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In particular, assuming that the distribution of each parameter to be estimated is known <jats:italic>a priori<\/jats:italic>, we focus on optimizing the targets\u2019 sensing performance. To this end, we derive and minimize the Bayesian Cram\u00e9r\u2013Rao bound, while ensuring certain communication quality of service by exploiting constructive interference. The latter scheme enforces that the received signals at the eavesdropping targets fall into the destructive region of the signal constellation, to deteriorate their decoding probability, thus enhancing the ISAC\u2019s system physical layer security capability. To tackle the nonconvexity of the formulated problem, a tailored successive convex approximation method is proposed for its efficient solution. Our extensive numerical results verify the effectiveness of the proposed secure ISAC design showing that the proposed algorithm outperforms block-level precoding techniques.<\/jats:p>","DOI":"10.1186\/s13638-025-02428-1","type":"journal-article","created":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T12:56:12Z","timestamp":1740747372000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Secure ISAC MIMO systems: exploiting interference with Bayesian Cram\u00e9r\u2013Rao bound optimization"],"prefix":"10.1186","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6424-9188","authenticated-orcid":false,"given":"Nanchi","family":"Su","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fan","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christos","family":"Masouros","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"George C.","family":"Alexandropoulos","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yifeng","family":"Xiong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qinyu","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,2,27]]},"reference":[{"issue":"5","key":"2428_CR1","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1109\/MSP.2023.3272881","volume":"40","author":"F Liu","year":"2023","unstructured":"F. 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