  We consider that a transmitter covertly communicates with multiple receivers
under the help of a friendly jammer. The messages intended for different
receivers are transmitted in mutually orthogonal frequency bands. An adversary
observes all these frequency bands aiming at detecting whether or not
communication occurs, while the friendly jammer broadcasts jamming signals to
degrade the detection performance of the adversary. We consider a block
Rayleigh fading channel model and evaluate the performance of covert
communication in two situations: 1) the wireless channels vary slowly such that
the transmission ends within one channel coherent time block, and 2) the
wireless channels vary fast such that the wireless channels have changed
several times before the whole transmission is finished. In the former case,
subject to a covertness constraint, we maximize the sum of the effective rates
by optimizing the transmit power allocation and the transmission rate for each
receiver. In the latter case, we take the channel training process into
consideration, and subject to a covertness constraint, we maximize the sum of
the ergodic rates by optimizing the power allocation and the pilot length.
Though both of the two optimization problems are non-convex, we presented
methods to find their global optimal solutions. Besides, we also present
methods to find sub-optimal solutions with lower computational complexities.
Numerical results are presented to evaluate the performance under the two
situations.
