  Covert communication prevents legitimate transmission from being detected by
a warden while maintaining certain covert rate at the intended user. Prior
works have considered the design of covert communication over conventional
low-frequency bands, but few works so far have explored the higher-frequency
millimeter-wave (mmWave) spectrum. The directional nature of mmWave
communication makes it attractive for covert transmission. However, how to
establish such directional link in a covert manner in the first place remains
as a significant challenge. In this paper, we consider a covert mmWave
communication system, where legitimate parties Alice and Bob adopt beam
training approach for directional link establishment. Accounting for the
training overhead, we develop a new design framework that jointly optimizes
beam training duration, training power and data transmission power to maximize
the effective throughput of Alice-Bob link while ensuring the covertness
constraint at warden Willie is met. We further propose a dual-decomposition
successive convex approximation algorithm to solve the problem efficiently.
Numerical studies demonstrate interesting tradeoff among the key design
parameters considered and also the necessity of joint design of beam training
and data transmission for covert mmWave communication.
