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Based on stochastic geometry technique, a novel random analysis method is proposed to derive the closed-form expression of secrecy transmission capacity and analyze the connection outage probability (COP) and secrecy outage probability (SOP) for both secondary (SR) and primary (PR) systems. Then, the concept of secrecy cognitive gain is produced to highlight the effect of SR systems with secrecy on the whole networks security. Comparing with a single PR system, the SR system is beneficial to enhance the secrecy level for overlaid CRSNs. In addition, the maximum achievable secrecy capacity is achieved through optimizing the density of SR systems satisfying outage constraints of PR and SR systems. Analytical results provide insights into regimes in which the SR system with secrecy is beneficial for the overlaid network secrecy. <\/jats:p>","DOI":"10.1155\/2015\/619150","type":"journal-article","created":{"date-parts":[[2015,6,12]],"date-time":"2015-06-12T01:40:30Z","timestamp":1434073230000},"page":"619150","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Secrecy Cognitive Gain of Cognitive Radio Sensor Networks with Primary Outage Constraint"],"prefix":"10.1177","volume":"11","author":[{"given":"Hongyu","family":"Ma","sequence":"first","affiliation":[{"name":"Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China"},{"name":"School of Electronic and Information Engineering, Liaoning University of Technology, Jinzhou 121001, China"}]},{"given":"Kai","family":"Niu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China"}]},{"given":"Weiling","family":"Wu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China"}]},{"given":"Shengyu","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China"}]},{"given":"Guangqian","family":"Chu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China"}]}],"member":"179","published-online":{"date-parts":[[2015,6,11]]},"reference":[{"key":"B1-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/mcom.2002.1024422"},{"key":"B2-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/jsac.2004.839380"},{"key":"B3-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/jproc.2009.2015717"},{"key":"B4-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/mnet.2009.5191144"},{"key":"B5-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/5.4440"},{"key":"B6-2015-619150","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1975.tb02040.x"},{"key":"B7-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/tit.1978.1055892"},{"key":"B8-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/tit.2008.921678"},{"key":"B9-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/tit.2009.2018322"},{"key":"B10-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/tit.2010.2068852"},{"key":"B11-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/tit.2008.921879"},{"key":"B12-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/tit.2008.928272"},{"key":"B13-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/jsac.2011.110219"},{"key":"B14-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/twc.2010.07.060438"},{"key":"B15-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/tit.2011.2173726"},{"key":"B16-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/jsac.2009.090902"},{"key":"B17-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/lcomm.2014.2327627"},{"key":"B18-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/twc.2011.061511.102257"},{"key":"B19-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/tnet.2013.2244230"},{"key":"B20-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/mnet.2014.6915445"},{"volume-title":"Proceedings of the Global Telecommunications Conference","author":"Shu Z.","key":"B21-2015-619150"},{"key":"B22-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/INFCOM.2012.6195787"},{"key":"B23-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/tvt.2014.2358624"},{"key":"B24-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/tifs.2014.2341453"},{"key":"B25-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/lwc.2014.2365808"},{"key":"B26-2015-619150","doi-asserted-by":"publisher","DOI":"10.1109\/tit.2005.858939"},{"volume-title":"Stochastic Geometry and It's Applications","year":"1995","author":"Stoyan D.","key":"B27-2015-619150"},{"volume-title":"Random Networks for Communication: From Statistical Physics to Information Systems","year":"2007","author":"Franceschetti M.","key":"B28-2015-619150"},{"volume-title":"Mathematical Methods for Physicists: A Comprehensive Guide","year":"2011","author":"Arfken G. 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