Real interference alignment for the MIMO multiple access wiretap channel

We consider a two-user multiple-input multiple-output (MIMO) multiple access wiretap channel with N antennas at each transmitter, N antennas at the legitimate receiver, and K antennas at the eavesdropper. We determine the optimal sum secure degrees of freedom (s.d.o.f.) when the channel gains are fixed for the duration of the communication. We provide optimal achievable schemes based on a combination of Gaussian signaling and real interference alignment for all regimes of N and K.