MIMO Secret Communications Against an Active Eavesdropper

Abstract: This paper considers a scenario in which an Alice-Bob pair wishes to communicate in secret in the presence of an active Eve, who is capable of jamming as well as eavesdropping in Full-Duplex (FD) mode. As countermeasure, Bob also operates in FD mode, using a subset of its antennas to act as receiver, and the remaining antennas to act as jammer and transmit noise. With a goal to maximize the achievable secrecy degrees of freedom (S.D.o.F.) of the system, we provide the optimal transmit/receive antennas allocation at Bob, based on which we determine in closed form the maximum achievable S.D.o.F.. We further investigate the adverse scenario in which Eve knows Bob's transmission strategy and optimizes its transmit/receive antennas allocation in order to minimize the achievable S.D.o.F.. For that case we find the worst-case achievable S.D.o.F.. We also provide a method for constructing the precoding matrices of Alice and Bob, based on which the maximum S.D.o.F. can be achieved. Numerical results validate the theoretical findings and demonstrate the performance of the proposed method in realistic settings.