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：针对具有非完美信道状态信息（CSI）的隐蔽式集成感知与通信（ISAC）系统，本文提出一种稳健收发机设计方法。考虑有界和概率两种CSI误差模型，我们构建了最坏情况约束和中断概率约束的稳健优化问题，涉及联合收发波束赋形与雷达波形设计，以在保证系统通信性能与隐蔽性的同时，平衡多目标的雷达探测性能。该优化问题因半无限约束（SIC）的非凸性及收发变量的耦合性而极具挑战性。为克服前者，引入S-procedure和Bernstein型不等式，将半无限约束转化为有限凸线性矩阵不等式（LMI）与二阶锥约束。针对收发机设计问题的解耦需求，提出一种名为"交替双重校验"的稳健交替优化框架：将问题分解为发射端与接收端可行性校验子问题，将秩一约束转换为线性矩阵不等式组，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式ISAC系统性能方面的有效性与鲁棒性。