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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.
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