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Linear Precoder Design for a MIMO Gaussian Wiretap Channel with Full-Duplex Source and Destination Nodes

We consider linear precoder design for a multiple-input multiple-output (MIMO) Gaussian wiretap channel, which comprises two legitimate nodes, i.e., Alice and Bob, operating in Full-Duplex (FD) mode and exchanging confidential messages in the presence of a passive eavesdropper. Using the sum secrecy degrees of freedoms (sum S.D.o.F.) as reliability measure, we formulate an optimization problem with respect to the precoding matrices. In order to solve this problem, we first propose a cooperative secrecy transmission scheme, and prove that its feasible set is sufficient to achieve the maximum sum S.D.o.F.. Based on that feasible set, we then determine the maximum achievable sum S.D.o.F. in closed form, and provide a method for constructing the precoding matrix pair which achieves the maximum sum S.D.o.F.. Results show that, the FD based network provides an attractive secrecy transmission rate performance.