Secure ISAC MIMO systems: exploiting interference with Bayesian Cramér–Rao bound optimization

(2025) 2025:10 Su et al. J Wireless Com Network https://doi.org/10.1186/s13638-025-02428-1 RESEARCH EURASIP Journal on Wireless Communications and Networking Open Access Secure ISAC MIMO systems: exploiting interference with Bayesian Cramér–Rao bound optimization Nanchi Su1,2,3* , Fan Liu2, Christos Masouros3, George C. Alexandropoulos4, Yifeng Xiong5 and Qinyu Zhang1,6 *Correspondence: 1 Guangdong Provincial Key Laboratory of Aerospace Communication and Networking Technology, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China 2 School of System Design and Intelligent Manufacturing, Southern University of Science and Technology, Shenzhen 518055, China 3 Department of Electronic and Electrical Engineering, University College London, London WC1E 7JE, UK 4 Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, 15784 Athens, Greece 5 School of Information and Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China 6 Peng Cheng Laboratory, Shenzhen 518055, China Abstract In this paper, we present a signaling design for secure integrated sensing and communication (ISAC) systems comprising a dual-functional multi-input multi-output base station that simultaneously communicates with multiple users while detecting targets present in their vicinity, which are regarded as potential eavesdroppers. In particular, assuming that the distribution of each parameter to be estimated is known a priori, we focus on optimizing the targets’ sensing performance. To this end, we derive and minimize the Bayesian Cramér–Rao 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’s 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. Keywords: Integrated sensing and communication, Physical layer security, Successive convex approximation, Bayesian Cramér–Rao bound, Constructive interference 1 Introduction Future radar and communication (R&C) systems will operate at higher frequencies with larger bandwidth, while possibly exploiting massive antenna arrays and multifunctional reconfigurable intelligent surfaces (RIS), resulting in striking similarities between R&C systems, including the hardware architecture, channel characteristics, and signal processing methods [1, 2]. This provides unique opportunities to develop co-design techniques aiming at improving the mutual performance gain of both systems. Meanwhile, with the emergence of smart cities, Internet of Things (IoT) networks, and other advanced applications, the integration of sensing and communication (S&C) systems is being seen as a transformative technology, enabling autonomous vehicle networks, activity recognition, and unmanned aerial vehicle (UAV) [3]. © The Author(s) 2025. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creativecommons.org/licenses/by/4.0/. Su et al. J Wireless Com Network (2025) 2025:10 In light of the above, the need for seamless cooperation between S&C promotes the technical development of integrated sensing and communication (ISAC) systems. The utilization of a communal spectrum frequency band, coupled with the intrinsic broadcasting characteristics of wireless transmission, introduces substantial security vulnerabilities in ISAC systems [4–6]. In conventional wireless communication systems, security designs are predominantly concerned at the physical layer and the network layer. Compared with network layer security (NLS), physical layer security (PLS) does not require complex cryptographic techniques or key distribution, reducing overhead and complexity. Moreover, PLS may provide a base level of security guarantee even when other layers are compromised, because it leverages the physical characteristics of wireless channels, which are independent of security at other layers of the communication stack. The PLS in ISAC systems has been widely studied in recent years. Initially, the artificial noise (AN) is deployed to interfere with eavesdroppers by maximizing the secrecy rate; thus, the target/eavesdropper is unable to decode the received signal. To this end, the confidential information is prevented from being intercepted by the target/ eavesdropper [5, 7–9]. Besides, the authors in [10] expand the AN-aided technique to full-duplex ISAC security, where the AN is utilized to enhance both downlink (DL) and uplink (UL) secrecy rates in the presence of multiple eavesdroppers. The work presents a power-efficient optimization model that maximizes UL/DL secrecy while targeting radar beams at eavesdroppers to extract their physical parameters, revealing key trade-offs between sensing performance and communication security. Moreover, the directional modulation (DM) technique, which is based on the principle of constructive interference (CI), has been deployed to design the transmit signal at a symbol level [11–13]. In DM, as a step further from AN design, the signals received at multiple eavesdropping targets (Eves) are enforced to fall into the destructive constellation region for further PLS improvements, which leverages destructive interference (DI) as a PLS measure. In particular, the CI-DI technique enables direct alteration of the amplitude and phase of signals at both intended users and potential Eves. Consequently, this paradigm promotes an enhanced symbol error rate (SER) for communication users (CUs), while deteriorating the decoding probability at potential eavesdroppers. In this work, we consider the estimation task of random parameters of multiple targets, where the prior distribution of parameters is assumed to be known a priori. This is common in a number of practical scenarios, such as vehi (...truncated)