{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:16:11Z","timestamp":1760242571964,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2017,11,22]],"date-time":"2017-11-22T00:00:00Z","timestamp":1511308800000},"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>This paper presents a price-searching model in which a source node (Alice) seeks friendly jammers that prevent eavesdroppers (Eves) from snooping legitimate communications by generating interference or noise. Unlike existing models, the distributed jammers also have data to send to their respective destinations and are allowed to access Alice\u2019s channel if it can transmit sufficient jamming power, which is referred to as collaborative jamming in this paper. For the power used to deliver its own signal, the jammer should pay Alice. The price of the jammers\u2019 signal power is set by Alice and provides a tradeoff between the signal and the jamming power. This paper presents, in closed-form, an optimal price that maximizes Alice\u2019s benefit and the corresponding optimal power allocation from a jammers\u2019 perspective by assuming that the network-wide channel knowledge is shared by Alice and jammers. For a multiple-jammer scenario where Alice hardly has the channel knowledge, this paper provides a distributed and interactive price-searching procedure that geometrically converges to an optimal price and shows that Alice by a greedy selection policy achieves certain diversity gain, which increases log-linearly as the number of (potential) jammers grows. Various numerical examples are presented to illustrate the behavior of the proposed model.<\/jats:p>","DOI":"10.3390\/s17112697","type":"journal-article","created":{"date-parts":[[2017,11,22]],"date-time":"2017-11-22T10:47:38Z","timestamp":1511347658000},"page":"2697","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Optimal Pricing and Power Allocation for Collaborative Jamming with Full Channel Knowledge in Wireless Sensor Networks"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5977-4156","authenticated-orcid":false,"given":"Dae-Kyo","family":"Jeong","sequence":"first","affiliation":[{"name":"Department of Electronics and Communication Engineering, Hanyang University, Ansan 15588, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Insook","family":"Kim","sequence":"additional","affiliation":[{"name":"Division of Electrical Engineering, Hanyang University, Ansan 15588, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5541-5738","authenticated-orcid":false,"given":"Dongwoo","family":"Kim","sequence":"additional","affiliation":[{"name":"Division of Electrical Engineering, Hanyang University, Ansan 15588, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,11,22]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1109\/TIT.1978.1055917","article-title":"The Gaussian Wiretap Channel","volume":"24","author":"Hellman","year":"1978","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1727","DOI":"10.1109\/JPROC.2016.2558521","article-title":"A Survey on Wireless Security: Technical Challenges, Recent Advances, and Future Trends","volume":"104","author":"Zou","year":"2016","journal-title":"Proc. IEEE"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1109\/TIFS.2011.2111370","article-title":"Wireless Secrecy Regions with Friendly Jamming","volume":"6","author":"Vilela","year":"2011","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"7495","DOI":"10.1109\/TVT.2017.2657629","article-title":"Secure Communications with Cooperative Jamming: Optimal Power Allocation and Secrecy Outage Analysis","volume":"66","author":"Cumanan","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2735","DOI":"10.1109\/TIT.2008.921680","article-title":"The General Gaussian Multiple-Access and Two-Way Wiretap Channels: Achievable Rates and Cooperative Jamming","volume":"54","author":"Tekin","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4005","DOI":"10.1109\/TIT.2008.928272","article-title":"The Relay-Eavesdropper Channel: Cooperation for Secrecy","volume":"54","author":"Lai","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"9448","DOI":"10.1109\/TVT.2017.2703305","article-title":"Strategic Antieavesdropping Game for Physical Layer Security in Wireless Cooperative Networks","volume":"66","author":"Wang","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"339","DOI":"10.3390\/s16030339","article-title":"Worst-Case Cooperative Jamming for Secure Communications in CIoT Networks","volume":"16","author":"Li","year":"2016","journal-title":"Sensors"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"384","DOI":"10.3390\/e19080384","article-title":"Securing Relay Networks with Artificial Noise: An Error Performance-Based Approach","volume":"19","author":"Liu","year":"2017","journal-title":"Entropy"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"452907","DOI":"10.1155\/2009\/452907","article-title":"Physical Layer Security Game: Interaction between Source, Eavesdropper, and Friendly Jammer","volume":"2009","author":"Han","year":"2010","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Barros, J., and Rodrigues, M.R.D. (2006, January 9\u201314). Secrecy Capacity of Wireless Channnels. Proceedings of the 2006 IEEE International Symposium on Information Theory, Seattle, WA, USA.","DOI":"10.1109\/ISIT.2006.261613"},{"key":"ref_13","unstructured":"Kim, I., and Kim, D. (2010, January 21\u201324). Pricing and Optimal Power Allocation in Collaborative Primary-Secondary Transmission using Superposition Coding. Proceedings of the 2010 IEEE Region 10 Conference (TENCON 2010), Hukuoka, Japan."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Alexandropoulos, G.C., and Peppas, K.P. (2017). Secrecy Outage Analysis over Correlated Composite Nakagami-m\/ Gamma Fading Channels. IEEE Commun. Lett., PP.","DOI":"10.1109\/LCOMM.2017.2760255"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/11\/2697\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:50:46Z","timestamp":1760208646000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/11\/2697"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,22]]},"references-count":14,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2017,11]]}},"alternative-id":["s17112697"],"URL":"https:\/\/doi.org\/10.3390\/s17112697","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,11,22]]}}}