Filter Design With Secrecy Constraints: The MIMO Gaussian Wiretap Channel
This paper considers the problem of filter design with secrecy constraints, where two legitimate parties (Alice and Bob) communicate in the presence of an Eavesdropper (Eve), over a Gaussian Multiple-Input Multiple-Output (MIMO) wiretap channel. This problem involves designing, subject to a power constraint, the transmit and the receive filters which minimize the Mean-Squared Error (MSE) between the legitimate parties whilst assuring that the eavesdropper MSE remains above a certain threshold. The authors consider a general MIMO Gaussian wiretap scenario, where the legitimate receiver uses a linear Zero-Forcing (ZF) filter and the eavesdropper receiver uses either a ZF or an optimal linear Wiener filter. They provide a characterization of the optimal filter designs by demonstrating the convexity of the optimization problems.