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：

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用于隐蔽通信的稳健波束成形设计


在本文中，我们考虑一个常见的单播波束成形网络，其中 Alice 利用与 Carol 的通信作为掩护，在不被 Willie 识别的情况下秘密向 Bob 发送消息。我们研究了 Alice 的波束形成器设计，以在 Alice 对 Willie 的信道状态信息 (WCSI) 有完美或不完美的了解时最大化 Bob 的隐蔽率。对于完美的 WCSI 情况，问题是在完美的隐性约束下制定的，我们通过应用半定松弛和二分法开发了隐性波束形成器。然后，为了降低计算复杂度，我们进一步提出了一种具有单次迭代处理的迫零波束形成器设计。针对WCSI不完美的情况，利用Kullback-Leibler发散特性，基于松弛和限制方法开发了鲁棒波束形成器。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误报和漏检概率。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。