On Covert Communication Over Infinite-Bandwidth Gaussian Channels

We consider a problem of communication over a continuous-time additive Gaussian noise channel. A covertness constraint is imposed on the communication protocol, which says that the channel output must statistically resemble pure noise. When there is no bandwidth constraint on the input, we argue that the covert communication capacity of this channel is positive, in contrast to the band-limited case where covertness requires that the amount of transmission grow at most like the square root of total communication time. This claim is formally proven in the case where the Gaussian noise is white with respect to the bandwidth used by the transmitter.