  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.
