time":"2020-02-29T00:00:00Z","timestamp":1582934400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Nature Science Foundation of China","award":["61771194","61931001"],"award-info":[{"award-number":["61771194","61931001"]}]},{"name":"Science and Technology Project of State Grid Corporation of China","award":["SGSDDK00KJJS1900405"],"award-info":[{"award-number":["SGSDDK00KJJS1900405"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Wireless mesh networks (WMNs) can provide flexible wireless connections in a smart city, internet of things (IoT), and device-to-device (D2D) communications. The performance of WMNs can be greatly enhanced by adopting a multi-radio technique, which enables a node to communicate with more nodes simultaneously. However, multi-radio WMNs face two main challenges, namely, energy consumption and physical layer secrecy. In this paper, both simultaneous wireless information and power transfer (SWIPT) and cooperative jamming technologies were adopted to overcome these two problems. We designed the SWIPT and cooperative jamming scheme, minimizing the total transmission power by properly selecting beamforming vectors of the WMN nodes and jammer to satisfy the individual signal-to-interference-plus-noise ratio (SINR) and energy harvesting (EH) constrains. Especially, we considered the channel estimate error caused by the imperfect channel state information. The SINR of eavesdropper (Eve) was suppressed to protect the secrecy of WMN nodes. Due to the fractional form, the problem was proved to be non-convex. We developed a tractable algorithm by transforming it into a convex one, utilizing semi-definite programming (SDP) relaxation and S-procedure methods. The simulation results validated the effectiveness of the proposed algorithm compared with the non-robust design.<\/jats:p>","DOI":"10.3390\/info11030138","type":"journal-article","created":{"date-parts":[[2020,3,2]],"date-time":"2020-03-02T06:34:23Z","timestamp":1583130863000},"page":"138","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Robust Beamforming Design for SWIPT-Based Multi-Radio Wireless Mesh Network with Cooperative Jamming"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3846-9803","authenticated-orcid":false,"given":"Liang","family":"Li","sequence":"first","affiliation":[{"name":"School of Electrical &amp; Electronic Engineering, North China Electric Power University, Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiongwen","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Electrical &amp; Electronic Engineering, North China Electric Power University, Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Suiyan","family":"Geng","sequence":"additional","affiliation":[{"name":"School of Electrical &amp; Electronic Engineering, North China Electric Power University, Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electrical &amp; Electronic Engineering, North China Electric Power University, Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"Zhang","sequence":"additional","affiliation":[{"name":"Shandong Electric Power Research Institute of the State Grid Corporation of China, Jinan 100031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1342","DOI":"10.1109\/TNET.2014.2324976","article-title":"A Systematic Study of Maximal Scheduling Algorithms in Multiradio Multichannel Wireless Networks","volume":"23","author":"Cheng","year":"2015","journal-title":"IEEE\/ACM Trans. Netw."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4917","DOI":"10.3390\/s110504917","article-title":"Multi-Channel Multi-Radio Using 802.11 Based Media Access for Sink Nodes in Wireless Sensor Networks","volume":"11","author":"Campbell","year":"2011","journal-title":"Sensors"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"500","DOI":"10.3390\/s120100500","article-title":"Performance Evaluation of Multi-Channel Wireless Mesh Networks with Embedded Systems","volume":"12","author":"Lam","year":"2012","journal-title":"Sensors"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Santana, J., Marrero, D., Mac\u00edas, E., Mena, V., and Su\u00e1rez, \u00c1. (2017). Interference Effects Redress over Power-Efficient Wireless-Friendly Mesh Networks for Ubiquitous Sensor Communications across Smart Cities. Sensors, 17.","DOI":"10.3390\/s17071678"},{"key":"ref_5","first-page":"1016","article-title":"An Intrusion Detection System for Connected Vehicles in Smart Cities","volume":"10","author":"Moayad","year":"2019","journal-title":"Ad Hoc Netw."