Filter Design with Secrecy Constraints: The Degraded Multiple-Input Multiple-Output 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 multiple-input multiple-output (MIMO) Gaussian channels. In particular, we consider the design of transmit and receive filters that minimize the mean-squared error (MSE) between the legitimate parties subject to a certain eavesdropper MSE level, in the situation where the eavesdropper MIMO channel is a degraded version of the main MIMO channel. We characterize the form of the optimal receive filters as well as the form of optimal transmit filter in different scenarios. We also put forth an iterative algorithm to obtain the optimal values of the transmit and receive filters. Finally, we present a set of numerical results that illustrate the conclusions.