{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:15:12Z","timestamp":1760242512984,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2017,10,6]],"date-time":"2017-10-06T00:00:00Z","timestamp":1507248000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we consider multiuser simultaneous wireless information and power transfer (SWIPT) for cognitive radio systems where a secondary transmitter (ST) with an antenna array provides information and energy to multiple single-antenna secondary receivers (SRs) equipped with a power splitting (PS) receiving scheme when multiple primary users (PUs) exist. The main objective of the paper is to maximize weighted sum harvested energy for SRs while satisfying their minimum required signal-to-interference-plus-noise ratio (SINR), the limited transmission power at the ST, and the interference threshold of each PU. For the perfect channel state information (CSI), the optimal beamforming vectors and PS ratios are achieved by the proposed PSO-SDR in which semidefinite relaxation (SDR) and particle swarm optimization (PSO) methods are jointly combined. We prove that SDR always has a rank-1 solution, and is indeed tight. For the imperfect CSI with bounded channel vector errors, the upper bound of weighted sum harvested energy (WSHE) is also obtained through the S-Procedure. Finally, simulation results demonstrate that the proposed PSO-SDR has fast convergence and better performance as compared to the other baseline schemes.<\/jats:p>","DOI":"10.3390\/s17102275","type":"journal-article","created":{"date-parts":[[2017,10,6]],"date-time":"2017-10-06T10:56:34Z","timestamp":1507287394000},"page":"2275","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Robust Weighted Sum Harvested Energy Maximization for SWIPT Cognitive Radio Networks Based on Particle Swarm Optimization"],"prefix":"10.3390","volume":"17","author":[{"given":"Pham","family":"Tuan","sequence":"first","affiliation":[{"name":"School of Electrical and Computer Engineering, University of Ulsan, Ulsan 680-749, Korea"},{"name":"Faculty of Physics, University of Education, Hue University, 34 Le Loi Str., Hue City 530000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7476-8782","authenticated-orcid":false,"given":"Insoo","family":"Koo","sequence":"additional","affiliation":[{"name":"School of Electrical and Computer Engineering, University of Ulsan, Ulsan 680-749, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,10,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1109\/MCOM.2015.7081084","article-title":"Wireless powered communication: Opportunities and challenges","volume":"53","author":"Bi","year":"2015","journal-title":"IEEE Commun. Mag."},{"key":"ref_2","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":"53","author":"Ding","year":"2015","journal-title":"IEEE Commun. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3269","DOI":"10.1109\/TWC.2014.041714.131688","article-title":"Joint transmit beamforming and receive power splitting for MISO SWIPT systems","volume":"13","author":"Shi","year":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2189","DOI":"10.1109\/LSP.2015.2464082","article-title":"An Efficiency Maximization Design for SWIPT","volume":"22","author":"Vu","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_5","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":"12","author":"Zhang","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4440","DOI":"10.1109\/TWC.2014.2314114","article-title":"Wireless information and power transfer in cooperative networks with spatially random relays","volume":"13","author":"Ding","year":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2646","DOI":"10.1109\/TWC.2014.032514.131199","article-title":"Beamforming for MISO Interference Channels with QoS and RF Energy Transfer","volume":"13","author":"Timotheou","year":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1109\/TVT.2014.2322076","article-title":"Robust Secure Transmission in MISO Simultaneous Wireless Information and Power Transfer System","volume":"64","author":"Feng","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1109\/LCOMM.2015.2498928","article-title":"Robust power-splitting SWIPT beamforming for broadcast channels","volume":"20","author":"Liao","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1492","DOI":"10.1109\/LSP.2015.2410833","article-title":"Robust transceiver optimization for power-splitting based downlink MISO SWIPT systems","volume":"22","author":"Wang","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1049\/iet-com.2015.0475","article-title":"Robust beamforming and power splitting design in MISO SWIPT downlink system","volume":"10","author":"Chu","year":"2016","journal-title":"IET Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1687","DOI":"10.1109\/LCOMM.2016.2578921","article-title":"Path-Following Algorithms for Beamforming and Signal Splitting in RF Energy Harvesting Networks","volume":"20","author":"Nasir","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"894","DOI":"10.1109\/JPROC.2009.2015717","article-title":"Breaking spectrum gridlock with cognitive radios: An information theoretic perspective","volume":"97","author":"Goldsmith","year":"2009","journal-title":"Proc. IEEE"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1109\/MCOM.2015.7081081","article-title":"RF-powered cognitive radio networks: Technical challenges and limitations","volume":"53","author":"Mohjazi","year":"2015","journal-title":"IEEE Commun. Mag."