{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T14:26:57Z","timestamp":1777127217959,"version":"3.51.4"},"reference-count":45,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,9,30]],"date-time":"2018-09-30T00:00:00Z","timestamp":1538265600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Jiangsu Province  for Colleges and Universities;the Doctoral Program of  New Teachers of Jiangsu Normal University;  National Natural Science Foundation of China; 863 Program of China","award":["17KJB510016;17XLR029, 17XLR003, and 17XLR046; 61372101, 61422105, 61671144, and U1404615;2015AA01A703"],"award-info":[{"award-number":["17KJB510016;17XLR029, 17XLR003, and 17XLR046; 61372101, 61422105, 61671144, and U1404615;2015AA01A703"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Vehicle to everything (V2X) has been deemed a promising technology due to its potential to achieve traffic safety and efficiency. This paper considers a V2X downlink system with a simultaneous wireless information and power transfer (SWIPT) system where the base station not only conveys data and energy to two types of wireless vehicular receivers, such as one hybrid power-splitting vehicular receiver, and multiple energy vehicular receivers, but also prevents information from being intercepted by the potential eavesdroppers (idle energy vehicular receivers). Both the base station and the energy vehicular receivers are equipped with multiple antennas, whereas the information vehicular receiver is equipped with a single antenna. In particular, the imperfect channel state information (CSI) and the practical nonlinear energy harvesting (EH) model are taken into account. The non-convex optimization problem is formulated to maximize the minimum harvested energy power among the energy vehicular receivers satisfying the lowest harvested energy power threshold at the information vehicular receiver and secure vehicular communication requirements. In light of the intractability of the optimization problem, the semidefinite relaxation (SDR) technique and variable substitutions are applied, and the optimal solution is proven to be tight. A number of results demonstrate that the proposed robust secure beamforming scheme has better performance than other schemes.<\/jats:p>","DOI":"10.3390\/s18103294","type":"journal-article","created":{"date-parts":[[2018,10,2]],"date-time":"2018-10-02T08:23:50Z","timestamp":1538468630000},"page":"3294","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Robust Beamforming Design for Secure V2X Downlink System with Wireless Information and Power Transfer under a Nonlinear Energy Harvesting Model"],"prefix":"10.3390","volume":"18","author":[{"given":"Shidang","family":"Li","sequence":"first","affiliation":[{"name":"School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunguo","family":"Li","sequence":"additional","affiliation":[{"name":"National Communications Research Laboratory, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weiqiang","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Computer Science and Educational Software, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Baofeng","family":"Ji","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Henan University of Science and Technology, Luoyang 471023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luxi","family":"Yang","sequence":"additional","affiliation":[{"name":"National Communications Research Laboratory, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1109\/TITS.2016.2568759","article-title":"An optimal estimation approach for the calibration of the car-following behavior of connected vehicles in a mixed traffic environment","volume":"18","author":"Zhu","year":"2017","journal-title":"IEEE Trans. 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