We propose a robust transceiver design for a covert integrated sensing and communications (ISAC) system with imperfect channel state information (CSI). Considering both bounded and probabilistic CSI error models, we formulate worst-case and outage-constrained robust optimization problems of joint trasceiver beamforming and radar waveform design to balance the radar performance of multiple targets while ensuring communications performance and covertness of the system. The optimization problems are challenging due to the non-convexity arising from the semi-infinite constraints (SICs) and the coupled transceiver variables. In an effort to tackle the former difficulty, S-procedure and Bernstein-type inequality are introduced for converting the SICs into finite convex linear matrix inequalities (LMIs) and second-order cone constraints. A robust alternating optimization framework referred to alternating double-checking is developed for decoupling the transceiver design problem into feasibility-checking transmitter- and receiver-side subproblems, transforming the rank-one constraints into a set of LMIs, and verifying the feasibility of beamforming by invoking the matrix-lifting scheme. Numerical results are provided to demonstrate the effectiveness and robustness of the proposed algorithm in improving the performance of covert ISAC systems.

翻译：本文针对具有非完美信道状态信息（CSI）的隐蔽通感一体化（ISAC）系统，提出了一种鲁棒收发机设计方案。考虑有界和概率性CSI误差模型，我们构建了最坏情况与中断约束下的鲁棒优化问题，通过联合设计收发机波束赋形与雷达波形，在确保系统通信性能与隐蔽性的同时，平衡对多目标的雷达探测性能。由于半无限约束（SICs）及收发机变量耦合导致的非凸性，该优化问题具有挑战性。为克服前者困难，引入S-过程和伯恩斯坦型不等式，将SICs转化为有限凸线性矩阵不等式（LMIs）与二阶锥约束。针对收发机解耦问题，提出一种名为交替双重检验的鲁棒交替优化框架：将收发机设计问题分解为可行性校验的发射端与接收端子问题，将秩一约束转化为LMIs集合，并借助矩阵提升方案验证波束赋形的可行性。数值结果验证了所提算法在提升隐蔽ISAC系统性能方面的有效性与鲁棒性。