MIMO multiple access channel with an arbitrarily varying eavesdropper

We investigate a two-transmitter Gaussian multiple access wiretap channel with multiple antennas at each of the nodes. The channel transfer matrices at the legitimate terminals are fixed and revealed to all the terminals, whereas the channel transfer matrix of the eavesdropper is arbitrarily varying and only revealed to the eavesdropper. We characterize the secrecy degrees of freedom (s.d.o.f.) region under a strong secrecy constraint. A transmission scheme that orthogonalizes the transmit signals of the two users at the intended receiver and uses a single-user wiretap code is sufficient to achieve the s.d.o.f. region. The converse involves establishing an upper bound on a weighted-sum-rate expression. This is accomplished by using an induction procedure, where at each step we combine the secrecy and multiple-access constraints associated with an adversary eavesdropping a carefully selected group of sub-channels.