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"47379","DOI":"10.1109\/ACCESS.2019.2906863","article-title":"Resource Efficient Allocation and RRH Placement for Backhaul of Moving Small Cells","volume":"7","author":"Zaeema","year":"2019","journal-title":"IEEE Access."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1109\/COMST.2015.2510164","article-title":"Channel Assignment Techniques for Multi-Radio Wireless Mesh Networks: A Survey","volume":"18","author":"Islam","year":"2016","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1109\/MWC.2012.6189415","article-title":"A theoretical framework for optimal cooperative networking in multiradio multichannel wireless networks","volume":"19","author":"Cheng","year":"2012","journal-title":"IEEE Wirel. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1528","DOI":"10.1109\/TC.2015.2448089","article-title":"Interference-Aware Cooperative Communication in Multi-Radio Multi-Channel Wireless Networks","volume":"5","author":"Xie","year":"2016","journal-title":"IEEE Trans. Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1109\/JCN.2018.000055","article-title":"RA-eV2V: relaying systems for LTE-V2V communications","volume":"20","author":"Park","year":"2018","journal-title":"J. Commun. Netw."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1109\/COMST.2017.2783901","article-title":"Simultaneous Wireless Information and Power Transfer (SWIPT): Recent Advances and Future Challenges","volume":"1","author":"Ponnimbaduge","year":"2018","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_12","unstructured":"Muhammad, S.K., Sobia, J., Moayad, A., Yaser, J., and Thar, B. (2020, February 29). EPS-TRA: Energy efficient Peer Selection and Time switching Ratio Allocation for SWIPT-enabled D2D Communication. Available online: https:\/\/ieeexplore.ieee.org\/document\/8952654."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"102035","DOI":"10.1016\/j.adhoc.2019.102035","article-title":"Intelligent jamming-aware routing in multi-hop IoT-based opportunistic cognitive radio networks","volume":"98","author":"Haythem","year":"2020","journal-title":"Ad Hoc Netw."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1109\/MCOM.2005.1404606","article-title":"Mesh networks: commodity multihop ad hoc networks","volume":"43","author":"Bruno","year":"2005","journal-title":"IEEE Commun. Mag."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1109\/TSG.2011.2167354","article-title":"Security Framework for Wireless Communications in Smart Distribution Grid","volume":"4","author":"Wang","year":"2011","journal-title":"IEEE Trans. Smart Grid."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1109\/MIC.2008.85","article-title":"Securing Wireless Mesh Networks","volume":"4","author":"Glass","year":"2008","journal-title":"IEEE Internet Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3205","DOI":"10.1109\/TWC.2017.2676087","article-title":"Secure Communications in Millimeter Wave Ad Hoc Networks","volume":"5","author":"Zhu","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1802","DOI":"10.1109\/TIFS.2013.2279842","article-title":"Enhancing Secrecy With Multi-Antenna Transmission in Wireless Ad Hoc Networks","volume":"11","author":"Zhang","year":"2013","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_19","first-page":"419","article-title":"A Security Analysis for Wireless Sensor Mesh Networks in Highly Critical Systems","volume":"4","author":"Alcaraz","year":"2010","journal-title":"IEEE Trans. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1400","DOI":"10.1109\/TCOMM.2015.2398862","article-title":"Wireless information and power transfer in relay systems with multiple antennas and interference","volume":"4","author":"Zhu","year":"2015","journal-title":"IEEE Trans. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Liu, D., Wen, Z., Liu, X., Li, S., and Zou, J. (2019). Joint Source-Relay Optimization for MIMO Full-Duplex Bidirectional Wireless Sensor Networks with SWIPT. Sensors, 19.","DOI":"10.3390\/s19081827"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4210","DOI":"10.1109\/TWC.2013.071913.130084","article-title":"Joint wireless information and energy transfer in a two-user MIMO interference channel","volume":"8","author":"Park","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Xue, L., Wang, J., Li, J., Wang, Y., and Guan, X. (2019). Precoding Design for Energy Efficiency Maximization in MIMO Half-Duplex Wireless Sensor