Secure Degrees of Freedom of the Asymmetric Gaussian MIMO Interference Channel

We study the secure degrees of freedom (s.d.o.f.) for a two-user multiple-input multiple-output (MIMO) Gaussian interference channel with confidential messages, each transmitter-receiver pair of which intends to keep secret from the other pair. Different from existing works on symmetric scenario, in this paper, an asymmetric system is considered, where transmitters have M-1, M-2 antennas and receivers have N-1, N-2 antennas, respectively. The channel is assumed to be fast fading and channel matrices are fixed and full rank. We subdivide the problem into several regimes based on the configuration of antennas at each node and present the exact secure degrees of freedom of corresponding regime. To prove a converse, the outer bound is developed by combining information theoretic derivation and the results of fundamental models. We also provide the achievable schemes based on zero forcing, real interference alignment, and cooperative jamming. One part of private signal is sent in the null space, while the other part is sent in a way that it aligns with cooperative jamming signal at unintended receiver, but leaves the secret message intact at intended receiver. As a consequence of the scheme, the objective s.d.o.f. can be achieved and the system ensures that the confidential messages cannot be eavesdropped by unintended receivers.