Interference Alignment for the Multiantenna Compound Wiretap Channel

We study a wiretap channel model where the sender has
$M $
transmit antennas and there are two groups consisting of
$J_{1}$
and
$J_{2}$
receivers respectively. Each receiver has a single antenna. We consider two scenarios. First we consider the compound wiretap model — group 1 constitutes the set of legitimate receivers, all interested in a common message, whereas group 2 is the set of eavesdroppers. We establish new lower and upper bounds on the secure degrees of freedom (d.o.f.). Our lower bound is based on the recently proposed real interference alignment scheme. The upper bound provides the first known example which illustrates that the pairwise upper bound used in earlier works is not tight. The second scenario we study is the compound private broadcast channel. Each group is interested in a message that must be protected from the other group. Upper and lower bounds on the d.o.f. are developed by extending the results on the compound wiretap channel.