Networks with SWIPT. Sensors, 19.","DOI":"10.3390\/s19224923"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1463","DOI":"10.1109\/JSAC.2016.2520238","article-title":"A Channel Assignment and Routing Algorithm for Energy Harvesting Multiradio Wireless Mesh Networks","volume":"5","author":"Avallone","year":"2016","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1002\/j.1538-7305.1975.tb02040.x","article-title":"The wire-tap channel","volume":"8","author":"Wyner","year":"1975","journal-title":"Bell Syst. Tech. J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1264","DOI":"10.1049\/iet-com.2016.1168","article-title":"Joint design of jammer selection and beamforming for securing MIMO cooperative cognitive radio networks","volume":"8","author":"Gao","year":"2017","journal-title":"IET Commun."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3500","DOI":"10.1109\/TVT.2019.2895639","article-title":"A Scheme for Trustworthy Friendly Jammer Selection in Cooperative Cognitive Radio Networks","volume":"4","author":"Wen","year":"2019","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1109\/TCOMM.2015.2405063","article-title":"Cooperative jamming aided robust secure transmission for wireless information and power transfer in MISO channels","volume":"3","author":"Zhang","year":"2015","journal-title":"IEEE Trans. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1109\/TVT.2015.2395725","article-title":"Secrecy wireless information and power transfer in fading wiretap channel","volume":"1","author":"Xing","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Xing, H., Chu, Z., Ding, Z., and Nallanathan, A. (2014, January 8\u201312). Harvest-and-jam: Improving security for wireless energy harvesting cooperative networks. Proceedings of the IEEE Global Communication (GLOBECOM), Austin, TX, USA.","DOI":"10.1109\/GLOCOM.2014.7037289"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2462","DOI":"10.1109\/TVT.2013.2288318","article-title":"Secure Relay Beamforming for Simultaneous Wireless Information and Power Transfer in Nonregenerative Relay Networks","volume":"5","author":"Li","year":"2014","journal-title":"IEEE Transactions on Vehicular Technology."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Varshney, L.R. (2008, January 6\u201311). Transporting information and energy simultaneously. Proceedings of the IEEE International Symposium on Information Theory (ISIT), Toronto, CA, USA.","DOI":"10.1109\/ISIT.2008.4595260"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Grover, P., and Sahai, A. (2010, January 13\u201318). Shannon meets Tesla: Wireless information and power transfer. Proceedings of the IEEE International Symposium on Information Theory (ISIT), Austin, TX, USA.","DOI":"10.1109\/ISIT.2010.5513714"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"4754","DOI":"10.1109\/TCOMM.2013.13.120855","article-title":"Wireless information and power transfer: Architecture design and rate-energy tradeoff","volume":"11","author":"Zhou","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3990","DOI":"10.1109\/TCOMM.2013.071813.130105","article-title":"Wireless information and power transfer: A dynamic power splitting approach","volume":"9","author":"Liu","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1109\/MCOM.2015.7081080","article-title":"Application of smart antenna technologies in simultaneous wireless information and power transfer","volume":"4","author":"Ding","year":"2015","journal-title":"IEEE Commun. Mag."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"4798","DOI":"10.1109\/TSP.2014.2340817","article-title":"Multiuser MISO beamforming for simultaneous wireless information and power transfer","volume":"18","author":"Xu","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1989","DOI":"10.1109\/TWC.2013.031813.120224","article-title":"MIMO broadcasting for simultaneous wireless information and power transfer","volume":"5","author":"Zhang","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Wen, Y., Jing, T., Huo, Y., Li, Z., and Gao, Q. (2018, January 5\u20138). Secrecy Energy Efficiency Optimization for Cooperative Jamming in Cognitive Radio Network. Proceedings of the International Conference on Computing, Networking and Communications (ICNC), Maui, HI, USA.","DOI":"10.1109\/ICCNC.2018.8390398"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.sigpro.2014.09.025","article-title":"Radio self-interference cancellation by transmit beamforming, all-analog cancellation and blind digital tuning","volume":"4","author":"Hua","year":"2015","journal-title":"Signal Process."