Filter design with secrecy constraints: Zero-forcing constraint at the legitimate receiver

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. In particular, this problem involves the design of the transmit and the receive filters, subject to a power constraint, which minimize the mean-squared error (MSE) between the legitimate parties whilst assuring that the eavesdropper MSE remains above a certain level. We consider a general Multiple-Input Multiple-Output (MIMO) Gaussian wiretap scenario, where a Zero-Forcing (ZF) filter is used at the legitimate receiver, whilst the eavesdropper uses an optimal linear receive filter, and characterize the receive and transmit filters in various power regimes. Finally, we present a set of numerical results that support some of the main conclusions.