In this paper, we consider a common unicast beamforming network where Alice utilizes the communication to Carol as a cover and covertly transmits a message to Bob without being recognized by Willie. We investigate the beamformer design of Alice to maximize the covert rate to Bob when Alice has either perfect or imperfect knowledge about Willie’s channel state information (WCSI). For the perfect WCSI case, the problem is formulated under the perfect covert constraint, and we develop a covert beamformer by applying semidefinite relaxation and the bisection method. Then, to reduce the computational complexity, we further propose a zero-forcing beamformer design with a single iteration processing. For the case of the imperfect WCSI, the robust beamformer is developed based on a relaxation and restriction approach by utilizing the property of Kullback-Leibler divergence. Furthermore, we derive the optimal decision threshold of Willie, and analyze the false alarm and the missed detection probabilities in this case. Finally, the performance of the proposed beamformer designs is evaluated through numerical experiments.

中文翻译：

---

隐蔽通信的稳健波束成形设计

在本文中，我们考虑了一个普通的单播波束成形网络，其中Alice利用与Carol的通信作为掩护，并秘密地向Bob传输消息，而不会被Willie识别。当Alice对Willie的信道状态信息（WCSI）有完全或不完全的了解时，我们将研究Alice的波束成形器设计，以最大程度地提高Bob的隐蔽率。对于理想的WCSI情况，问题是在理想的隐蔽约束条件下提出的，我们通过应用半确定松弛和二分法开发了一种隐秘波束形成器。然后，为降低计算复杂度，我们进一步提出了采用单次迭代处理的迫零波束形成器设计。对于不完善的WCSI，利用Kullback-Leibler发散特性，基于松弛和限制方法开发了鲁棒的波束形成器。此外，我们推导了Willie的最佳决策阈值，并分析了这种情况下的虚警和漏检概率。最后，通过数值实验评估了所提出的波束形成器设计的性能。