},{"key":"ref_15","first-page":"2290","article-title":"Information and Energy Cooperation in Cognitive Radio Networks","volume":"62","author":"Zheng","year":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3166","DOI":"10.1109\/TVT.2015.2436334","article-title":"Multi-Objective Resource Allocation for Secure Communication in Cognitive Radio Networks with Wireless Information and Power Transfer","volume":"65","author":"Ng","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3828","DOI":"10.1109\/TVT.2015.2443875","article-title":"Outage performance of cognitive relay networks with wireless information and power transfer","volume":"65","author":"Yang","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1109\/TCCN.2015.2508028","article-title":"Cognitive wireless powered network: Spectrum sharing models and throughput maximization","volume":"1","author":"Lee","year":"2015","journal-title":"IEEE Trans. Cogn. Commun. Netw."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"14141","DOI":"10.1109\/ACCESS.2017.2727073","article-title":"Optimal Multiuser MISO Beamforming for Power-Splitting SWIPT Cognitive Radio Networks","volume":"5","author":"Tuan","year":"2017","journal-title":"IEEE Access"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1109\/MSP.2010.936019","article-title":"Semidefinite relaxation of quadratic optimization problems","volume":"27","author":"Luo","year":"2010","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_21","unstructured":"Grant, M., and Boyd, S. (2017, February 22). CVX: Matlab Software for Disciplined Convex Programming Version 2.1. Available online: http:\/\/cvxr.com\/cvx."},{"key":"ref_22","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle swarm optimization. Proceedings of the IEEE International Conference on Neural Networks, Perth, Australia."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1109\/TWC.2007.05447","article-title":"Fundamental limits of spectrum sharing in fading environment","volume":"6","author":"Ghasemi","year":"2007","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2312","DOI":"10.1109\/TWC.2015.2502590","article-title":"Energy-efficient resource allocation for wireless powered communication networks","volume":"15","author":"Wu","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"6898","DOI":"10.1109\/TWC.2016.2593440","article-title":"User-Centric Energy Efficiency Maximization for Wireless Powered Communication Networks","volume":"15","author":"Wu","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Boyd, S., and Vandenberghe, L. (2004). Convex Optimization, Cambridge University Press.","DOI":"10.1017\/CBO9780511804441"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Bengtsson, M., and Ottersten, B. (2001). Optimal and suboptimal transmit beamforming. Handbook of Antennas in Wireless Communications, CRC Press. Chapter 18.","DOI":"10.1201\/9781420042146.ch18"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"664","DOI":"10.1109\/TSP.2009.2031732","article-title":"Rank-constrained separable semidefinite programming with applications to optimal beamforming","volume":"58","author":"Huang","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2740","DOI":"10.1109\/TSP.2007.893762","article-title":"Complex-Valued Matrix Differentiation: Techniques and Key Results","volume":"55","author":"Hjorungnes","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4871","DOI":"10.1109\/TSP.2009.2027462","article-title":"Robust cognitive beamforming with bounded channel uncertainties","volume":"57","author":"Zheng","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Hjorungnes, A. (2011). Complex-Valued Matrix Derivatives with Applications, Cambridge University Press.","DOI":"10.1017\/CBO9780511921490"},{"key":"ref_32","first-page":"11","article-title":"A complex gradient operator and its application in adaptive array theory","volume":"130","author":"Brandwood","year":"1983","journal-title":"Proc. Inst. Elect. Eng."},{"key":"ref_33","unstructured":"Chi, C.Y., Li, W.C., and Lin, C.H. (2017). Convex Optimization for Signal Processing and Communications: From Fundamentals to Applications, CRC Press."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1109\/TAP.2004.823969","article-title":"Particle swarm optimization in electromagnetics","volume":"52","author":"Robinson","year":"2004","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1049\/iet-com.2015.1186","article-title":"Throughput maximisation by optimising detection thresholds in full-duplex cognitive radio networks","volume":"10","author":"Tuan","year":"2016","journal-title":"IET Commun."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1268","DOI":"10.1109\/TSP.2007.909010","article-title":"Quality of service and max-min-fair transmit beamforming to multiple co-channel multicast groups","volume":"56","author":"Karipidis","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"5297","DOI":"10.1109\/TSP.2016.2593681","article-title":"Consensus-ADMM for general quadratically constrained quadratic programming","volume":"64","author":"Huang","year":"2016","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/10\/2275\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:46:39Z","timestamp":1760208399000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/10\/2275"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,6]]},"references-count":37,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2017,10]]}},"alternative-id":["s17102275"],"URL":"https:\/\/doi.org\/10.3390\/s17102275","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,10,6]]}}}