  Covert communication conceals transmission of messages from Alice to Bob out
of a watchful adversary, Willie, who tries to determine if a transmission took
place or not. While covert communication in a basic, vanilla setting where all
variables are known to Willie, results in the well-known square-root law, when
a jammer is present and assists Alice by creating uncertainty in Willie's
decoder, a strictly positive transmission rate is possible.
  In this work, we analyze the case where the jammer is equipped with multiple
antennas. Specifically, we analyze the effect of multiple antennas at the
jammer on Alice's transmission power and consequently on the transmission rate.
We consider both cases, one in which the channel knowledge is known and one in
which it is unknown by the jammer. We formulate several optimization problems
for the transmission strategies of the jammer, to maximize his assistance to
Alice, in terms of maximizing a ratio between Willie's and Bob's noise
variances.
  When the channel information is known to the jammer, we show that the optimal
strategy of the jammer is to perform beamforming towards a single direction
with all his available power. This direction though, is not trivial, since it
reflects an optimal tradeoff point between minimizing the interference at Bob
and maximizing the interference at Willie. When the channel knowledge is
unknown, we show that the optimal strategy of the jammer is either to transmit
isotropically to all directions or to the null-space of Bob, where this choice
depends on certain channel conditions. This is in contrast to current schemes
in the literature. Furthermore, we extend the optimization problems to the case
where Bob is also equipped with multiple antennas, and provide insightful
results, shown to be asymptotically optimal, accompanied by simulations.
