MIMO Secret Communications Against an Active Eavesdropper

This paper considers a scenario in which an <italic>Alice</italic>–<italic>Bob</italic> pair wishes to communicate in secret in the presence of an active <italic>Eve</italic>, who is capable of jamming as well as eavesdropping and operates in full-duplex (FD) mode. As countermeasure, <italic>Bob</italic> operates in FD mode, using a subset of its antennas to receive, and the remaining antennas to transmit jamming noise. <italic>Alice</italic> and <italic>Bob</italic> employ linear precoding, and all nodes use Gaussian code books. In that context, our goal is to maximize the achievable secrecy degrees of freedom (S.D.o.F.) of the system. We provide the optimal receive/transmit antennas allocation at <italic>Bob</italic>, based on which we determine in closed form the maximum achievable S.D.o.F. We also provide a method for constructing the precoding matrices of <italic>Alice</italic> and <italic>Bob</italic>, based on which the maximum S.D.o.F. can be achieved. We further investigate the adverse scenario in which <italic>Eve</italic> knows <italic>Bob</italic>’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. Numerical results validate the theoretical findings and demonstrate the performance of the proposed method.