Secure Degrees of Freedom of the Multiple Access Wiretap Channel with   Multiple Antennas
  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.) for this model for all values of $N$ and $K$. We subdivide our problem into several regimes based on the values of $N$ and $K$, and provide achievable schemes based on real and vector space alignment techniques for fixed and fading channel gains, respectively. To prove the optimality of the achievable schemes, we provide matching converses for each regime. Our results show how the number of eavesdropper antennas affects the optimal sum s.d.o.f. of the multiple access wiretap channel. 
Pritam Mukherjee and Sennur Ulukus
cs.IT cs.CR math.IT