Joint Beamforming Design for Integrated Sensing and Communication Systems with Hybrid-Colluding Eavesdroppers

TL;DR

This paper addresses secure integrated sensing and communication (ISAC) in the presence of hybrid-colluding eavesdroppers, comprising an active AE and a passive PE. It proposes an alternating-optimization, two-stage scheme (AO-TSS): the first stage designs joint information and sensing beamformers under perfect AE CSI and statistical PE CSI using SDR or a low-complexity ZF approach to minimize a weighted beampattern error plus cross-correlation, while the second stage adjusts SINR thresholds to maximize secrecy rate under radar constraints via successive convex approximation. The authors further extend the design to imperfect AE CSI and unknown PE CSI, incorporating robust handling of AE direction uncertainty and unknown PE directions, and provide convergence proofs for AO-TSS. Numerical results show the proposed methods achieve near radar-only sensing performance and high secrecy rates, with ZF offering favorable scalability and SDR delivering better sensing accuracy. Overall, the work delivers a practical, theoretically grounded framework for secure ISAC in challenging hybrid-eavesdropping environments with robust extensions and concrete performance gains.

Abstract

In this paper, we consider the physical layer security (PLS) problem for integrated sensing and communication (ISAC) systems in the presence of hybrid-colluding eavesdroppers, where an active eavesdropper (AE) and a passive eavesdropper (PE) collude to intercept the confidential information. To ensure the accuracy of sensing while preventing the eavesdropping, a base station transmits a signal consisting of information symbols and sensing waveform, in which the sensing waveform can be also used as artificial noise to interfere with eavesdroppers. Under this setup, we propose an alternating optimization-based two stage scheme (AO-TSS) for improving the sensing and communication performance. In the first stage, based on the assumptions that the perfect channel state information (CSI) of the AE and statistical CSI of the PE are known, the communication and sensing beamforming problem is formulated with the objective of minimizing the weighted sum of the beampattern matching mean squared error (MSE) and cross-correlation, subject to the secure transmission constraint. To tackle the non-convexity, we propose a semi-definite relaxation (SDR) algorithm and a reduced-complexity zero-forcing (ZF) algorithm. Then, the scenarios are further extended to more general cases with imperfect AE CSI and unknown PE CSI. To further improve the communication performance, the second-stage problem is developed to optimize the secrecy rate threshold under the radar performance constraint. Finally, numerical results demonstrate the superiority of the proposed scheme in terms of sensing and secure communication.

Figures (10)

• Figure 1: The ISAC system model of the secure beamforming with hybrid-colluding eavesdroppers.
• Figure 2: The transmit beampatterns with angles with respect to ${\it{K}} = 2$, ${\varepsilon _{{\rm{u}}}} = 16~{\rm{dB}}$, ${{\varepsilon _{\rm{a}}}} = 2~{\rm{dB}}$ and ${{\varepsilon _{\rm{p}}}} = 2~{\rm{dB}}$.
• Figure 3: The sensing objective $L({\bf{R}},{\delta _1})$ with respect to the SINR threshold of LUs under different number of LUs $K$ ($M$ = 10, ${{\varepsilon _{\rm{a}}}} = 2~{\rm{dB}}$ and ${{\varepsilon _{\rm{p}}}} = 2~{\rm{dB}}$).
• Figure 4: The sensing objective $L({\bf{R}},{\delta _1})$ with respect to the SINR threshold of LUs under different number of transmit antennas $M$ ($K$ = 2, ${{\varepsilon _{\rm{a}}}} = 2~{\rm{dB}}$ and ${{\varepsilon _{\rm{p}}}} = 2~{\rm{dB}}$).
• Figure 5: The sensing performance metric with respect to the weighting factor ${\delta _2}$$({\varepsilon _{{\rm{u}}}} = 12~{\rm{dB}}$, ${{\varepsilon _{\rm{a}}}} = 2~ {\rm{dB}}$, ${{\varepsilon _{\rm{p}}}} = 2 ~{\rm{dB}})$.