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1984","DOI":"10.1109\/TCOMM.2017.2664860","article-title":"Robust resource allocation for MIMO wireless powered communication networks based on a non-linear EH model","volume":"5","author":"Boshkovska","year":"2017","journal-title":"IEEE Trans. Commun."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Nguyen, T., Nguyen, M., Do, D., and Voznak, M. (2019). Enabling Non-Linear Energy Harvesting in Power Domain Based Multiple Access in Relaying Networks: Outage and Ergodic Capacity Performance Analysis. Electronics, 8.","DOI":"10.3390\/electronics8070817"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1874","DOI":"10.1109\/LCOMM.2018.2850767","article-title":"Robust Resource Allocation for MISO Cognitive Radio Networks Under Two Practical Non-Linear Energy Harvesting Models","volume":"9","author":"Zhang","year":"2018","journal-title":"IEEE Commun. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1164","DOI":"10.1109\/JIOT.2019.2953312","article-title":"Hybrid Precoding for an Adaptive Interference Decoding SWIPT System with Full-Duplex IoT Devices","volume":"7","author":"Zhao","year":"2020","journal-title":"IEEE Internet Things J. press."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Boyd, S., and Vandenberghe, L. (2004). Convex Optimization, Cambridge University Press.","DOI":"10.1017\/CBO9780511804441"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1955","DOI":"10.1109\/TCOMM.2018.2801870","article-title":"Transceiver Design of Optimum Wirelessly Powered Full-Duplex MIMO IoT Devices","volume":"5","author":"Xue","year":"2018","journal-title":"IEEE Trans. Commun."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1942","DOI":"10.1109\/TVT.2018.2884514","article-title":"Robust Beamforming Design for Multi-User MISO Full-Duplex SWIPT System with Channel State Information Uncertainty","volume":"2","author":"Wen","year":"2019","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2829","DOI":"10.1109\/JIOT.2018.2825334","article-title":"Simultaneous Wireless Information and Power Transfer for Internet of Things Sensor Networks","volume":"4","author":"Chae","year":"2018","journal-title":"IEEE Internet Things J."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"6194","DOI":"10.1109\/TSP.2014.2362092","article-title":"Joint beamforming and power splitting for MISO interference channel with SWIPT: An SOCP relaxation and decentralized algorithm","volume":"23","author":"Shi","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_50","first-page":"95","article-title":"Graph Implementations for Non-smooth Convex Programs","volume":"37","author":"Grant","year":"2008","journal-title":"Lect. Notes Control Inf. Sci."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1109\/MSP.2010.936019","article-title":"Semidefinite relaxation of quadratic optimization problems","volume":"3","author":"Luo","year":"2010","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1109\/TSP.2010.2084997","article-title":"Rank-constrained Schur-convex optimization with multiple trace\/log-det constraints","volume":"1","author":"Yu","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"2334","DOI":"10.1109\/TIT.2009.2016061","article-title":"Degrees of freedom of wireless networks with relays, feedback, cooperation, and full duplex operation","volume":"5","author":"Cadambe","year":"2009","journal-title":"IEEE Trans. Inf. Theory."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Goldsmith, A. (2005). Wireless Communications, Cambridge University Press.","DOI":"10.1017\/CBO9780511841224"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Ben-Tal, A., and Nemirovski, A. (2001). Lectures on Modern Convex Optimization: Analysis, Algorithms, Engineering Applications, SIAM.","DOI":"10.1137\/1.9780898718829"}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/11\/3\/138\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:02:48Z","timestamp":1760173368000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/11\/3\/138"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,29]]},"references-count":55,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["info11030138"],"URL":"https:\/\/doi.org\/10.3390\/info11030138","relation":{},"ISSN":["2078-2489"],"issn-type":[{"type":"electronic","value":"2078-2489"}],"subject":[],"published":{"date-parts":[[2020,2,29]]}}}