In this paper, we investigate a secure integrated sensing and communication (ISAC) system in which multiple communication users (CUs) coexist with multiple untrusted sensing users (SUs) that may eavesdrop on the confidential information intended for the CUs. To promote security fairness among users, we formulate a max-min secrecy rate optimization problem subject to a transmit power budget and sensing quality requirements characterized by beampattern matching error constraints. The resulting design problem is highly non-convex due to the secrecy rate expressions and non-convex sensing constraints. To address these challenges, we first reformulate the problem using semidefinite relaxation (SDR). Based on the reformulated problem, we develop a branch-and-bound (BB) framework combined with convex relaxations to obtain the globally optimal solution within a prescribed accuracy. To further reduce computational complexity, we propose a low-complexity algorithm based on successive convex approximation (SCA), which iteratively solves a sequence of convex subproblems and converges to a local solution. Numerical results demonstrate that the proposed BB algorithm achieves the global optimum and provides a benchmark for performance evaluation. Moreover, the proposed SCA-based algorithm attains near-optimal secrecy performance with significantly lower computational complexity, making it attractive for practical ISAC deployments.

翻译：本文研究了一种安全集成感知与通信（ISAC）系统，其中多个通信用户与多个不可信感知用户共存，这些感知用户可能窃听面向通信用户的机密信息。为提升用户间的安全公平性，我们构建了一个在发射功率预算和以波束图案匹配误差约束表征的感知质量要求下的极大极小安全速率优化问题。由于安全速率表达式和非凸感知约束，所得设计问题高度非凸。为应对这些挑战，我们首先利用半定松弛（SDR）对问题进行重构。基于重构后的模型，我们开发了结合凸松弛的分支定界（BB）框架，以在指定精度内获得全局最优解。为进一步降低计算复杂度，我们提出了一种基于逐次凸近似（SCA）的低复杂度算法，该算法通过迭代求解一系列凸子问题并收敛到局部解。数值结果表明，所提出的BB算法能够实现全局最优解，并为性能评估提供基准。此外，基于SCA的算法在显著降低计算复杂度的同时实现了接近最优的安全性能，使其成为实际ISAC部署中的有吸引力的方案。